9"""Z3 is a high performance theorem prover developed at Microsoft Research.
11Z3 is used in many applications such as: software/hardware verification and testing,
12constraint solving, analysis of hybrid systems, security, biology (in silico analysis),
13and geometrical problems.
16Please send feedback, comments and/or corrections on the Issue tracker for
17https://github.com/Z3prover/z3.git. Your comments are very valuable.
38... x = BitVec('x', 32)
40... # the expression x + y is type incorrect
42... except Z3Exception as ex:
43... print("failed: %s" % ex)
49from .z3consts
import *
50from .z3printer
import *
51from fractions
import Fraction
56if sys.version_info.major >= 3:
57 from typing
import Iterable, Iterator
59from collections.abc
import Callable
75if sys.version_info.major < 3:
77 return isinstance(v, (int, long))
80 return isinstance(v, int)
92 major = ctypes.c_uint(0)
93 minor = ctypes.c_uint(0)
94 build = ctypes.c_uint(0)
95 rev = ctypes.c_uint(0)
97 return "%s.%s.%s" % (major.value, minor.value, build.value)
101 major = ctypes.c_uint(0)
102 minor = ctypes.c_uint(0)
103 build = ctypes.c_uint(0)
104 rev = ctypes.c_uint(0)
106 return (major.value, minor.value, build.value, rev.value)
115 raise Z3Exception(msg)
119 _z3_assert(ctypes.c_int(n).value == n, name +
" is too large")
123 """Log interaction to a file. This function must be invoked immediately after init(). """
128 """Append user-defined string to interaction log. """
133 """Convert an integer or string into a Z3 symbol."""
141 """Convert a Z3 symbol back into a Python object. """
154 if len(args) == 1
and (isinstance(args[0], tuple)
or isinstance(args[0], list)):
156 elif len(args) == 1
and (isinstance(args[0], set)
or isinstance(args[0], AstVector)):
157 return [arg
for arg
in args[0]]
158 elif len(args) == 1
and isinstance(args[0], Iterator):
170 if isinstance(args, (set, AstVector, tuple)):
171 return [arg
for arg
in args]
179 if isinstance(val, bool):
180 return "true" if val
else "false"
191 """A Context manages all other Z3 objects, global configuration options, etc.
193 Z3Py uses a default global context. For most applications this is sufficient.
194 An application may use multiple Z3 contexts. Objects created in one context
195 cannot be used in another one. However, several objects may be "translated" from
196 one context to another. It is not safe to access Z3 objects from multiple threads.
197 The only exception is the method `interrupt()` that can be used to interrupt() a long
199 The initialization method receives global configuration options for the new context.
204 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
223 if Z3_del_context
is not None and self.
owner:
229 """Return a reference to the actual C pointer to the Z3 context."""
233 """Interrupt a solver performing a satisfiability test, a tactic processing a goal, or simplify functions.
235 This method can be invoked from a thread different from the one executing the
236 interruptible procedure.
241 """Return the global parameter description set."""
250 """Return a reference to the global Z3 context.
253 >>> x.ctx == main_ctx()
258 >>> x2 = Real('x', c)
265 if _main_ctx
is None:
282 """Set Z3 global (or module) parameters.
284 >>> set_param(precision=10)
287 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
291 if not set_pp_option(k, v):
306 """Reset all global (or module) parameters.
312 """Alias for 'set_param' for backward compatibility.
318 """Return the value of a Z3 global (or module) parameter
320 >>> get_param('nlsat.reorder')
323 ptr = (ctypes.c_char_p * 1)()
325 r = z3core._to_pystr(ptr[0])
327 raise Z3Exception(
"failed to retrieve value for '%s'" % name)
339 """Superclass for all Z3 objects that have support for pretty printing."""
345 in_html = in_html_mode()
348 set_html_mode(in_html)
353 """AST are Direct Acyclic Graphs (DAGs) used to represent sorts, declarations and expressions."""
361 if self.
ctx.ref()
is not None and self.
ast is not None and Z3_dec_ref
is not None:
369 return obj_to_string(self)
372 return obj_to_string(self)
375 return self.
eq(other)
388 elif is_eq(self)
and self.num_args() == 2:
389 return self.arg(0).
eq(self.arg(1))
391 raise Z3Exception(
"Symbolic expressions cannot be cast to concrete Boolean values.")
394 """Return a string representing the AST node in s-expression notation.
397 >>> ((x + 1)*x).sexpr()
403 """Return a pointer to the corresponding C Z3_ast object."""
407 """Return unique identifier for object. It can be used for hash-tables and maps."""
411 """Return a reference to the C context where this AST node is stored."""
412 return self.
ctx.ref()
415 """Return `True` if `self` and `other` are structurally identical.
422 >>> n1 = simplify(n1)
423 >>> n2 = simplify(n2)
432 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
438 >>> # Nodes in different contexts can't be mixed.
439 >>> # However, we can translate nodes from one context to another.
440 >>> x.translate(c2) + y
444 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
451 """Return a hashcode for the `self`.
453 >>> n1 = simplify(Int('x') + 1)
454 >>> n2 = simplify(2 + Int('x') - 1)
455 >>> n1.hash() == n2.hash()
461 """Return a Python value that is equivalent to `self`."""
466 """Return `True` if `a` is an AST node.
470 >>> is_ast(IntVal(10))
474 >>> is_ast(BoolSort())
476 >>> is_ast(Function('f', IntSort(), IntSort()))
483 return isinstance(a, AstRef)
486def eq(a : AstRef, b : AstRef) -> bool:
487 """Return `True` if `a` and `b` are structurally identical AST nodes.
497 >>> eq(simplify(x + 1), simplify(1 + x))
531 _args = (FuncDecl * sz)()
533 _args[i] = args[i].as_func_decl()
541 _args[i] = args[i].as_ast()
549 _args[i] = args[i].as_ast()
557 elif k == Z3_FUNC_DECL_AST:
574 """A Sort is essentially a type. Every Z3 expression has a sort. A sort is an AST node."""
583 """Return the Z3 internal kind of a sort.
584 This method can be used to test if `self` is one of the Z3 builtin sorts.
587 >>> b.kind() == Z3_BOOL_SORT
589 >>> b.kind() == Z3_INT_SORT
591 >>> A = ArraySort(IntSort(), IntSort())
592 >>> A.kind() == Z3_ARRAY_SORT
594 >>> A.kind() == Z3_INT_SORT
600 """Return `True` if `self` is a subsort of `other`.
602 >>> IntSort().subsort(RealSort())
608 """Try to cast `val` as an element of sort `self`.
610 This method is used in Z3Py to convert Python objects such as integers,
611 floats, longs and strings into Z3 expressions.
614 >>> RealSort().cast(x)
623 """Return the name (string) of sort `self`.
625 >>> BoolSort().name()
627 >>> ArraySort(IntSort(), IntSort()).name()
633 """Return `True` if `self` and `other` are the same Z3 sort.
636 >>> p.sort() == BoolSort()
638 >>> p.sort() == IntSort()
646 """Return `True` if `self` and `other` are not the same Z3 sort.
649 >>> p.sort() != BoolSort()
651 >>> p.sort() != IntSort()
658 return AstRef.__hash__(self)
662 """Return `True` if `s` is a Z3 sort.
664 >>> is_sort(IntSort())
666 >>> is_sort(Int('x'))
668 >>> is_expr(Int('x'))
671 return isinstance(s, SortRef)
676 _z3_assert(isinstance(s, Sort),
"Z3 Sort expected")
678 if k == Z3_BOOL_SORT:
680 elif k == Z3_INT_SORT
or k == Z3_REAL_SORT:
682 elif k == Z3_BV_SORT:
684 elif k == Z3_ARRAY_SORT:
686 elif k == Z3_DATATYPE_SORT:
688 elif k == Z3_FINITE_DOMAIN_SORT:
690 elif k == Z3_FLOATING_POINT_SORT:
692 elif k == Z3_ROUNDING_MODE_SORT:
694 elif k == Z3_RE_SORT:
696 elif k == Z3_SEQ_SORT:
698 elif k == Z3_CHAR_SORT:
700 elif k == Z3_TYPE_VAR:
705def _sort(ctx : Context, a : Any) -> SortRef:
710 """Create a new uninterpreted sort named `name`.
712 If `ctx=None`, then the new sort is declared in the global Z3Py context.
714 >>> A = DeclareSort('A')
715 >>> a = Const('a', A)
716 >>> b = Const('b', A)
728 """Type variable reference"""
738 """Create a new type variable named `name`.
740 If `ctx=None`, then the new sort is declared in the global Z3Py context.
755 """Function declaration. Every constant and function have an associated declaration.
757 The declaration assigns a name, a sort (i.e., type), and for function
758 the sort (i.e., type) of each of its arguments. Note that, in Z3,
759 a constant is a function with 0 arguments.
772 """Return the name of the function declaration `self`.
774 >>> f = Function('f', IntSort(), IntSort())
777 >>> isinstance(f.name(), str)
783 """Return the number of arguments of a function declaration.
784 If `self` is a constant, then `self.arity()` is 0.
786 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
793 """Return the sort of the argument `i` of a function declaration.
794 This method assumes that `0 <= i < self.arity()`.
796 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
805 """Return the sort of the range of a function declaration.
806 For constants, this is the sort of the constant.
808 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
815 """Return the internal kind of a function declaration.
816 It can be used to identify Z3 built-in functions such as addition, multiplication, etc.
819 >>> d = (x + 1).decl()
820 >>> d.kind() == Z3_OP_ADD
822 >>> d.kind() == Z3_OP_MUL
830 result = [
None for i
in range(n)]
833 if k == Z3_PARAMETER_INT:
835 elif k == Z3_PARAMETER_DOUBLE:
837 elif k == Z3_PARAMETER_RATIONAL:
839 elif k == Z3_PARAMETER_SYMBOL:
841 elif k == Z3_PARAMETER_SORT:
843 elif k == Z3_PARAMETER_AST:
845 elif k == Z3_PARAMETER_FUNC_DECL:
847 elif k == Z3_PARAMETER_INTERNAL:
848 result[i] =
"internal parameter"
849 elif k == Z3_PARAMETER_ZSTRING:
850 result[i] =
"internal string"
856 """Create a Z3 application expression using the function `self`, and the given arguments.
858 The arguments must be Z3 expressions. This method assumes that
859 the sorts of the elements in `args` match the sorts of the
860 domain. Limited coercion is supported. For example, if
861 args[0] is a Python integer, and the function expects a Z3
862 integer, then the argument is automatically converted into a
865 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
875 _args = (Ast * num)()
880 tmp = self.
domain(i).cast(args[i])
882 _args[i] = tmp.as_ast()
887 """Return `True` if `a` is a Z3 function declaration.
889 >>> f = Function('f', IntSort(), IntSort())
896 return isinstance(a, FuncDeclRef)
900 """Create a new Z3 uninterpreted function with the given sorts.
902 >>> f = Function('f', IntSort(), IntSort())
908 _z3_assert(len(sig) > 0,
"At least two arguments expected")
913 dom = (Sort * arity)()
914 for i
in range(arity):
923 """Create a new fresh Z3 uninterpreted function with the given sorts.
927 _z3_assert(len(sig) > 0,
"At least two arguments expected")
932 dom = (z3.Sort * arity)()
933 for i
in range(arity):
946 """Create a new Z3 recursive with the given sorts."""
949 _z3_assert(len(sig) > 0,
"At least two arguments expected")
954 dom = (Sort * arity)()
955 for i
in range(arity):
964 """Set the body of a recursive function.
965 Recursive definitions can be simplified if they are applied to ground
968 >>> fac = RecFunction('fac', IntSort(ctx), IntSort(ctx))
969 >>> n = Int('n', ctx)
970 >>> RecAddDefinition(fac, n, If(n == 0, 1, n*fac(n-1)))
973 >>> s = Solver(ctx=ctx)
974 >>> s.add(fac(n) < 3)
977 >>> s.model().eval(fac(5))
987 _args[i] = args[i].ast
998 """Constraints, formulas and terms are expressions in Z3.
1000 Expressions are ASTs. Every expression has a sort.
1001 There are three main kinds of expressions:
1002 function applications, quantifiers and bounded variables.
1003 A constant is a function application with 0 arguments.
1004 For quantifier free problems, all expressions are
1005 function applications.
1015 """Return the sort of expression `self`.
1027 """Shorthand for `self.sort().kind()`.
1029 >>> a = Array('a', IntSort(), IntSort())
1030 >>> a.sort_kind() == Z3_ARRAY_SORT
1032 >>> a.sort_kind() == Z3_INT_SORT
1038 """Return a Z3 expression that represents the constraint `self == other`.
1040 If `other` is `None`, then this method simply returns `False`.
1056 return AstRef.__hash__(self)
1059 """Return a Z3 expression that represents the constraint `self != other`.
1061 If `other` is `None`, then this method simply returns `True`.
1080 """Return the Z3 function declaration associated with a Z3 application.
1082 >>> f = Function('f', IntSort(), IntSort())
1095 """Return the Z3 internal kind of a function application."""
1102 """Return the number of arguments of a Z3 application.
1106 >>> (a + b).num_args()
1108 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1118 """Return argument `idx` of the application `self`.
1120 This method assumes that `self` is a function application with at least `idx+1` arguments.
1124 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1139 """Return a list containing the children of the given expression
1143 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1149 return [self.
arg(i)
for i
in range(self.
num_args())]
1163 """inverse function to the serialize method on ExprRef.
1164 It is made available to make it easier for users to serialize expressions back and forth between
1165 strings. Solvers can be serialized using the 'sexpr()' method.
1169 if len(s.assertions()) != 1:
1170 raise Z3Exception(
"single assertion expected")
1171 fml = s.assertions()[0]
1172 if fml.num_args() != 1:
1173 raise Z3Exception(
"dummy function 'F' expected")
1177 if isinstance(a, Pattern):
1181 if k == Z3_QUANTIFIER_AST:
1184 if sk == Z3_BOOL_SORT:
1186 if sk == Z3_INT_SORT:
1187 if k == Z3_NUMERAL_AST:
1190 if sk == Z3_REAL_SORT:
1191 if k == Z3_NUMERAL_AST:
1196 if sk == Z3_BV_SORT:
1197 if k == Z3_NUMERAL_AST:
1201 if sk == Z3_ARRAY_SORT:
1203 if sk == Z3_DATATYPE_SORT:
1205 if sk == Z3_FLOATING_POINT_SORT:
1209 return FPRef(a, ctx)
1210 if sk == Z3_FINITE_DOMAIN_SORT:
1211 if k == Z3_NUMERAL_AST:
1215 if sk == Z3_ROUNDING_MODE_SORT:
1217 if sk == Z3_SEQ_SORT:
1219 if sk == Z3_CHAR_SORT:
1221 if sk == Z3_RE_SORT:
1222 return ReRef(a, ctx)
1239 _z3_assert(s1.ctx == s.ctx,
"context mismatch")
1249 if isinstance(a, str)
and isinstance(b, SeqRef):
1251 if isinstance(b, str)
and isinstance(a, SeqRef):
1253 if isinstance(a, float)
and isinstance(b, ArithRef):
1255 if isinstance(b, float)
and isinstance(a, ArithRef):
1268 for element
in sequence:
1269 result = func(result, element)
1280 alist = [
_py2expr(a, ctx)
for a
in alist]
1281 s =
_reduce(_coerce_expr_merge, alist,
None)
1282 return [s.cast(a)
for a
in alist]
1286 """Return `True` if `a` is a Z3 expression.
1293 >>> is_expr(IntSort())
1297 >>> is_expr(IntVal(1))
1300 >>> is_expr(ForAll(x, x >= 0))
1302 >>> is_expr(FPVal(1.0))
1305 return isinstance(a, ExprRef)
1309 """Return `True` if `a` is a Z3 function application.
1311 Note that, constants are function applications with 0 arguments.
1318 >>> is_app(IntSort())
1322 >>> is_app(IntVal(1))
1325 >>> is_app(ForAll(x, x >= 0))
1328 if not isinstance(a, ExprRef):
1331 return k == Z3_NUMERAL_AST
or k == Z3_APP_AST
1335 """Return `True` if `a` is Z3 constant/variable expression.
1344 >>> is_const(IntVal(1))
1347 >>> is_const(ForAll(x, x >= 0))
1350 return is_app(a)
and a.num_args() == 0
1354 """Return `True` if `a` is variable.
1356 Z3 uses de-Bruijn indices for representing bound variables in
1364 >>> f = Function('f', IntSort(), IntSort())
1365 >>> # Z3 replaces x with bound variables when ForAll is executed.
1366 >>> q = ForAll(x, f(x) == x)
1372 >>> is_var(b.arg(1))
1379 """Return the de-Bruijn index of the Z3 bounded variable `a`.
1387 >>> f = Function('f', IntSort(), IntSort(), IntSort())
1388 >>> # Z3 replaces x and y with bound variables when ForAll is executed.
1389 >>> q = ForAll([x, y], f(x, y) == x + y)
1391 f(Var(1), Var(0)) == Var(1) + Var(0)
1395 >>> v1 = b.arg(0).arg(0)
1396 >>> v2 = b.arg(0).arg(1)
1401 >>> get_var_index(v1)
1403 >>> get_var_index(v2)
1412 """Return `True` if `a` is an application of the given kind `k`.
1416 >>> is_app_of(n, Z3_OP_ADD)
1418 >>> is_app_of(n, Z3_OP_MUL)
1421 return is_app(a)
and a.kind() == k
1424def If(a, b, c, ctx=None):
1425 """Create a Z3 if-then-else expression.
1429 >>> max = If(x > y, x, y)
1435 if isinstance(a, Probe)
or isinstance(b, Tactic)
or isinstance(c, Tactic):
1436 return Cond(a, b, c, ctx)
1443 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1448 """Create a Z3 distinct expression.
1455 >>> Distinct(x, y, z)
1457 >>> simplify(Distinct(x, y, z))
1459 >>> simplify(Distinct(x, y, z), blast_distinct=True)
1460 And(Not(x == y), Not(x == z), Not(y == z))
1465 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
1474 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1475 args[0] = a.as_ast()
1476 args[1] = b.as_ast()
1477 return f(a.ctx.ref(), 2, args)
1481 """Create a constant of the given sort.
1483 >>> Const('x', IntSort())
1487 _z3_assert(isinstance(sort, SortRef),
"Z3 sort expected")
1493 """Create several constants of the given sort.
1495 `names` is a string containing the names of all constants to be created.
1496 Blank spaces separate the names of different constants.
1498 >>> x, y, z = Consts('x y z', IntSort())
1502 if isinstance(names, str):
1503 names = names.split(
" ")
1504 return [
Const(name, sort)
for name
in names]
1508 """Create a fresh constant of a specified sort"""
1513def Var(idx : int, s : SortRef) -> ExprRef:
1514 """Create a Z3 free variable. Free variables are used to create quantified formulas.
1515 A free variable with index n is bound when it occurs within the scope of n+1 quantified
1518 >>> Var(0, IntSort())
1520 >>> eq(Var(0, IntSort()), Var(0, BoolSort()))
1530 Create a real free variable. Free variables are used to create quantified formulas.
1531 They are also used to create polynomials.
1540 Create a list of Real free variables.
1541 The variables have ids: 0, 1, ..., n-1
1543 >>> x0, x1, x2, x3 = RealVarVector(4)
1547 return [
RealVar(i, ctx)
for i
in range(n)]
1560 """Try to cast `val` as a Boolean.
1562 >>> x = BoolSort().cast(True)
1572 if isinstance(val, bool):
1576 msg =
"True, False or Z3 Boolean expression expected. Received %s of type %s"
1578 if not self.
eq(val.sort()):
1579 _z3_assert(self.
eq(val.sort()),
"Value cannot be converted into a Z3 Boolean value")
1583 return isinstance(other, ArithSortRef)
1593 """All Boolean expressions are instances of this class."""
1599 if isinstance(other, BoolRef):
1600 other =
If(other, 1, 0)
1601 return If(self, 1, 0) + other
1610 """Create the Z3 expression `self * other`.
1612 if isinstance(other, int)
and other == 1:
1613 return If(self, 1, 0)
1614 if isinstance(other, int)
and other == 0:
1616 if isinstance(other, BoolRef):
1617 other =
If(other, 1, 0)
1618 return If(self, other, 0)
1621 return And(self, other)
1624 return Or(self, other)
1627 return Xor(self, other)
1643 """Return `True` if `a` is a Z3 Boolean expression.
1649 >>> is_bool(And(p, q))
1657 return isinstance(a, BoolRef)
1661 """Return `True` if `a` is the Z3 true expression.
1666 >>> is_true(simplify(p == p))
1671 >>> # True is a Python Boolean expression
1679 """Return `True` if `a` is the Z3 false expression.
1686 >>> is_false(BoolVal(False))
1693 """Return `True` if `a` is a Z3 and expression.
1695 >>> p, q = Bools('p q')
1696 >>> is_and(And(p, q))
1698 >>> is_and(Or(p, q))
1705 """Return `True` if `a` is a Z3 or expression.
1707 >>> p, q = Bools('p q')
1710 >>> is_or(And(p, q))
1717 """Return `True` if `a` is a Z3 implication expression.
1719 >>> p, q = Bools('p q')
1720 >>> is_implies(Implies(p, q))
1722 >>> is_implies(And(p, q))
1729 """Return `True` if `a` is a Z3 not expression.
1741 """Return `True` if `a` is a Z3 equality expression.
1743 >>> x, y = Ints('x y')
1751 """Return `True` if `a` is a Z3 distinct expression.
1753 >>> x, y, z = Ints('x y z')
1754 >>> is_distinct(x == y)
1756 >>> is_distinct(Distinct(x, y, z))
1763 """Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
1767 >>> p = Const('p', BoolSort())
1770 >>> r = Function('r', IntSort(), IntSort(), BoolSort())
1773 >>> is_bool(r(0, 1))
1781 """Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used.
1785 >>> is_true(BoolVal(True))
1789 >>> is_false(BoolVal(False))
1800 """Return a Boolean constant named `name`. If `ctx=None`, then the global context is used.
1812 """Return a tuple of Boolean constants.
1814 `names` is a single string containing all names separated by blank spaces.
1815 If `ctx=None`, then the global context is used.
1817 >>> p, q, r = Bools('p q r')
1818 >>> And(p, Or(q, r))
1822 if isinstance(names, str):
1823 names = names.split(
" ")
1824 return [
Bool(name, ctx)
for name
in names]
1828 """Return a list of Boolean constants of size `sz`.
1830 The constants are named using the given prefix.
1831 If `ctx=None`, then the global context is used.
1833 >>> P = BoolVector('p', 3)
1837 And(p__0, p__1, p__2)
1839 return [
Bool(
"%s__%s" % (prefix, i))
for i
in range(sz)]
1843 """Return a fresh Boolean constant in the given context using the given prefix.
1845 If `ctx=None`, then the global context is used.
1847 >>> b1 = FreshBool()
1848 >>> b2 = FreshBool()
1857 """Create a Z3 implies expression.
1859 >>> p, q = Bools('p q')
1871 """Create a Z3 Xor expression.
1873 >>> p, q = Bools('p q')
1876 >>> simplify(Xor(p, q))
1887 """Create a Z3 not expression or probe.
1892 >>> simplify(Not(Not(p)))
1913 """Return `True` if one of the elements of the given collection is a Z3 probe."""
1921 """Create a Z3 and-expression or and-probe.
1923 >>> p, q, r = Bools('p q r')
1926 >>> P = BoolVector('p', 5)
1928 And(p__0, p__1, p__2, p__3, p__4)
1932 last_arg = args[len(args) - 1]
1933 if isinstance(last_arg, Context):
1934 ctx = args[len(args) - 1]
1935 args = args[:len(args) - 1]
1936 elif len(args) == 1
and isinstance(args[0], AstVector):
1938 args = [a
for a
in args[0]]
1944 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1954 """Create a Z3 or-expression or or-probe.
1956 >>> p, q, r = Bools('p q r')
1959 >>> P = BoolVector('p', 5)
1961 Or(p__0, p__1, p__2, p__3, p__4)
1965 last_arg = args[len(args) - 1]
1966 if isinstance(last_arg, Context):
1967 ctx = args[len(args) - 1]
1968 args = args[:len(args) - 1]
1969 elif len(args) == 1
and isinstance(args[0], AstVector):
1971 args = [a
for a
in args[0]]
1977 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1993 """Patterns are hints for quantifier instantiation.
2005 """Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation.
2007 >>> f = Function('f', IntSort(), IntSort())
2009 >>> q = ForAll(x, f(x) == 0, patterns = [ f(x) ])
2011 ForAll(x, f(x) == 0)
2012 >>> q.num_patterns()
2014 >>> is_pattern(q.pattern(0))
2019 return isinstance(a, PatternRef)
2023 """Create a Z3 multi-pattern using the given expressions `*args`
2025 >>> f = Function('f', IntSort(), IntSort())
2026 >>> g = Function('g', IntSort(), IntSort())
2028 >>> q = ForAll(x, f(x) != g(x), patterns = [ MultiPattern(f(x), g(x)) ])
2030 ForAll(x, f(x) != g(x))
2031 >>> q.num_patterns()
2033 >>> is_pattern(q.pattern(0))
2036 MultiPattern(f(Var(0)), g(Var(0)))
2039 _z3_assert(len(args) > 0,
"At least one argument expected")
2060 """Universally and Existentially quantified formulas."""
2069 """Return the Boolean sort or sort of Lambda."""
2075 """Return `True` if `self` is a universal quantifier.
2077 >>> f = Function('f', IntSort(), IntSort())
2079 >>> q = ForAll(x, f(x) == 0)
2082 >>> q = Exists(x, f(x) != 0)
2089 """Return `True` if `self` is an existential quantifier.
2091 >>> f = Function('f', IntSort(), IntSort())
2093 >>> q = ForAll(x, f(x) == 0)
2096 >>> q = Exists(x, f(x) != 0)
2103 """Return `True` if `self` is a lambda expression.
2105 >>> f = Function('f', IntSort(), IntSort())
2107 >>> q = Lambda(x, f(x))
2110 >>> q = Exists(x, f(x) != 0)
2117 """Return the Z3 expression `self[arg]`.
2124 """Return the weight annotation of `self`.
2126 >>> f = Function('f', IntSort(), IntSort())
2128 >>> q = ForAll(x, f(x) == 0)
2131 >>> q = ForAll(x, f(x) == 0, weight=10)
2138 """Return the skolem id of `self`.
2143 """Return the quantifier id of `self`.
2148 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2150 >>> f = Function('f', IntSort(), IntSort())
2151 >>> g = Function('g', IntSort(), IntSort())
2153 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2154 >>> q.num_patterns()
2160 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2162 >>> f = Function('f', IntSort(), IntSort())
2163 >>> g = Function('g', IntSort(), IntSort())
2165 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2166 >>> q.num_patterns()
2178 """Return the number of no-patterns."""
2182 """Return a no-pattern."""
2188 """Return the expression being quantified.
2190 >>> f = Function('f', IntSort(), IntSort())
2192 >>> q = ForAll(x, f(x) == 0)
2199 """Return the number of variables bounded by this quantifier.
2201 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2204 >>> q = ForAll([x, y], f(x, y) >= x)
2211 """Return a string representing a name used when displaying the quantifier.
2213 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2216 >>> q = ForAll([x, y], f(x, y) >= x)
2227 """Return the sort of a bound variable.
2229 >>> f = Function('f', IntSort(), RealSort(), IntSort())
2232 >>> q = ForAll([x, y], f(x, y) >= x)
2243 """Return a list containing a single element self.body()
2245 >>> f = Function('f', IntSort(), IntSort())
2247 >>> q = ForAll(x, f(x) == 0)
2251 return [self.
body()]
2255 """Return `True` if `a` is a Z3 quantifier.
2257 >>> f = Function('f', IntSort(), IntSort())
2259 >>> q = ForAll(x, f(x) == 0)
2260 >>> is_quantifier(q)
2262 >>> is_quantifier(f(x))
2265 return isinstance(a, QuantifierRef)
2268def _mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2273 _z3_assert(all([
is_expr(p)
for p
in no_patterns]),
"no patterns are Z3 expressions")
2284 _vs = (Ast * num_vars)()
2285 for i
in range(num_vars):
2287 _vs[i] = vs[i].as_ast()
2289 num_pats = len(patterns)
2290 _pats = (Pattern * num_pats)()
2291 for i
in range(num_pats):
2292 _pats[i] = patterns[i].ast
2299 num_no_pats, _no_pats,
2300 body.as_ast()), ctx)
2303def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2304 """Create a Z3 forall formula.
2306 The parameters `weight`, `qid`, `skid`, `patterns` and `no_patterns` are optional annotations.
2308 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2311 >>> ForAll([x, y], f(x, y) >= x)
2312 ForAll([x, y], f(x, y) >= x)
2313 >>> ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
2314 ForAll([x, y], f(x, y) >= x)
2315 >>> ForAll([x, y], f(x, y) >= x, weight=10)
2316 ForAll([x, y], f(x, y) >= x)
2318 return _mk_quantifier(
True, vs, body, weight, qid, skid, patterns, no_patterns)
2321def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2322 """Create a Z3 exists formula.
2324 The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.
2327 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2330 >>> q = Exists([x, y], f(x, y) >= x, skid="foo")
2332 Exists([x, y], f(x, y) >= x)
2333 >>> is_quantifier(q)
2335 >>> r = Tactic('nnf')(q).as_expr()
2336 >>> is_quantifier(r)
2339 return _mk_quantifier(
False, vs, body, weight, qid, skid, patterns, no_patterns)
2343 """Create a Z3 lambda expression.
2345 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2346 >>> mem0 = Array('mem0', IntSort(), IntSort())
2347 >>> lo, hi, e, i = Ints('lo hi e i')
2348 >>> mem1 = Lambda([i], If(And(lo <= i, i <= hi), e, mem0[i]))
2350 Lambda(i, If(And(lo <= i, i <= hi), e, mem0[i]))
2356 _vs = (Ast * num_vars)()
2357 for i
in range(num_vars):
2359 _vs[i] = vs[i].as_ast()
2370 """Real and Integer sorts."""
2373 """Return `True` if `self` is of the sort Real.
2378 >>> (x + 1).is_real()
2384 return self.
kind() == Z3_REAL_SORT
2387 """Return `True` if `self` is of the sort Integer.
2392 >>> (x + 1).is_int()
2398 return self.
kind() == Z3_INT_SORT
2404 """Return `True` if `self` is a subsort of `other`."""
2408 """Try to cast `val` as an Integer or Real.
2410 >>> IntSort().cast(10)
2412 >>> is_int(IntSort().cast(10))
2416 >>> RealSort().cast(10)
2418 >>> is_real(RealSort().cast(10))
2427 if val_s.is_int()
and self.
is_real():
2429 if val_s.is_bool()
and self.
is_int():
2430 return If(val, 1, 0)
2431 if val_s.is_bool()
and self.
is_real():
2434 _z3_assert(
False,
"Z3 Integer/Real expression expected")
2441 msg =
"int, long, float, string (numeral), or Z3 Integer/Real expression expected. Got %s"
2446 """Return `True` if s is an arithmetical sort (type).
2448 >>> is_arith_sort(IntSort())
2450 >>> is_arith_sort(RealSort())
2452 >>> is_arith_sort(BoolSort())
2454 >>> n = Int('x') + 1
2455 >>> is_arith_sort(n.sort())
2458 return isinstance(s, ArithSortRef)
2462 """Integer and Real expressions."""
2465 """Return the sort (type) of the arithmetical expression `self`.
2469 >>> (Real('x') + 1).sort()
2475 """Return `True` if `self` is an integer expression.
2480 >>> (x + 1).is_int()
2483 >>> (x + y).is_int()
2489 """Return `True` if `self` is an real expression.
2494 >>> (x + 1).is_real()
2500 """Create the Z3 expression `self + other`.
2513 """Create the Z3 expression `other + self`.
2523 """Create the Z3 expression `self * other`.
2532 if isinstance(other, BoolRef):
2533 return If(other, self, 0)
2538 """Create the Z3 expression `other * self`.
2548 """Create the Z3 expression `self - other`.
2561 """Create the Z3 expression `other - self`.
2571 """Create the Z3 expression `self**other` (** is the power operator).
2578 >>> simplify(IntVal(2)**8)
2585 """Create the Z3 expression `other**self` (** is the power operator).
2592 >>> simplify(2**IntVal(8))
2599 """Create the Z3 expression `other/self`.
2622 """Create the Z3 expression `other/self`."""
2626 """Create the Z3 expression `other/self`.
2643 """Create the Z3 expression `other/self`."""
2647 """Create the Z3 expression `other%self`.
2653 >>> simplify(IntVal(10) % IntVal(3))
2658 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2662 """Create the Z3 expression `other%self`.
2670 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2674 """Return an expression representing `-self`.
2694 """Create the Z3 expression `other <= self`.
2696 >>> x, y = Ints('x y')
2707 """Create the Z3 expression `other < self`.
2709 >>> x, y = Ints('x y')
2720 """Create the Z3 expression `other > self`.
2722 >>> x, y = Ints('x y')
2733 """Create the Z3 expression `other >= self`.
2735 >>> x, y = Ints('x y')
2747 """Return `True` if `a` is an arithmetical expression.
2756 >>> is_arith(IntVal(1))
2764 return isinstance(a, ArithRef)
2768 """Return `True` if `a` is an integer expression.
2775 >>> is_int(IntVal(1))
2787 """Return `True` if `a` is a real expression.
2799 >>> is_real(RealVal(1))
2814 """Return `True` if `a` is an integer value of sort Int.
2816 >>> is_int_value(IntVal(1))
2820 >>> is_int_value(Int('x'))
2822 >>> n = Int('x') + 1
2827 >>> is_int_value(n.arg(1))
2829 >>> is_int_value(RealVal("1/3"))
2831 >>> is_int_value(RealVal(1))
2838 """Return `True` if `a` is rational value of sort Real.
2840 >>> is_rational_value(RealVal(1))
2842 >>> is_rational_value(RealVal("3/5"))
2844 >>> is_rational_value(IntVal(1))
2846 >>> is_rational_value(1)
2848 >>> n = Real('x') + 1
2851 >>> is_rational_value(n.arg(1))
2853 >>> is_rational_value(Real('x'))
2860 """Return `True` if `a` is an algebraic value of sort Real.
2862 >>> is_algebraic_value(RealVal("3/5"))
2864 >>> n = simplify(Sqrt(2))
2867 >>> is_algebraic_value(n)
2874 """Return `True` if `a` is an expression of the form b + c.
2876 >>> x, y = Ints('x y')
2886 """Return `True` if `a` is an expression of the form b * c.
2888 >>> x, y = Ints('x y')
2898 """Return `True` if `a` is an expression of the form b - c.
2900 >>> x, y = Ints('x y')
2910 """Return `True` if `a` is an expression of the form b / c.
2912 >>> x, y = Reals('x y')
2917 >>> x, y = Ints('x y')
2927 """Return `True` if `a` is an expression of the form b div c.
2929 >>> x, y = Ints('x y')
2939 """Return `True` if `a` is an expression of the form b % c.
2941 >>> x, y = Ints('x y')
2951 """Return `True` if `a` is an expression of the form b <= c.
2953 >>> x, y = Ints('x y')
2963 """Return `True` if `a` is an expression of the form b < c.
2965 >>> x, y = Ints('x y')
2975 """Return `True` if `a` is an expression of the form b >= c.
2977 >>> x, y = Ints('x y')
2987 """Return `True` if `a` is an expression of the form b > c.
2989 >>> x, y = Ints('x y')
2999 """Return `True` if `a` is an expression of the form IsInt(b).
3002 >>> is_is_int(IsInt(x))
3011 """Return `True` if `a` is an expression of the form ToReal(b).
3026 """Return `True` if `a` is an expression of the form ToInt(b).
3041 """Integer values."""
3044 """Return a Z3 integer numeral as a Python long (bignum) numeral.
3057 """Return a Z3 integer numeral as a Python string.
3065 """Return a Z3 integer numeral as a Python binary string.
3067 >>> v.as_binary_string()
3077 """Rational values."""
3080 """ Return the numerator of a Z3 rational numeral.
3082 >>> is_rational_value(RealVal("3/5"))
3084 >>> n = RealVal("3/5")
3087 >>> is_rational_value(Q(3,5))
3089 >>> Q(3,5).numerator()
3095 """ Return the denominator of a Z3 rational numeral.
3097 >>> is_rational_value(Q(3,5))
3106 """ Return the numerator as a Python long.
3108 >>> v = RealVal(10000000000)
3113 >>> v.numerator_as_long() + 1 == 10000000001
3119 """ Return the denominator as a Python long.
3121 >>> v = RealVal("1/3")
3124 >>> v.denominator_as_long()
3143 """ Return a Z3 rational value as a string in decimal notation using at most `prec` decimal places.
3145 >>> v = RealVal("1/5")
3148 >>> v = RealVal("1/3")
3155 """Return a Z3 rational numeral as a Python string.
3164 """Return a Z3 rational as a Python Fraction object.
3166 >>> v = RealVal("1/5")
3177 """Algebraic irrational values."""
3180 """Return a Z3 rational number that approximates the algebraic number `self`.
3181 The result `r` is such that |r - self| <= 1/10^precision
3183 >>> x = simplify(Sqrt(2))
3185 6838717160008073720548335/4835703278458516698824704
3192 """Return a string representation of the algebraic number `self` in decimal notation
3193 using `prec` decimal places.
3195 >>> x = simplify(Sqrt(2))
3196 >>> x.as_decimal(10)
3198 >>> x.as_decimal(20)
3199 '1.41421356237309504880?'
3211 if isinstance(a, bool):
3215 if isinstance(a, float):
3217 if isinstance(a, str):
3222 _z3_assert(
False,
"Python bool, int, long or float expected")
3226 """Return the integer sort in the given context. If `ctx=None`, then the global context is used.
3230 >>> x = Const('x', IntSort())
3233 >>> x.sort() == IntSort()
3235 >>> x.sort() == BoolSort()
3243 """Return the real sort in the given context. If `ctx=None`, then the global context is used.
3247 >>> x = Const('x', RealSort())
3252 >>> x.sort() == RealSort()
3260 if isinstance(val, float):
3261 return str(int(val))
3262 elif isinstance(val, bool):
3272 """Return a Z3 integer value. If `ctx=None`, then the global context is used.
3284 """Return a Z3 real value.
3286 `val` may be a Python int, long, float or string representing a number in decimal or rational notation.
3287 If `ctx=None`, then the global context is used.
3291 >>> RealVal(1).sort()
3303 """Return a Z3 rational a/b.
3305 If `ctx=None`, then the global context is used.
3309 >>> RatVal(3,5).sort()
3313 _z3_assert(
_is_int(a)
or isinstance(a, str),
"First argument cannot be converted into an integer")
3314 _z3_assert(
_is_int(b)
or isinstance(b, str),
"Second argument cannot be converted into an integer")
3318def Q(a, b, ctx=None):
3319 """Return a Z3 rational a/b.
3321 If `ctx=None`, then the global context is used.
3332 """Return an integer constant named `name`. If `ctx=None`, then the global context is used.
3345 """Return a tuple of Integer constants.
3347 >>> x, y, z = Ints('x y z')
3352 if isinstance(names, str):
3353 names = names.split(
" ")
3354 return [
Int(name, ctx)
for name
in names]
3358 """Return a list of integer constants of size `sz`.
3360 >>> X = IntVector('x', 3)
3367 return [
Int(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3371 """Return a fresh integer constant in the given context using the given prefix.
3385 """Return a real constant named `name`. If `ctx=None`, then the global context is used.
3398 """Return a tuple of real constants.
3400 >>> x, y, z = Reals('x y z')
3403 >>> Sum(x, y, z).sort()
3407 if isinstance(names, str):
3408 names = names.split(
" ")
3409 return [
Real(name, ctx)
for name
in names]
3413 """Return a list of real constants of size `sz`.
3415 >>> X = RealVector('x', 3)
3424 return [
Real(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3428 """Return a fresh real constant in the given context using the given prefix.
3442 """ Return the Z3 expression ToReal(a).
3454 if isinstance(a, BoolRef):
3457 _z3_assert(a.is_int(),
"Z3 integer expression expected.")
3462 """ Return the Z3 expression ToInt(a).
3474 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3480 """ Return the Z3 predicate IsInt(a).
3483 >>> IsInt(x + "1/2")
3485 >>> solve(IsInt(x + "1/2"), x > 0, x < 1)
3487 >>> solve(IsInt(x + "1/2"), x > 0, x < 1, x != "1/2")
3491 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3497 """ Return a Z3 expression which represents the square root of a.
3510 """ Return a Z3 expression which represents the cubic root of a.
3529 """Bit-vector sort."""
3532 """Return the size (number of bits) of the bit-vector sort `self`.
3534 >>> b = BitVecSort(32)
3544 """Try to cast `val` as a Bit-Vector.
3546 >>> b = BitVecSort(32)
3549 >>> b.cast(10).sexpr()
3562 """Return True if `s` is a Z3 bit-vector sort.
3564 >>> is_bv_sort(BitVecSort(32))
3566 >>> is_bv_sort(IntSort())
3569 return isinstance(s, BitVecSortRef)
3573 """Bit-vector expressions."""
3576 """Return the sort of the bit-vector expression `self`.
3578 >>> x = BitVec('x', 32)
3581 >>> x.sort() == BitVecSort(32)
3587 """Return the number of bits of the bit-vector expression `self`.
3589 >>> x = BitVec('x', 32)
3592 >>> Concat(x, x).size()
3598 """Create the Z3 expression `self + other`.
3600 >>> x = BitVec('x', 32)
3601 >>> y = BitVec('y', 32)
3611 """Create the Z3 expression `other + self`.
3613 >>> x = BitVec('x', 32)
3621 """Create the Z3 expression `self * other`.
3623 >>> x = BitVec('x', 32)
3624 >>> y = BitVec('y', 32)
3634 """Create the Z3 expression `other * self`.
3636 >>> x = BitVec('x', 32)
3644 """Create the Z3 expression `self - other`.
3646 >>> x = BitVec('x', 32)
3647 >>> y = BitVec('y', 32)
3657 """Create the Z3 expression `other - self`.
3659 >>> x = BitVec('x', 32)
3667 """Create the Z3 expression bitwise-or `self | other`.
3669 >>> x = BitVec('x', 32)
3670 >>> y = BitVec('y', 32)
3680 """Create the Z3 expression bitwise-or `other | self`.
3682 >>> x = BitVec('x', 32)
3690 """Create the Z3 expression bitwise-and `self & other`.
3692 >>> x = BitVec('x', 32)
3693 >>> y = BitVec('y', 32)
3703 """Create the Z3 expression bitwise-or `other & self`.
3705 >>> x = BitVec('x', 32)
3713 """Create the Z3 expression bitwise-xor `self ^ other`.
3715 >>> x = BitVec('x', 32)
3716 >>> y = BitVec('y', 32)
3726 """Create the Z3 expression bitwise-xor `other ^ self`.
3728 >>> x = BitVec('x', 32)
3738 >>> x = BitVec('x', 32)
3745 """Return an expression representing `-self`.
3747 >>> x = BitVec('x', 32)
3756 """Create the Z3 expression bitwise-not `~self`.
3758 >>> x = BitVec('x', 32)
3767 """Create the Z3 expression (signed) division `self / other`.
3769 Use the function UDiv() for unsigned division.
3771 >>> x = BitVec('x', 32)
3772 >>> y = BitVec('y', 32)
3779 >>> UDiv(x, y).sexpr()
3786 """Create the Z3 expression (signed) division `self / other`."""
3790 """Create the Z3 expression (signed) division `other / self`.
3792 Use the function UDiv() for unsigned division.
3794 >>> x = BitVec('x', 32)
3797 >>> (10 / x).sexpr()
3798 '(bvsdiv #x0000000a x)'
3799 >>> UDiv(10, x).sexpr()
3800 '(bvudiv #x0000000a x)'
3806 """Create the Z3 expression (signed) division `other / self`."""
3810 """Create the Z3 expression (signed) mod `self % other`.
3812 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3814 >>> x = BitVec('x', 32)
3815 >>> y = BitVec('y', 32)
3822 >>> URem(x, y).sexpr()
3824 >>> SRem(x, y).sexpr()
3831 """Create the Z3 expression (signed) mod `other % self`.
3833 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3835 >>> x = BitVec('x', 32)
3838 >>> (10 % x).sexpr()
3839 '(bvsmod #x0000000a x)'
3840 >>> URem(10, x).sexpr()
3841 '(bvurem #x0000000a x)'
3842 >>> SRem(10, x).sexpr()
3843 '(bvsrem #x0000000a x)'
3849 """Create the Z3 expression (signed) `other <= self`.
3851 Use the function ULE() for unsigned less than or equal to.
3853 >>> x, y = BitVecs('x y', 32)
3856 >>> (x <= y).sexpr()
3858 >>> ULE(x, y).sexpr()
3865 """Create the Z3 expression (signed) `other < self`.
3867 Use the function ULT() for unsigned less than.
3869 >>> x, y = BitVecs('x y', 32)
3874 >>> ULT(x, y).sexpr()
3881 """Create the Z3 expression (signed) `other > self`.
3883 Use the function UGT() for unsigned greater than.
3885 >>> x, y = BitVecs('x y', 32)
3890 >>> UGT(x, y).sexpr()
3897 """Create the Z3 expression (signed) `other >= self`.
3899 Use the function UGE() for unsigned greater than or equal to.
3901 >>> x, y = BitVecs('x y', 32)
3904 >>> (x >= y).sexpr()
3906 >>> UGE(x, y).sexpr()
3913 """Create the Z3 expression (arithmetical) right shift `self >> other`
3915 Use the function LShR() for the right logical shift
3917 >>> x, y = BitVecs('x y', 32)
3920 >>> (x >> y).sexpr()
3922 >>> LShR(x, y).sexpr()
3926 >>> BitVecVal(4, 3).as_signed_long()
3928 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
3930 >>> simplify(BitVecVal(4, 3) >> 1)
3932 >>> simplify(LShR(BitVecVal(4, 3), 1))
3934 >>> simplify(BitVecVal(2, 3) >> 1)
3936 >>> simplify(LShR(BitVecVal(2, 3), 1))
3943 """Create the Z3 expression left shift `self << other`
3945 >>> x, y = BitVecs('x y', 32)
3948 >>> (x << y).sexpr()
3950 >>> simplify(BitVecVal(2, 3) << 1)
3957 """Create the Z3 expression (arithmetical) right shift `other` >> `self`.
3959 Use the function LShR() for the right logical shift
3961 >>> x = BitVec('x', 32)
3964 >>> (10 >> x).sexpr()
3965 '(bvashr #x0000000a x)'
3971 """Create the Z3 expression left shift `other << self`.
3973 Use the function LShR() for the right logical shift
3975 >>> x = BitVec('x', 32)
3978 >>> (10 << x).sexpr()
3979 '(bvshl #x0000000a x)'
3986 """Bit-vector values."""
3989 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3991 >>> v = BitVecVal(0xbadc0de, 32)
3994 >>> print("0x%.8x" % v.as_long())
4000 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
4001 The most significant bit is assumed to be the sign.
4003 >>> BitVecVal(4, 3).as_signed_long()
4005 >>> BitVecVal(7, 3).as_signed_long()
4007 >>> BitVecVal(3, 3).as_signed_long()
4009 >>> BitVecVal(2**32 - 1, 32).as_signed_long()
4011 >>> BitVecVal(2**64 - 1, 64).as_signed_long()
4016 if val >= 2**(sz - 1):
4018 if val < -2**(sz - 1):
4029 """Return the Python value of a Z3 bit-vector numeral."""
4035 """Return `True` if `a` is a Z3 bit-vector expression.
4037 >>> b = BitVec('b', 32)
4045 return isinstance(a, BitVecRef)
4049 """Return `True` if `a` is a Z3 bit-vector numeral value.
4051 >>> b = BitVec('b', 32)
4054 >>> b = BitVecVal(10, 32)
4064 """Return the Z3 expression BV2Int(a).
4066 >>> b = BitVec('b', 3)
4067 >>> BV2Int(b).sort()
4072 >>> x > BV2Int(b, is_signed=False)
4074 >>> x > BV2Int(b, is_signed=True)
4075 x > If(b < 0, BV2Int(b) - 8, BV2Int(b))
4076 >>> solve(x > BV2Int(b), b == 1, x < 3)
4080 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4087 """Return the z3 expression Int2BV(a, num_bits).
4088 It is a bit-vector of width num_bits and represents the
4089 modulo of a by 2^num_bits
4096 """Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used.
4098 >>> Byte = BitVecSort(8)
4099 >>> Word = BitVecSort(16)
4102 >>> x = Const('x', Byte)
4103 >>> eq(x, BitVec('x', 8))
4111 """Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used.
4113 >>> v = BitVecVal(10, 32)
4116 >>> print("0x%.8x" % v.as_long())
4128 """Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
4129 If `ctx=None`, then the global context is used.
4131 >>> x = BitVec('x', 16)
4138 >>> word = BitVecSort(16)
4139 >>> x2 = BitVec('x', word)
4143 if isinstance(bv, BitVecSortRef):
4152 """Return a tuple of bit-vector constants of size bv.
4154 >>> x, y, z = BitVecs('x y z', 16)
4161 >>> Product(x, y, z)
4163 >>> simplify(Product(x, y, z))
4167 if isinstance(names, str):
4168 names = names.split(
" ")
4169 return [
BitVec(name, bv, ctx)
for name
in names]
4173 """Create a Z3 bit-vector concatenation expression.
4175 >>> v = BitVecVal(1, 4)
4176 >>> Concat(v, v+1, v)
4177 Concat(Concat(1, 1 + 1), 1)
4178 >>> simplify(Concat(v, v+1, v))
4180 >>> print("%.3x" % simplify(Concat(v, v+1, v)).as_long())
4186 _z3_assert(sz >= 2,
"At least two arguments expected.")
4193 if is_seq(args[0])
or isinstance(args[0], str):
4196 _z3_assert(all([
is_seq(a)
for a
in args]),
"All arguments must be sequence expressions.")
4199 v[i] = args[i].as_ast()
4204 _z3_assert(all([
is_re(a)
for a
in args]),
"All arguments must be regular expressions.")
4207 v[i] = args[i].as_ast()
4211 _z3_assert(all([
is_bv(a)
for a
in args]),
"All arguments must be Z3 bit-vector expressions.")
4213 for i
in range(sz - 1):
4219 """Create a Z3 bit-vector extraction expression.
4220 Extract is overloaded to also work on sequence extraction.
4221 The functions SubString and SubSeq are redirected to Extract.
4222 For this case, the arguments are reinterpreted as:
4223 high - is a sequence (string)
4225 a - is the length to be extracted
4227 >>> x = BitVec('x', 8)
4228 >>> Extract(6, 2, x)
4230 >>> Extract(6, 2, x).sort()
4232 >>> simplify(Extract(StringVal("abcd"),2,1))
4235 if isinstance(high, str):
4242 _z3_assert(low <= high,
"First argument must be greater than or equal to second argument")
4244 "First and second arguments must be non negative integers")
4245 _z3_assert(
is_bv(a),
"Third argument must be a Z3 bit-vector expression")
4251 _z3_assert(
is_bv(a)
or is_bv(b),
"First or second argument must be a Z3 bit-vector expression")
4255 """Create the Z3 expression (unsigned) `other <= self`.
4257 Use the operator <= for signed less than or equal to.
4259 >>> x, y = BitVecs('x y', 32)
4262 >>> (x <= y).sexpr()
4264 >>> ULE(x, y).sexpr()
4273 """Create the Z3 expression (unsigned) `other < self`.
4275 Use the operator < for signed less than.
4277 >>> x, y = BitVecs('x y', 32)
4282 >>> ULT(x, y).sexpr()
4291 """Create the Z3 expression (unsigned) `other >= self`.
4293 Use the operator >= for signed greater than or equal to.
4295 >>> x, y = BitVecs('x y', 32)
4298 >>> (x >= y).sexpr()
4300 >>> UGE(x, y).sexpr()
4309 """Create the Z3 expression (unsigned) `other > self`.
4311 Use the operator > for signed greater than.
4313 >>> x, y = BitVecs('x y', 32)
4318 >>> UGT(x, y).sexpr()
4327 """Create the Z3 expression (unsigned) division `self / other`.
4329 Use the operator / for signed division.
4331 >>> x = BitVec('x', 32)
4332 >>> y = BitVec('y', 32)
4335 >>> UDiv(x, y).sort()
4339 >>> UDiv(x, y).sexpr()
4348 """Create the Z3 expression (unsigned) remainder `self % other`.
4350 Use the operator % for signed modulus, and SRem() for signed remainder.
4352 >>> x = BitVec('x', 32)
4353 >>> y = BitVec('y', 32)
4356 >>> URem(x, y).sort()
4360 >>> URem(x, y).sexpr()
4369 """Create the Z3 expression signed remainder.
4371 Use the operator % for signed modulus, and URem() for unsigned remainder.
4373 >>> x = BitVec('x', 32)
4374 >>> y = BitVec('y', 32)
4377 >>> SRem(x, y).sort()
4381 >>> SRem(x, y).sexpr()
4390 """Create the Z3 expression logical right shift.
4392 Use the operator >> for the arithmetical right shift.
4394 >>> x, y = BitVecs('x y', 32)
4397 >>> (x >> y).sexpr()
4399 >>> LShR(x, y).sexpr()
4403 >>> BitVecVal(4, 3).as_signed_long()
4405 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
4407 >>> simplify(BitVecVal(4, 3) >> 1)
4409 >>> simplify(LShR(BitVecVal(4, 3), 1))
4411 >>> simplify(BitVecVal(2, 3) >> 1)
4413 >>> simplify(LShR(BitVecVal(2, 3), 1))
4422 """Return an expression representing `a` rotated to the left `b` times.
4424 >>> a, b = BitVecs('a b', 16)
4425 >>> RotateLeft(a, b)
4427 >>> simplify(RotateLeft(a, 0))
4429 >>> simplify(RotateLeft(a, 16))
4438 """Return an expression representing `a` rotated to the right `b` times.
4440 >>> a, b = BitVecs('a b', 16)
4441 >>> RotateRight(a, b)
4443 >>> simplify(RotateRight(a, 0))
4445 >>> simplify(RotateRight(a, 16))
4454 """Return a bit-vector expression with `n` extra sign-bits.
4456 >>> x = BitVec('x', 16)
4457 >>> n = SignExt(8, x)
4464 >>> v0 = BitVecVal(2, 2)
4469 >>> v = simplify(SignExt(6, v0))
4474 >>> print("%.x" % v.as_long())
4479 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4484 """Return a bit-vector expression with `n` extra zero-bits.
4486 >>> x = BitVec('x', 16)
4487 >>> n = ZeroExt(8, x)
4494 >>> v0 = BitVecVal(2, 2)
4499 >>> v = simplify(ZeroExt(6, v0))
4507 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4512 """Return an expression representing `n` copies of `a`.
4514 >>> x = BitVec('x', 8)
4515 >>> n = RepeatBitVec(4, x)
4520 >>> v0 = BitVecVal(10, 4)
4521 >>> print("%.x" % v0.as_long())
4523 >>> v = simplify(RepeatBitVec(4, v0))
4526 >>> print("%.x" % v.as_long())
4531 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4536 """Return the reduction-and expression of `a`."""
4538 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4543 """Return the reduction-or expression of `a`."""
4545 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4550 """A predicate the determines that bit-vector addition does not overflow"""
4557 """A predicate the determines that signed bit-vector addition does not underflow"""
4564 """A predicate the determines that bit-vector subtraction does not overflow"""
4571 """A predicate the determines that bit-vector subtraction does not underflow"""
4578 """A predicate the determines that bit-vector signed division does not overflow"""
4585 """A predicate the determines that bit-vector unary negation does not overflow"""
4587 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4592 """A predicate the determines that bit-vector multiplication does not overflow"""
4599 """A predicate the determines that bit-vector signed multiplication does not underflow"""
4615 """Return the domain of the array sort `self`.
4617 >>> A = ArraySort(IntSort(), BoolSort())
4624 """Return the domain of the array sort `self`.
4629 """Return the range of the array sort `self`.
4631 >>> A = ArraySort(IntSort(), BoolSort())
4639 """Array expressions. """
4642 """Return the array sort of the array expression `self`.
4644 >>> a = Array('a', IntSort(), BoolSort())
4651 """Shorthand for `self.sort().domain()`.
4653 >>> a = Array('a', IntSort(), BoolSort())
4660 """Shorthand for self.sort().domain_n(i)`."""
4664 """Shorthand for `self.sort().range()`.
4666 >>> a = Array('a', IntSort(), BoolSort())
4673 """Return the Z3 expression `self[arg]`.
4675 >>> a = Array('a', IntSort(), BoolSort())
4689 if isinstance(arg, tuple):
4690 args = [ar.sort().domain_n(i).cast(arg[i])
for i
in range(len(arg))]
4693 arg = ar.sort().domain().cast(arg)
4702 """Return `True` if `a` is a Z3 array expression.
4704 >>> a = Array('a', IntSort(), IntSort())
4707 >>> is_array(Store(a, 0, 1))
4712 return isinstance(a, ArrayRef)
4716 """Return `True` if `a` is a Z3 constant array.
4718 >>> a = K(IntSort(), 10)
4719 >>> is_const_array(a)
4721 >>> a = Array('a', IntSort(), IntSort())
4722 >>> is_const_array(a)
4729 """Return `True` if `a` is a Z3 constant array.
4731 >>> a = K(IntSort(), 10)
4734 >>> a = Array('a', IntSort(), IntSort())
4742 """Return `True` if `a` is a Z3 map array expression.
4744 >>> f = Function('f', IntSort(), IntSort())
4745 >>> b = Array('b', IntSort(), IntSort())
4758 """Return `True` if `a` is a Z3 default array expression.
4759 >>> d = Default(K(IntSort(), 10))
4763 return is_app_of(a, Z3_OP_ARRAY_DEFAULT)
4767 """Return the function declaration associated with a Z3 map array expression.
4769 >>> f = Function('f', IntSort(), IntSort())
4770 >>> b = Array('b', IntSort(), IntSort())
4772 >>> eq(f, get_map_func(a))
4776 >>> get_map_func(a)(0)
4791 """Return the Z3 array sort with the given domain and range sorts.
4793 >>> A = ArraySort(IntSort(), BoolSort())
4800 >>> AA = ArraySort(IntSort(), A)
4802 Array(Int, Array(Int, Bool))
4806 _z3_assert(len(sig) > 1,
"At least two arguments expected")
4807 arity = len(sig) - 1
4813 _z3_assert(s.ctx == r.ctx,
"Context mismatch")
4817 dom = (Sort * arity)()
4818 for i
in range(arity):
4824 """Return an array constant named `name` with the given domain and range sorts.
4826 >>> a = Array('a', IntSort(), IntSort())
4838 """Return a Z3 store array expression.
4840 >>> a = Array('a', IntSort(), IntSort())
4841 >>> i, v = Ints('i v')
4842 >>> s = Update(a, i, v)
4845 >>> prove(s[i] == v)
4848 >>> prove(Implies(i != j, s[j] == a[j]))
4856 raise Z3Exception(
"array update requires index and value arguments")
4860 i = a.sort().domain().cast(i)
4861 v = a.sort().range().cast(v)
4863 v = a.sort().range().cast(args[-1])
4864 idxs = [a.sort().domain_n(i).cast(args[i])
for i
in range(len(args)-1)]
4870 """ Return a default value for array expression.
4871 >>> b = K(IntSort(), 1)
4872 >>> prove(Default(b) == 1)
4881 """Return a Z3 store array expression.
4883 >>> a = Array('a', IntSort(), IntSort())
4884 >>> i, v = Ints('i v')
4885 >>> s = Store(a, i, v)
4888 >>> prove(s[i] == v)
4891 >>> prove(Implies(i != j, s[j] == a[j]))
4898 """Return a Z3 select array expression.
4900 >>> a = Array('a', IntSort(), IntSort())
4904 >>> eq(Select(a, i), a[i])
4914 """Return a Z3 map array expression.
4916 >>> f = Function('f', IntSort(), IntSort(), IntSort())
4917 >>> a1 = Array('a1', IntSort(), IntSort())
4918 >>> a2 = Array('a2', IntSort(), IntSort())
4919 >>> b = Map(f, a1, a2)
4922 >>> prove(b[0] == f(a1[0], a2[0]))
4927 _z3_assert(len(args) > 0,
"At least one Z3 array expression expected")
4930 _z3_assert(len(args) == f.arity(),
"Number of arguments mismatch")
4937 """Return a Z3 constant array expression.
4939 >>> a = K(IntSort(), 10)
4959 """Return extensionality index for one-dimensional arrays.
4960 >> a, b = Consts('a b', SetSort(IntSort()))
4977 """Return `True` if `a` is a Z3 array select application.
4979 >>> a = Array('a', IntSort(), IntSort())
4990 """Return `True` if `a` is a Z3 array store application.
4992 >>> a = Array('a', IntSort(), IntSort())
4995 >>> is_store(Store(a, 0, 1))
5008 """ Create a set sort over element sort s"""
5013 """Create the empty set
5014 >>> EmptySet(IntSort())
5022 """Create the full set
5023 >>> FullSet(IntSort())
5031 """ Take the union of sets
5032 >>> a = Const('a', SetSort(IntSort()))
5033 >>> b = Const('b', SetSort(IntSort()))
5044 """ Take the union of sets
5045 >>> a = Const('a', SetSort(IntSort()))
5046 >>> b = Const('b', SetSort(IntSort()))
5047 >>> SetIntersect(a, b)
5057 """ Add element e to set s
5058 >>> a = Const('a', SetSort(IntSort()))
5068 """ Remove element e to set s
5069 >>> a = Const('a', SetSort(IntSort()))
5079 """ The complement of set s
5080 >>> a = Const('a', SetSort(IntSort()))
5081 >>> SetComplement(a)
5089 """ The set difference of a and b
5090 >>> a = Const('a', SetSort(IntSort()))
5091 >>> b = Const('b', SetSort(IntSort()))
5092 >>> SetDifference(a, b)
5100 """ Check if e is a member of set s
5101 >>> a = Const('a', SetSort(IntSort()))
5111 """ Check if a is a subset of b
5112 >>> a = Const('a', SetSort(IntSort()))
5113 >>> b = Const('b', SetSort(IntSort()))
5128 """Return `True` if acc is pair of the form (String, Datatype or Sort). """
5129 if not isinstance(acc, tuple):
5133 return isinstance(acc[0], str)
and (isinstance(acc[1], Datatype)
or is_sort(acc[1]))
5137 """Helper class for declaring Z3 datatypes.
5139 >>> List = Datatype('List')
5140 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5141 >>> List.declare('nil')
5142 >>> List = List.create()
5143 >>> # List is now a Z3 declaration
5146 >>> List.cons(10, List.nil)
5148 >>> List.cons(10, List.nil).sort()
5150 >>> cons = List.cons
5154 >>> n = cons(1, cons(0, nil))
5156 cons(1, cons(0, nil))
5157 >>> simplify(cdr(n))
5159 >>> simplify(car(n))
5175 _z3_assert(isinstance(name, str),
"String expected")
5176 _z3_assert(isinstance(rec_name, str),
"String expected")
5179 "Valid list of accessors expected. An accessor is a pair of the form (String, Datatype|Sort)",
5184 """Declare constructor named `name` with the given accessors `args`.
5185 Each accessor is a pair `(name, sort)`, where `name` is a string and `sort` a Z3 sort
5186 or a reference to the datatypes being declared.
5188 In the following example `List.declare('cons', ('car', IntSort()), ('cdr', List))`
5189 declares the constructor named `cons` that builds a new List using an integer and a List.
5190 It also declares the accessors `car` and `cdr`. The accessor `car` extracts the integer
5191 of a `cons` cell, and `cdr` the list of a `cons` cell. After all constructors were declared,
5192 we use the method create() to create the actual datatype in Z3.
5194 >>> List = Datatype('List')
5195 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5196 >>> List.declare('nil')
5197 >>> List = List.create()
5200 _z3_assert(isinstance(name, str),
"String expected")
5201 _z3_assert(name !=
"",
"Constructor name cannot be empty")
5208 """Create a Z3 datatype based on the constructors declared using the method `declare()`.
5210 The function `CreateDatatypes()` must be used to define mutually recursive datatypes.
5212 >>> List = Datatype('List')
5213 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5214 >>> List.declare('nil')
5215 >>> List = List.create()
5218 >>> List.cons(10, List.nil)
5225 """Auxiliary object used to create Z3 datatypes."""
5232 if self.
ctx.ref()
is not None and Z3_del_constructor
is not None:
5237 """Auxiliary object used to create Z3 datatypes."""
5244 if self.
ctx.ref()
is not None and Z3_del_constructor_list
is not None:
5249 """Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects.
5251 In the following example we define a Tree-List using two mutually recursive datatypes.
5253 >>> TreeList = Datatype('TreeList')
5254 >>> Tree = Datatype('Tree')
5255 >>> # Tree has two constructors: leaf and node
5256 >>> Tree.declare('leaf', ('val', IntSort()))
5257 >>> # a node contains a list of trees
5258 >>> Tree.declare('node', ('children', TreeList))
5259 >>> TreeList.declare('nil')
5260 >>> TreeList.declare('cons', ('car', Tree), ('cdr', TreeList))
5261 >>> Tree, TreeList = CreateDatatypes(Tree, TreeList)
5262 >>> Tree.val(Tree.leaf(10))
5264 >>> simplify(Tree.val(Tree.leaf(10)))
5266 >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
5268 node(cons(leaf(10), cons(leaf(20), nil)))
5269 >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
5270 >>> simplify(n2 == n1)
5272 >>> simplify(TreeList.car(Tree.children(n2)) == n1)
5277 _z3_assert(len(ds) > 0,
"At least one Datatype must be specified")
5278 _z3_assert(all([isinstance(d, Datatype)
for d
in ds]),
"Arguments must be Datatypes")
5279 _z3_assert(all([d.ctx == ds[0].ctx
for d
in ds]),
"Context mismatch")
5280 _z3_assert(all([d.constructors != []
for d
in ds]),
"Non-empty Datatypes expected")
5283 names = (Symbol * num)()
5284 out = (Sort * num)()
5285 clists = (ConstructorList * num)()
5287 for i
in range(num):
5290 num_cs = len(d.constructors)
5291 cs = (Constructor * num_cs)()
5292 for j
in range(num_cs):
5293 c = d.constructors[j]
5298 fnames = (Symbol * num_fs)()
5299 sorts = (Sort * num_fs)()
5300 refs = (ctypes.c_uint * num_fs)()
5301 for k
in range(num_fs):
5305 if isinstance(ftype, Datatype):
5308 ds.count(ftype) == 1,
5309 "One and only one occurrence of each datatype is expected",
5312 refs[k] = ds.index(ftype)
5316 sorts[k] = ftype.ast
5325 for i
in range(num):
5327 num_cs = dref.num_constructors()
5328 for j
in range(num_cs):
5329 cref = dref.constructor(j)
5330 cref_name = cref.name()
5331 cref_arity = cref.arity()
5332 if cref.arity() == 0:
5334 setattr(dref, cref_name, cref)
5335 rref = dref.recognizer(j)
5336 setattr(dref,
"is_" + cref_name, rref)
5337 for k
in range(cref_arity):
5338 aref = dref.accessor(j, k)
5339 setattr(dref, aref.name(), aref)
5341 return tuple(result)
5345 """Datatype sorts."""
5348 """Return the number of constructors in the given Z3 datatype.
5350 >>> List = Datatype('List')
5351 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5352 >>> List.declare('nil')
5353 >>> List = List.create()
5354 >>> # List is now a Z3 declaration
5355 >>> List.num_constructors()
5361 """Return a constructor of the datatype `self`.
5363 >>> List = Datatype('List')
5364 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5365 >>> List.declare('nil')
5366 >>> List = List.create()
5367 >>> # List is now a Z3 declaration
5368 >>> List.num_constructors()
5370 >>> List.constructor(0)
5372 >>> List.constructor(1)
5380 """In Z3, each constructor has an associated recognizer predicate.
5382 If the constructor is named `name`, then the recognizer `is_name`.
5384 >>> List = Datatype('List')
5385 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5386 >>> List.declare('nil')
5387 >>> List = List.create()
5388 >>> # List is now a Z3 declaration
5389 >>> List.num_constructors()
5391 >>> List.recognizer(0)
5393 >>> List.recognizer(1)
5395 >>> simplify(List.is_nil(List.cons(10, List.nil)))
5397 >>> simplify(List.is_cons(List.cons(10, List.nil)))
5399 >>> l = Const('l', List)
5400 >>> simplify(List.is_cons(l))
5408 """In Z3, each constructor has 0 or more accessor.
5409 The number of accessors is equal to the arity of the constructor.
5411 >>> List = Datatype('List')
5412 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5413 >>> List.declare('nil')
5414 >>> List = List.create()
5415 >>> List.num_constructors()
5417 >>> List.constructor(0)
5419 >>> num_accs = List.constructor(0).arity()
5422 >>> List.accessor(0, 0)
5424 >>> List.accessor(0, 1)
5426 >>> List.constructor(1)
5428 >>> num_accs = List.constructor(1).arity()
5442 """Datatype expressions."""
5445 """Return the datatype sort of the datatype expression `self`."""
5449 """Create a reference to a sort that was declared, or will be declared, as a recursive datatype"""
5454 """Create a named tuple sort base on a set of underlying sorts
5456 >>> pair, mk_pair, (first, second) = TupleSort("pair", [IntSort(), StringSort()])
5459 projects = [(
"project%d" % i, sorts[i])
for i
in range(len(sorts))]
5460 tuple.declare(name, *projects)
5461 tuple = tuple.create()
5462 return tuple, tuple.constructor(0), [tuple.accessor(0, i)
for i
in range(len(sorts))]
5466 """Create a named tagged union sort base on a set of underlying sorts
5468 >>> sum, ((inject0, extract0), (inject1, extract1)) = DisjointSum("+", [IntSort(), StringSort()])
5471 for i
in range(len(sorts)):
5472 sum.declare(
"inject%d" % i, (
"project%d" % i, sorts[i]))
5474 return sum, [(sum.constructor(i), sum.accessor(i, 0))
for i
in range(len(sorts))]
5478 """Return a new enumeration sort named `name` containing the given values.
5480 The result is a pair (sort, list of constants).
5482 >>> Color, (red, green, blue) = EnumSort('Color', ['red', 'green', 'blue'])
5485 _z3_assert(isinstance(name, str),
"Name must be a string")
5486 _z3_assert(all([isinstance(v, str)
for v
in values]),
"Enumeration sort values must be strings")
5487 _z3_assert(len(values) > 0,
"At least one value expected")
5490 _val_names = (Symbol * num)()
5491 for i
in range(num):
5492 _val_names[i] =
to_symbol(values[i], ctx)
5493 _values = (FuncDecl * num)()
5494 _testers = (FuncDecl * num)()
5498 for i
in range(num):
5500 V = [a()
for a
in V]
5511 """Set of parameters used to configure Solvers, Tactics and Simplifiers in Z3.
5513 Consider using the function `args2params` to create instances of this object.
5528 if self.
ctx.ref()
is not None and Z3_params_dec_ref
is not None:
5532 """Set parameter name with value val."""
5534 _z3_assert(isinstance(name, str),
"parameter name must be a string")
5536 if isinstance(val, bool):
5540 elif isinstance(val, float):
5542 elif isinstance(val, str):
5552 _z3_assert(isinstance(ds, ParamDescrsRef),
"parameter description set expected")
5557 """Convert python arguments into a Z3_params object.
5558 A ':' is added to the keywords, and '_' is replaced with '-'
5560 >>> args2params(['model', True, 'relevancy', 2], {'elim_and' : True})
5561 (params model true relevancy 2 elim_and true)
5564 _z3_assert(len(arguments) % 2 == 0,
"Argument list must have an even number of elements.")
5580 """Set of parameter descriptions for Solvers, Tactics and Simplifiers in Z3.
5584 _z3_assert(isinstance(descr, ParamDescrs),
"parameter description object expected")
5590 return ParamsDescrsRef(self.
descr, self.
ctx)
5593 if self.
ctx.ref()
is not None and Z3_param_descrs_dec_ref
is not None:
5597 """Return the size of in the parameter description `self`.
5602 """Return the size of in the parameter description `self`.
5607 """Return the i-th parameter name in the parameter description `self`.
5612 """Return the kind of the parameter named `n`.
5617 """Return the documentation string of the parameter named `n`.
5638 """Goal is a collection of constraints we want to find a solution or show to be unsatisfiable (infeasible).
5640 Goals are processed using Tactics. A Tactic transforms a goal into a set of subgoals.
5641 A goal has a solution if one of its subgoals has a solution.
5642 A goal is unsatisfiable if all subgoals are unsatisfiable.
5645 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5648 "If goal is different from None, then ctx must be also different from None")
5651 if self.
goal is None:
5656 if self.
goal is not None and self.
ctx.ref()
is not None and Z3_goal_dec_ref
is not None:
5660 """Return the depth of the goal `self`.
5661 The depth corresponds to the number of tactics applied to `self`.
5663 >>> x, y = Ints('x y')
5665 >>> g.add(x == 0, y >= x + 1)
5668 >>> r = Then('simplify', 'solve-eqs')(g)
5669 >>> # r has 1 subgoal
5678 """Return `True` if `self` contains the `False` constraints.
5680 >>> x, y = Ints('x y')
5682 >>> g.inconsistent()
5684 >>> g.add(x == 0, x == 1)
5687 >>> g.inconsistent()
5689 >>> g2 = Tactic('propagate-values')(g)[0]
5690 >>> g2.inconsistent()
5696 """Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.
5699 >>> g.prec() == Z3_GOAL_PRECISE
5701 >>> x, y = Ints('x y')
5702 >>> g.add(x == y + 1)
5703 >>> g.prec() == Z3_GOAL_PRECISE
5705 >>> t = With(Tactic('add-bounds'), add_bound_lower=0, add_bound_upper=10)
5708 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5709 >>> g2.prec() == Z3_GOAL_PRECISE
5711 >>> g2.prec() == Z3_GOAL_UNDER
5717 """Alias for `prec()`.
5720 >>> g.precision() == Z3_GOAL_PRECISE
5726 """Return the number of constraints in the goal `self`.
5731 >>> x, y = Ints('x y')
5732 >>> g.add(x == 0, y > x)
5739 """Return the number of constraints in the goal `self`.
5744 >>> x, y = Ints('x y')
5745 >>> g.add(x == 0, y > x)
5752 """Return a constraint in the goal `self`.
5755 >>> x, y = Ints('x y')
5756 >>> g.add(x == 0, y > x)
5765 """Return a constraint in the goal `self`.
5768 >>> x, y = Ints('x y')
5769 >>> g.add(x == 0, y > x)
5775 if arg >= len(self):
5777 return self.
get(arg)
5780 """Assert constraints into the goal.
5784 >>> g.assert_exprs(x > 0, x < 2)
5799 >>> g.append(x > 0, x < 2)
5810 >>> g.insert(x > 0, x < 2)
5821 >>> g.add(x > 0, x < 2)
5828 """Retrieve model from a satisfiable goal
5829 >>> a, b = Ints('a b')
5831 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
5832 >>> t = Then(Tactic('split-clause'), Tactic('solve-eqs'))
5835 [Or(b == 0, b == 1), Not(0 <= b)]
5837 [Or(b == 0, b == 1), Not(1 <= b)]
5838 >>> # Remark: the subgoal r[0] is unsatisfiable
5839 >>> # Creating a solver for solving the second subgoal
5846 >>> # Model s.model() does not assign a value to `a`
5847 >>> # It is a model for subgoal `r[1]`, but not for goal `g`
5848 >>> # The method convert_model creates a model for `g` from a model for `r[1]`.
5849 >>> r[1].convert_model(s.model())
5853 _z3_assert(isinstance(model, ModelRef),
"Z3 Model expected")
5857 return obj_to_string(self)
5860 """Return a textual representation of the s-expression representing the goal."""
5864 """Return a textual representation of the goal in DIMACS format."""
5868 """Copy goal `self` to context `target`.
5876 >>> g2 = g.translate(c2)
5879 >>> g.ctx == main_ctx()
5883 >>> g2.ctx == main_ctx()
5887 _z3_assert(isinstance(target, Context),
"target must be a context")
5897 """Return a new simplified goal.
5899 This method is essentially invoking the simplify tactic.
5903 >>> g.add(x + 1 >= 2)
5906 >>> g2 = g.simplify()
5909 >>> # g was not modified
5914 return t.apply(self, *arguments, **keywords)[0]
5917 """Return goal `self` as a single Z3 expression.
5936 return And([self.
get(i)
for i
in range(len(self))], self.
ctx)
5946 """A collection (vector) of ASTs."""
5955 assert ctx
is not None
5960 if self.
vector is not None and self.
ctx.ref()
is not None and Z3_ast_vector_dec_ref
is not None:
5964 """Return the size of the vector `self`.
5969 >>> A.push(Int('x'))
5970 >>> A.push(Int('x'))
5977 """Return the AST at position `i`.
5980 >>> A.push(Int('x') + 1)
5981 >>> A.push(Int('y'))
5988 if isinstance(i, int):
5996 elif isinstance(i, slice):
5998 for ii
in range(*i.indices(self.
__len__())):
6006 """Update AST at position `i`.
6009 >>> A.push(Int('x') + 1)
6010 >>> A.push(Int('y'))
6022 """Add `v` in the end of the vector.
6027 >>> A.push(Int('x'))
6034 """Resize the vector to `sz` elements.
6040 >>> for i in range(10): A[i] = Int('x')
6047 """Return `True` if the vector contains `item`.
6070 """Copy vector `self` to context `other_ctx`.
6076 >>> B = A.translate(c2)
6092 return obj_to_string(self)
6095 """Return a textual representation of the s-expression representing the vector."""
6106 """A mapping from ASTs to ASTs."""
6115 assert ctx
is not None
6123 if self.
map is not None and self.
ctx.ref()
is not None and Z3_ast_map_dec_ref
is not None:
6127 """Return the size of the map.
6133 >>> M[x] = IntVal(1)
6140 """Return `True` if the map contains key `key`.
6153 """Retrieve the value associated with key `key`.
6164 """Add/Update key `k` with value `v`.
6173 >>> M[x] = IntVal(1)
6183 """Remove the entry associated with key `k`.
6197 """Remove all entries from the map.
6202 >>> M[x+x] = IntVal(1)
6212 """Return an AstVector containing all keys in the map.
6217 >>> M[x+x] = IntVal(1)
6231 """Store the value of the interpretation of a function in a particular point."""
6242 if self.
ctx.ref()
is not None and Z3_func_entry_dec_ref
is not None:
6246 """Return the number of arguments in the given entry.
6248 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6250 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6255 >>> f_i.num_entries()
6257 >>> e = f_i.entry(0)
6264 """Return the value of argument `idx`.
6266 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6268 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6273 >>> f_i.num_entries()
6275 >>> e = f_i.entry(0)
6286 ... except IndexError:
6287 ... print("index error")
6295 """Return the value of the function at point `self`.
6297 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6299 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6304 >>> f_i.num_entries()
6306 >>> e = f_i.entry(0)
6317 """Return entry `self` as a Python list.
6318 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6320 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6325 >>> f_i.num_entries()
6327 >>> e = f_i.entry(0)
6332 args.append(self.
value())
6340 """Stores the interpretation of a function in a Z3 model."""
6345 if self.
f is not None:
6349 if self.
f is not None and self.
ctx.ref()
is not None and Z3_func_interp_dec_ref
is not None:
6354 Return the `else` value for a function interpretation.
6355 Return None if Z3 did not specify the `else` value for
6358 >>> f = Function('f', IntSort(), IntSort())
6360 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6366 >>> m[f].else_value()
6376 """Return the number of entries/points in the function interpretation `self`.
6378 >>> f = Function('f', IntSort(), IntSort())
6380 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6386 >>> m[f].num_entries()
6392 """Return the number of arguments for each entry in the function interpretation `self`.
6394 >>> f = Function('f', IntSort(), IntSort())
6396 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6406 """Return an entry at position `idx < self.num_entries()` in the function interpretation `self`.
6408 >>> f = Function('f', IntSort(), IntSort())
6410 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6416 >>> m[f].num_entries()
6426 """Copy model 'self' to context 'other_ctx'.
6437 """Return the function interpretation as a Python list.
6438 >>> f = Function('f', IntSort(), IntSort())
6440 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6454 return obj_to_string(self)
6458 """Model/Solution of a satisfiability problem (aka system of constraints)."""
6461 assert ctx
is not None
6467 if self.
ctx.ref()
is not None and Z3_model_dec_ref
is not None:
6471 return obj_to_string(self)
6474 """Return a textual representation of the s-expression representing the model."""
6477 def eval(self, t, model_completion=False):
6478 """Evaluate the expression `t` in the model `self`.
6479 If `model_completion` is enabled, then a default interpretation is automatically added
6480 for symbols that do not have an interpretation in the model `self`.
6484 >>> s.add(x > 0, x < 2)
6497 >>> m.eval(y, model_completion=True)
6499 >>> # Now, m contains an interpretation for y
6506 raise Z3Exception(
"failed to evaluate expression in the model")
6509 """Alias for `eval`.
6513 >>> s.add(x > 0, x < 2)
6517 >>> m.evaluate(x + 1)
6519 >>> m.evaluate(x == 1)
6522 >>> m.evaluate(y + x)
6526 >>> m.evaluate(y, model_completion=True)
6528 >>> # Now, m contains an interpretation for y
6529 >>> m.evaluate(y + x)
6532 return self.
eval(t, model_completion)
6535 """Return the number of constant and function declarations in the model `self`.
6537 >>> f = Function('f', IntSort(), IntSort())
6540 >>> s.add(x > 0, f(x) != x)
6549 return num_consts + num_funcs
6552 """Return the interpretation for a given declaration or constant.
6554 >>> f = Function('f', IntSort(), IntSort())
6557 >>> s.add(x > 0, x < 2, f(x) == 0)
6567 _z3_assert(isinstance(decl, FuncDeclRef)
or is_const(decl),
"Z3 declaration expected")
6571 if decl.arity() == 0:
6573 if _r.value
is None:
6589 sz = fi.num_entries()
6593 e =
Store(e, fe.arg_value(0), fe.value())
6604 """Return the number of uninterpreted sorts that contain an interpretation in the model `self`.
6606 >>> A = DeclareSort('A')
6607 >>> a, b = Consts('a b', A)
6619 """Return the uninterpreted sort at position `idx` < self.num_sorts().
6621 >>> A = DeclareSort('A')
6622 >>> B = DeclareSort('B')
6623 >>> a1, a2 = Consts('a1 a2', A)
6624 >>> b1, b2 = Consts('b1 b2', B)
6626 >>> s.add(a1 != a2, b1 != b2)
6642 """Return all uninterpreted sorts that have an interpretation in the model `self`.
6644 >>> A = DeclareSort('A')
6645 >>> B = DeclareSort('B')
6646 >>> a1, a2 = Consts('a1 a2', A)
6647 >>> b1, b2 = Consts('b1 b2', B)
6649 >>> s.add(a1 != a2, b1 != b2)
6659 """Return the interpretation for the uninterpreted sort `s` in the model `self`.
6661 >>> A = DeclareSort('A')
6662 >>> a, b = Consts('a b', A)
6668 >>> m.get_universe(A)
6672 _z3_assert(isinstance(s, SortRef),
"Z3 sort expected")
6679 """If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned.
6680 If `idx` is a declaration, then the actual interpretation is returned.
6682 The elements can be retrieved using position or the actual declaration.
6684 >>> f = Function('f', IntSort(), IntSort())
6687 >>> s.add(x > 0, x < 2, f(x) == 0)
6701 >>> for d in m: print("%s -> %s" % (d, m[d]))
6706 if idx >= len(self):
6709 if (idx < num_consts):
6713 if isinstance(idx, FuncDeclRef):
6717 if isinstance(idx, SortRef):
6720 _z3_assert(
False,
"Integer, Z3 declaration, or Z3 constant expected")
6724 """Return a list with all symbols that have an interpretation in the model `self`.
6725 >>> f = Function('f', IntSort(), IntSort())
6728 >>> s.add(x > 0, x < 2, f(x) == 0)
6743 """Update the interpretation of a constant"""
6746 if is_func_decl(x)
and x.arity() != 0
and isinstance(value, FuncInterp):
6750 for i
in range(value.num_entries()):
6755 v.push(e.arg_value(j))
6760 raise Z3Exception(
"Expecting 0-ary function or constant expression")
6765 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
6768 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
6773 """Perform model-based projection on fml with respect to vars.
6774 Assume that the model satisfies fml. Then compute a projection fml_p, such
6775 that vars do not occur free in fml_p, fml_p is true in the model and
6776 fml_p => exists vars . fml
6778 ctx = self.
ctx.ref()
6779 _vars = (Ast * len(vars))()
6780 for i
in range(len(vars)):
6781 _vars[i] = vars[i].as_ast()
6785 """Perform model-based projection, but also include realizer terms for the projected variables"""
6786 ctx = self.
ctx.ref()
6787 _vars = (Ast * len(vars))()
6788 for i
in range(len(vars)):
6789 _vars[i] = vars[i].as_ast()
6791 result = Z3_qe_model_project_with_witness(ctx, self.
model, len(vars), _vars, fml.ast, defs.map)
6806 for k, v
in eval.items():
6807 mdl.update_value(k, v)
6812 """Return true if n is a Z3 expression of the form (_ as-array f)."""
6813 return isinstance(n, ExprRef)
and Z3_is_as_array(n.ctx.ref(), n.as_ast())
6817 """Return the function declaration f associated with a Z3 expression of the form (_ as-array f)."""
6830 """Statistics for `Solver.check()`."""
6841 if self.
ctx.ref()
is not None and Z3_stats_dec_ref
is not None:
6848 out.write(u(
'<table border="1" cellpadding="2" cellspacing="0">'))
6851 out.write(u(
'<tr style="background-color:#CFCFCF">'))
6854 out.write(u(
"<tr>"))
6856 out.write(u(
"<td>%s</td><td>%s</td></tr>" % (k, v)))
6857 out.write(u(
"</table>"))
6858 return out.getvalue()
6863 """Return the number of statistical counters.
6866 >>> s = Then('simplify', 'nlsat').solver()
6870 >>> st = s.statistics()
6877 """Return the value of statistical counter at position `idx`. The result is a pair (key, value).
6880 >>> s = Then('simplify', 'nlsat').solver()
6884 >>> st = s.statistics()
6888 ('nlsat propagations', 2)
6890 ('nlsat restarts', 1)
6892 if idx >= len(self):
6901 """Return the list of statistical counters.
6904 >>> s = Then('simplify', 'nlsat').solver()
6908 >>> st = s.statistics()
6913 """Return the value of a particular statistical counter.
6916 >>> s = Then('simplify', 'nlsat').solver()
6920 >>> st = s.statistics()
6921 >>> st.get_key_value('nlsat propagations')
6924 for idx
in range(len(self)):
6930 raise Z3Exception(
"unknown key")
6933 """Access the value of statistical using attributes.
6935 Remark: to access a counter containing blank spaces (e.g., 'nlsat propagations'),
6936 we should use '_' (e.g., 'nlsat_propagations').
6939 >>> s = Then('simplify', 'nlsat').solver()
6943 >>> st = s.statistics()
6944 >>> st.nlsat_propagations
6949 key = name.replace(
"_",
" ")
6953 raise AttributeError
6963 """Represents the result of a satisfiability check: sat, unsat, unknown.
6969 >>> isinstance(r, CheckSatResult)
6980 return isinstance(other, CheckSatResult)
and self.
r == other.r
6983 return not self.
__eq__(other)
6987 if self.
r == Z3_L_TRUE:
6989 elif self.
r == Z3_L_FALSE:
6990 return "<b>unsat</b>"
6992 return "<b>unknown</b>"
6994 if self.
r == Z3_L_TRUE:
6996 elif self.
r == Z3_L_FALSE:
7002 in_html = in_html_mode()
7005 set_html_mode(in_html)
7016 Solver API provides methods for implementing the main SMT 2.0 commands:
7017 push, pop, check, get-model, etc.
7020 def __init__(self, solver=None, ctx=None, logFile=None):
7021 assert solver
is None or ctx
is not None
7030 if logFile
is not None:
7031 self.
set(
"smtlib2_log", logFile)
7034 if self.
solver is not None and self.
ctx.ref()
is not None and Z3_solver_dec_ref
is not None:
7045 """Set a configuration option.
7046 The method `help()` return a string containing all available options.
7049 >>> # The option MBQI can be set using three different approaches.
7050 >>> s.set(mbqi=True)
7051 >>> s.set('MBQI', True)
7052 >>> s.set(':mbqi', True)
7058 """Create a backtracking point.
7080 """Backtrack \\c num backtracking points.
7102 """Return the current number of backtracking points.
7120 """Remove all asserted constraints and backtracking points created using `push()`.
7134 """Assert constraints into the solver.
7138 >>> s.assert_exprs(x > 0, x < 2)
7145 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7153 """Assert constraints into the solver.
7157 >>> s.add(x > 0, x < 2)
7168 """Assert constraints into the solver.
7172 >>> s.append(x > 0, x < 2)
7179 """Assert constraints into the solver.
7183 >>> s.insert(x > 0, x < 2)
7190 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7192 If `p` is a string, it will be automatically converted into a Boolean constant.
7197 >>> s.set(unsat_core=True)
7198 >>> s.assert_and_track(x > 0, 'p1')
7199 >>> s.assert_and_track(x != 1, 'p2')
7200 >>> s.assert_and_track(x < 0, p3)
7201 >>> print(s.check())
7203 >>> c = s.unsat_core()
7213 if isinstance(p, str):
7215 _z3_assert(isinstance(a, BoolRef),
"Boolean expression expected")
7220 """Check whether the assertions in the given solver plus the optional assumptions are consistent or not.
7226 >>> s.add(x > 0, x < 2)
7229 >>> s.model().eval(x)
7235 >>> s.add(2**x == 4)
7241 num = len(assumptions)
7242 _assumptions = (Ast * num)()
7243 for i
in range(num):
7244 _assumptions[i] = s.cast(assumptions[i]).as_ast()
7249 """Return a model for the last `check()`.
7251 This function raises an exception if
7252 a model is not available (e.g., last `check()` returned unsat).
7256 >>> s.add(a + 2 == 0)
7265 raise Z3Exception(
"model is not available")
7268 """Import model converter from other into the current solver"""
7269 Z3_solver_import_model_converter(self.ctx.ref(), other.solver, self.solver)
7271 def interrupt(self):
7272 """Interrupt the execution of the solver object.
7273 Remarks: This ensures that the interrupt applies only
7274 to the given solver object and it applies only if it is running.
7276 Z3_solver_interrupt(self.ctx.ref(), self.solver)
7278 def unsat_core(self):
7279 """Return a subset (as an AST vector) of the assumptions provided to the last check().
7281 These are the assumptions Z3 used in the unsatisfiability proof.
7282 Assumptions are available in Z3. They are used to extract unsatisfiable cores.
7283 They may be also used to "retract" assumptions. Note that, assumptions are not really
7284 "soft constraints", but they can be used to implement them.
7286 >>> p1, p2, p3 = Bools('p1 p2 p3')
7287 >>> x, y = Ints('x y')
7289 >>> s.add(Implies(p1, x > 0))
7290 >>> s.add(Implies(p2, y > x))
7291 >>> s.add(Implies(p2, y < 1))
7292 >>> s.add(Implies(p3, y > -3))
7293 >>> s.check(p1, p2, p3)
7295 >>> core = s.unsat_core()
7304 >>> # "Retracting" p2
7308 return AstVector(Z3_solver_get_unsat_core(self.ctx.ref(), self.solver), self.ctx)
7310 def consequences(self, assumptions, variables):
7311 """Determine fixed values for the variables based on the solver state and assumptions.
7313 >>> a, b, c, d = Bools('a b c d')
7314 >>> s.add(Implies(a,b), Implies(b, c))
7315 >>> s.consequences([a],[b,c,d])
7316 (sat, [Implies(a, b), Implies(a, c)])
7317 >>> s.consequences([Not(c),d],[a,b,c,d])
7318 (sat, [Implies(d, d), Implies(Not(c), Not(c)), Implies(Not(c), Not(b)), Implies(Not(c), Not(a))])
7320 if isinstance(assumptions, list):
7321 _asms = AstVector(None, self.ctx)
7322 for a in assumptions:
7325 if isinstance(variables, list):
7326 _vars = AstVector(None, self.ctx)
7330 _z3_assert(isinstance(assumptions, AstVector), "ast vector expected")
7331 _z3_assert(isinstance(variables, AstVector), "ast vector expected")
7332 consequences = AstVector(None, self.ctx)
7333 r = Z3_solver_get_consequences(self.ctx.ref(), self.solver, assumptions.vector,
7334 variables.vector, consequences.vector)
7335 sz = len(consequences)
7336 consequences = [consequences[i] for i in range(sz)]
7337 return CheckSatResult(r), consequences
7339 def from_file(self, filename):
7340 """Parse assertions from a file"""
7341 Z3_solver_from_file(self.ctx.ref(), self.solver, filename)
7343 def from_string(self, s):
7344 """Parse assertions from a string"""
7345 Z3_solver_from_string(self.ctx.ref(), self.solver, s)
7347 def cube(self, vars=None):
7349 The method takes an optional set of variables that restrict which
7350 variables may be used as a starting point for cubing.
7351 If vars is not None, then the first case split is based on a variable in
7354 self.cube_vs = AstVector(None, self.ctx)
7355 if vars is not None:
7357 self.cube_vs.push(v)
7359 lvl = self.backtrack_level
7360 self.backtrack_level = 4000000000
7361 r = AstVector(Z3_solver_cube(self.ctx.ref(), self.solver, self.cube_vs.vector, lvl), self.ctx)
7362 if (len(r) == 1 and is_false(r[0])):
7368 def cube_vars(self):
7369 """Access the set of variables that were touched by the most recently generated cube.
7370 This set of variables can be used as a starting point for additional cubes.
7371 The idea is that variables that appear in clauses that are reduced by the most recent
7372 cube are likely more useful to cube on."""
7376 """Retrieve congruence closure root of the term t relative to the current search state
7377 The function primarily works for SimpleSolver. Terms and variables that are
7378 eliminated during pre-processing are not visible to the congruence closure.
7380 t = _py2expr(t, self.ctx)
7381 return _to_expr_ref(Z3_solver_congruence_root(self.ctx.ref(), self.solver, t.ast), self.ctx)
7384 """Retrieve congruence closure sibling of the term t relative to the current search state
7385 The function primarily works for SimpleSolver. Terms and variables that are
7386 eliminated during pre-processing are not visible to the congruence closure.
7388 t = _py2expr(t, self.ctx)
7389 return _to_expr_ref(Z3_solver_congruence_next(self.ctx.ref(), self.solver, t.ast), self.ctx)
7391 def explain_congruent(self, a, b):
7392 """Explain congruence of a and b relative to the current search state"""
7393 a = _py2expr(a, self.ctx)
7394 b = _py2expr(b, self.ctx)
7395 return _to_expr_ref(Z3_solver_congruence_explain(self.ctx.ref(), self.solver, a.ast, b.ast), self.ctx)
7398 def solve_for(self, ts):
7399 """Retrieve a solution for t relative to linear equations maintained in the current state."""
7400 vars = AstVector(ctx=self.ctx);
7401 terms = AstVector(ctx=self.ctx);
7402 guards = AstVector(ctx=self.ctx);
7404 t = _py2expr(t, self.ctx)
7406 Z3_solver_solve_for(self.ctx.ref(), self.solver, vars.vector, terms.vector, guards.vector)
7407 return [(vars[i], terms[i], guards[i]) for i in range(len(vars))]
7411 """Return a proof for the last `check()`. Proof construction must be enabled."""
7412 return _to_expr_ref(Z3_solver_get_proof(self.ctx.ref(), self.solver), self.ctx)
7414 def assertions(self):
7415 """Return an AST vector containing all added constraints.
7426 return AstVector(Z3_solver_get_assertions(self.ctx.ref(), self.solver), self.ctx)
7429 """Return an AST vector containing all currently inferred units.
7431 return AstVector(Z3_solver_get_units(self.ctx.ref(), self.solver), self.ctx)
7433 def non_units(self):
7434 """Return an AST vector containing all atomic formulas in solver state that are not units.
7436 return AstVector(Z3_solver_get_non_units(self.ctx.ref(), self.solver), self.ctx)
7438 def trail_levels(self):
7439 """Return trail and decision levels of the solver state after a check() call.
7441 trail = self.trail()
7442 levels = (ctypes.c_uint * len(trail))()
7443 Z3_solver_get_levels(self.ctx.ref(), self.solver, trail.vector, len(trail), levels)
7444 return trail, levels
7446 def set_initial_value(self, var, value):
7447 """initialize the solver's state by setting the initial value of var to value
7450 value = s.cast(value)
7451 Z3_solver_set_initial_value(self.ctx.ref(), self.solver, var.ast, value.ast)
7454 """Return trail of the solver state after a check() call.
7456 return AstVector(Z3_solver_get_trail(self.ctx.ref(), self.solver), self.ctx)
7458 def statistics(self):
7459 """Return statistics for the last `check()`.
7461 >>> s = SimpleSolver()
7466 >>> st = s.statistics()
7467 >>> st.get_key_value('final checks')
7474 return Statistics(Z3_solver_get_statistics(self.ctx.ref(), self.solver), self.ctx)
7476 def reason_unknown(self):
7477 """Return a string describing why the last `check()` returned `unknown`.
7480 >>> s = SimpleSolver()
7481 >>> s.add(2**x == 4)
7484 >>> s.reason_unknown()
7485 '(incomplete (theory arithmetic))'
7487 return Z3_solver_get_reason_unknown(self.ctx.ref(), self.solver)
7490 """Display a string describing all available options."""
7491 print(Z3_solver_get_help(self.ctx.ref(), self.solver))
7493 def param_descrs(self):
7494 """Return the parameter description set."""
7495 return ParamDescrsRef(Z3_solver_get_param_descrs(self.ctx.ref(), self.solver), self.ctx)
7498 """Return a formatted string with all added constraints."""
7499 return obj_to_string(self)
7501 def translate(self, target):
7502 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
7506 >>> s1 = Solver(ctx=c1)
7507 >>> s2 = s1.translate(c2)
7510 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
7511 solver = Z3_solver_translate(self.ctx.ref(), self.solver, target.ref())
7512 return Solver(solver, target)
7515 return self.translate(self.ctx)
7517 def __deepcopy__(self, memo={}):
7518 return self.translate(self.ctx)
7521 """Return a formatted string (in Lisp-like format) with all added constraints.
7522 We say the string is in s-expression format.
7530 return Z3_solver_to_string(self.ctx.ref(), self.solver)
7532 def dimacs(self, include_names=True):
7533 """Return a textual representation of the solver in DIMACS format."""
7534 return Z3_solver_to_dimacs_string(self.ctx.ref(), self.solver, include_names)
7537 """return SMTLIB2 formatted benchmark for solver's assertions"""
7538 es = self.assertions()
7544 for i in range(sz1):
7545 v[i] = es[i].as_ast()
7547 e = es[sz1].as_ast()
7549 e = BoolVal(True, self.ctx).as_ast()
7550 return Z3_benchmark_to_smtlib_string(
7551 self.ctx.ref(), "benchmark generated from python API", "", "unknown", "", sz1, v, e,
7555def SolverFor(logic, ctx=None, logFile=None):
7556 """Create a solver customized for the given logic.
7558 The parameter `logic` is a string. It should be contains
7559 the name of a SMT-LIB logic.
7560 See http://www.smtlib.org/ for the name of all available logics.
7562 >>> s = SolverFor("QF_LIA")
7572 logic = to_symbol(logic)
7573 return Solver(Z3_mk_solver_for_logic(ctx.ref(), logic), ctx, logFile)
7576def SimpleSolver(ctx=None, logFile=None):
7577 """Return a simple general purpose solver with limited amount of preprocessing.
7579 >>> s = SimpleSolver()
7586 return Solver(Z3_mk_simple_solver(ctx.ref()), ctx, logFile)
7588#########################################
7592#########################################
7595class Fixedpoint(Z3PPObject):
7596 """Fixedpoint API provides methods for solving with recursive predicates"""
7598 def __init__(self, fixedpoint=None, ctx=None):
7599 assert fixedpoint is None or ctx is not None
7600 self.ctx = _get_ctx(ctx)
7601 self.fixedpoint = None
7602 if fixedpoint is None:
7603 self.fixedpoint = Z3_mk_fixedpoint(self.ctx.ref())
7605 self.fixedpoint = fixedpoint
7606 Z3_fixedpoint_inc_ref(self.ctx.ref(), self.fixedpoint)
7609 def __deepcopy__(self, memo={}):
7610 return FixedPoint(self.fixedpoint, self.ctx)
7613 if self.fixedpoint is not None and self.ctx.ref() is not None and Z3_fixedpoint_dec_ref is not None:
7614 Z3_fixedpoint_dec_ref(self.ctx.ref(), self.fixedpoint)
7616 def set(self, *args, **keys):
7617 """Set a configuration option. The method `help()` return a string containing all available options.
7619 p = args2params(args, keys, self.ctx)
7620 Z3_fixedpoint_set_params(self.ctx.ref(), self.fixedpoint, p.params)
7623 """Display a string describing all available options."""
7624 print(Z3_fixedpoint_get_help(self.ctx.ref(), self.fixedpoint))
7626 def param_descrs(self):
7627 """Return the parameter description set."""
7628 return ParamDescrsRef(Z3_fixedpoint_get_param_descrs(self.ctx.ref(), self.fixedpoint), self.ctx)
7630 def assert_exprs(self, *args):
7631 """Assert constraints as background axioms for the fixedpoint solver."""
7632 args = _get_args(args)
7633 s = BoolSort(self.ctx)
7635 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7637 f = self.abstract(f)
7638 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, f.as_ast())
7641 arg = self.abstract(arg)
7642 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, arg.as_ast())
7644 def add(self, *args):
7645 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7646 self.assert_exprs(*args)
7648 def __iadd__(self, fml):
7652 def append(self, *args):
7653 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7654 self.assert_exprs(*args)
7656 def insert(self, *args):
7657 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7658 self.assert_exprs(*args)
7660 def add_rule(self, head, body=None, name=None):
7661 """Assert rules defining recursive predicates to the fixedpoint solver.
7664 >>> s = Fixedpoint()
7665 >>> s.register_relation(a.decl())
7666 >>> s.register_relation(b.decl())
7674 name = to_symbol(name, self.ctx)
7676 head = self.abstract(head)
7677 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, head.as_ast(), name)
7679 body = _get_args(body)
7680 f = self.abstract(Implies(And(body, self.ctx), head))
7681 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7683 def rule(self, head, body=None, name=None):
7684 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7685 self.add_rule(head, body, name)
7687 def fact(self, head, name=None):
7688 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7689 self.add_rule(head, None, name)
7691 def query(self, *query):
7692 """Query the fixedpoint engine whether formula is derivable.
7693 You can also pass an tuple or list of recursive predicates.
7695 query = _get_args(query)
7697 if sz >= 1 and isinstance(query[0], FuncDeclRef):
7698 _decls = (FuncDecl * sz)()
7703 r = Z3_fixedpoint_query_relations(self.ctx.ref(), self.fixedpoint, sz, _decls)
7708 query = And(query, self.ctx)
7709 query = self.abstract(query, False)
7710 r = Z3_fixedpoint_query(self.ctx.ref(), self.fixedpoint, query.as_ast())
7711 return CheckSatResult(r)
7713 def query_from_lvl(self, lvl, *query):
7714 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7716 query = _get_args(query)
7718 if sz >= 1 and isinstance(query[0], FuncDecl):
7719 _z3_assert(False, "unsupported")
7725 query = self.abstract(query, False)
7726 r = Z3_fixedpoint_query_from_lvl(self.ctx.ref(), self.fixedpoint, query.as_ast(), lvl)
7727 return CheckSatResult(r)
7729 def update_rule(self, head, body, name):
7733 name = to_symbol(name, self.ctx)
7734 body = _get_args(body)
7735 f = self.abstract(Implies(And(body, self.ctx), head))
7736 Z3_fixedpoint_update_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7738 def get_answer(self):
7739 """Retrieve answer from last query call."""
7740 r = Z3_fixedpoint_get_answer(self.ctx.ref(), self.fixedpoint)
7741 return _to_expr_ref(r, self.ctx)
7743 def get_ground_sat_answer(self):
7744 """Retrieve a ground cex from last query call."""
7745 r = Z3_fixedpoint_get_ground_sat_answer(self.ctx.ref(), self.fixedpoint)
7746 return _to_expr_ref(r, self.ctx)
7748 def get_rules_along_trace(self):
7749 """retrieve rules along the counterexample trace"""
7750 return AstVector(Z3_fixedpoint_get_rules_along_trace(self.ctx.ref(), self.fixedpoint), self.ctx)
7752 def get_rule_names_along_trace(self):
7753 """retrieve rule names along the counterexample trace"""
7754 # this is a hack as I don't know how to return a list of symbols from C++;
7755 # obtain names as a single string separated by semicolons
7756 names = _symbol2py(self.ctx, Z3_fixedpoint_get_rule_names_along_trace(self.ctx.ref(), self.fixedpoint))
7757 # split into individual names
7758 return names.split(";")
7760 def get_num_levels(self, predicate):
7761 """Retrieve number of levels used for predicate in PDR engine"""
7762 return Z3_fixedpoint_get_num_levels(self.ctx.ref(), self.fixedpoint, predicate.ast)
7764 def get_cover_delta(self, level, predicate):
7765 """Retrieve properties known about predicate for the level'th unfolding.
7766 -1 is treated as the limit (infinity)
7768 r = Z3_fixedpoint_get_cover_delta(self.ctx.ref(), self.fixedpoint, level, predicate.ast)
7769 return _to_expr_ref(r, self.ctx)
7771 def add_cover(self, level, predicate, property):
7772 """Add property to predicate for the level'th unfolding.
7773 -1 is treated as infinity (infinity)
7775 Z3_fixedpoint_add_cover(self.ctx.ref(), self.fixedpoint, level, predicate.ast, property.ast)
7777 def register_relation(self, *relations):
7778 """Register relation as recursive"""
7779 relations = _get_args(relations)
7781 Z3_fixedpoint_register_relation(self.ctx.ref(), self.fixedpoint, f.ast)
7783 def set_predicate_representation(self, f, *representations):
7784 """Control how relation is represented"""
7785 representations = _get_args(representations)
7786 representations = [to_symbol(s) for s in representations]
7787 sz = len(representations)
7788 args = (Symbol * sz)()
7790 args[i] = representations[i]
7791 Z3_fixedpoint_set_predicate_representation(self.ctx.ref(), self.fixedpoint, f.ast, sz, args)
7793 def parse_string(self, s):
7794 """Parse rules and queries from a string"""
7795 return AstVector(Z3_fixedpoint_from_string(self.ctx.ref(), self.fixedpoint, s), self.ctx)
7797 def parse_file(self, f):
7798 """Parse rules and queries from a file"""
7799 return AstVector(Z3_fixedpoint_from_file(self.ctx.ref(), self.fixedpoint, f), self.ctx)
7801 def get_rules(self):
7802 """retrieve rules that have been added to fixedpoint context"""
7803 return AstVector(Z3_fixedpoint_get_rules(self.ctx.ref(), self.fixedpoint), self.ctx)
7805 def get_assertions(self):
7806 """retrieve assertions that have been added to fixedpoint context"""
7807 return AstVector(Z3_fixedpoint_get_assertions(self.ctx.ref(), self.fixedpoint), self.ctx)
7810 """Return a formatted string with all added rules and constraints."""
7814 """Return a formatted string (in Lisp-like format) with all added constraints.
7815 We say the string is in s-expression format.
7817 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, 0, (Ast * 0)())
7819 def to_string(self, queries):
7820 """Return a formatted string (in Lisp-like format) with all added constraints.
7821 We say the string is in s-expression format.
7822 Include also queries.
7824 args, len = _to_ast_array(queries)
7825 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, len, args)
7827 def statistics(self):
7828 """Return statistics for the last `query()`.
7830 return Statistics(Z3_fixedpoint_get_statistics(self.ctx.ref(), self.fixedpoint), self.ctx)
7832 def reason_unknown(self):
7833 """Return a string describing why the last `query()` returned `unknown`.
7835 return Z3_fixedpoint_get_reason_unknown(self.ctx.ref(), self.fixedpoint)
7837 def declare_var(self, *vars):
7838 """Add variable or several variables.
7839 The added variable or variables will be bound in the rules
7842 vars = _get_args(vars)
7846 def abstract(self, fml, is_forall=True):
7850 return ForAll(self.vars, fml)
7852 return Exists(self.vars, fml)
7855#########################################
7859#########################################
7861class FiniteDomainSortRef(SortRef):
7862 """Finite domain sort."""
7865 """Return the size of the finite domain sort"""
7866 r = (ctypes.c_ulonglong * 1)()
7867 if Z3_get_finite_domain_sort_size(self.ctx_ref(), self.ast, r):
7870 raise Z3Exception("Failed to retrieve finite domain sort size")
7873def FiniteDomainSort(name, sz, ctx=None):
7874 """Create a named finite domain sort of a given size sz"""
7875 if not isinstance(name, Symbol):
7876 name = to_symbol(name)
7878 return FiniteDomainSortRef(Z3_mk_finite_domain_sort(ctx.ref(), name, sz), ctx)
7881def is_finite_domain_sort(s):
7882 """Return True if `s` is a Z3 finite-domain sort.
7884 >>> is_finite_domain_sort(FiniteDomainSort('S', 100))
7886 >>> is_finite_domain_sort(IntSort())
7889 return isinstance(s, FiniteDomainSortRef)
7892class FiniteDomainRef(ExprRef):
7893 """Finite-domain expressions."""
7896 """Return the sort of the finite-domain expression `self`."""
7897 return FiniteDomainSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
7899 def as_string(self):
7900 """Return a Z3 floating point expression as a Python string."""
7901 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
7904def is_finite_domain(a):
7905 """Return `True` if `a` is a Z3 finite-domain expression.
7907 >>> s = FiniteDomainSort('S', 100)
7908 >>> b = Const('b', s)
7909 >>> is_finite_domain(b)
7911 >>> is_finite_domain(Int('x'))
7914 return isinstance(a, FiniteDomainRef)
7917class FiniteDomainNumRef(FiniteDomainRef):
7918 """Integer values."""
7921 """Return a Z3 finite-domain numeral as a Python long (bignum) numeral.
7923 >>> s = FiniteDomainSort('S', 100)
7924 >>> v = FiniteDomainVal(3, s)
7930 return int(self.as_string())
7932 def as_string(self):
7933 """Return a Z3 finite-domain numeral as a Python string.
7935 >>> s = FiniteDomainSort('S', 100)
7936 >>> v = FiniteDomainVal(42, s)
7940 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
7943def FiniteDomainVal(val, sort, ctx=None):
7944 """Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.
7946 >>> s = FiniteDomainSort('S', 256)
7947 >>> FiniteDomainVal(255, s)
7949 >>> FiniteDomainVal('100', s)
7953 _z3_assert(is_finite_domain_sort(sort), "Expected finite-domain sort")
7955 return FiniteDomainNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), sort.ast), ctx)
7958def is_finite_domain_value(a):
7959 """Return `True` if `a` is a Z3 finite-domain value.
7961 >>> s = FiniteDomainSort('S', 100)
7962 >>> b = Const('b', s)
7963 >>> is_finite_domain_value(b)
7965 >>> b = FiniteDomainVal(10, s)
7968 >>> is_finite_domain_value(b)
7971 return is_finite_domain(a) and _is_numeral(a.ctx, a.as_ast())
7974#########################################
7978#########################################
7980class OptimizeObjective:
7981 def __init__(self, opt, value, is_max):
7984 self._is_max = is_max
7988 return _to_expr_ref(Z3_optimize_get_lower(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7992 return _to_expr_ref(Z3_optimize_get_upper(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7994 def lower_values(self):
7996 return AstVector(Z3_optimize_get_lower_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7998 def upper_values(self):
8000 return AstVector(Z3_optimize_get_upper_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
8009 return "%s:%s" % (self._value, self._is_max)
8015def _global_on_model(ctx):
8016 (fn, mdl) = _on_models[ctx]
8020_on_model_eh = on_model_eh_type(_global_on_model)
8023class Optimize(Z3PPObject):
8024 """Optimize API provides methods for solving using objective functions and weighted soft constraints"""
8026 def __init__(self, optimize=None, ctx=None):
8027 self.ctx = _get_ctx(ctx)
8028 if optimize is None:
8029 self.optimize = Z3_mk_optimize(self.ctx.ref())
8031 self.optimize = optimize
8032 self._on_models_id = None
8033 Z3_optimize_inc_ref(self.ctx.ref(), self.optimize)
8035 def __deepcopy__(self, memo={}):
8036 return Optimize(self.optimize, self.ctx)
8039 if self.optimize is not None and self.ctx.ref() is not None and Z3_optimize_dec_ref is not None:
8040 Z3_optimize_dec_ref(self.ctx.ref(), self.optimize)
8041 if self._on_models_id is not None:
8042 del _on_models[self._on_models_id]
8044 def __enter__(self):
8048 def __exit__(self, *exc_info):
8051 def set(self, *args, **keys):
8052 """Set a configuration option.
8053 The method `help()` return a string containing all available options.
8055 p = args2params(args, keys, self.ctx)
8056 Z3_optimize_set_params(self.ctx.ref(), self.optimize, p.params)
8059 """Display a string describing all available options."""
8060 print(Z3_optimize_get_help(self.ctx.ref(), self.optimize))
8062 def param_descrs(self):
8063 """Return the parameter description set."""
8064 return ParamDescrsRef(Z3_optimize_get_param_descrs(self.ctx.ref(), self.optimize), self.ctx)
8066 def assert_exprs(self, *args):
8067 """Assert constraints as background axioms for the optimize solver."""
8068 args = _get_args(args)
8069 s = BoolSort(self.ctx)
8071 if isinstance(arg, Goal) or isinstance(arg, AstVector):
8073 Z3_optimize_assert(self.ctx.ref(), self.optimize, f.as_ast())
8076 Z3_optimize_assert(self.ctx.ref(), self.optimize, arg.as_ast())
8078 def add(self, *args):
8079 """Assert constraints as background axioms for the optimize solver. Alias for assert_expr."""
8080 self.assert_exprs(*args)
8082 def __iadd__(self, fml):
8086 def assert_and_track(self, a, p):
8087 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
8089 If `p` is a string, it will be automatically converted into a Boolean constant.
8094 >>> s.assert_and_track(x > 0, 'p1')
8095 >>> s.assert_and_track(x != 1, 'p2')
8096 >>> s.assert_and_track(x < 0, p3)
8097 >>> print(s.check())
8099 >>> c = s.unsat_core()
8109 if isinstance(p, str):
8110 p = Bool(p, self.ctx)
8111 _z3_assert(isinstance(a, BoolRef), "Boolean expression expected")
8112 _z3_assert(isinstance(p, BoolRef) and is_const(p), "Boolean expression expected")
8113 Z3_optimize_assert_and_track(self.ctx.ref(), self.optimize, a.as_ast(), p.as_ast())
8115 def add_soft(self, arg, weight="1", id=None):
8116 """Add soft constraint with optional weight and optional identifier.
8117 If no weight is supplied, then the penalty for violating the soft constraint
8119 Soft constraints are grouped by identifiers. Soft constraints that are
8120 added without identifiers are grouped by default.
8123 weight = "%d" % weight
8124 elif isinstance(weight, float):
8125 weight = "%f" % weight
8126 if not isinstance(weight, str):
8127 raise Z3Exception("weight should be a string or an integer")
8130 id = to_symbol(id, self.ctx)
8133 v = Z3_optimize_assert_soft(self.ctx.ref(), self.optimize, a.as_ast(), weight, id)
8134 return OptimizeObjective(self, v, False)
8135 if sys.version_info.major >= 3 and isinstance(arg, Iterable):
8136 return [asoft(a) for a in arg]
8139 def set_initial_value(self, var, value):
8140 """initialize the solver's state by setting the initial value of var to value
8143 value = s.cast(value)
8144 Z3_optimize_set_initial_value(self.ctx.ref(), self.optimize, var.ast, value.ast)
8146 def maximize(self, arg):
8147 """Add objective function to maximize."""
8148 return OptimizeObjective(
8150 Z3_optimize_maximize(self.ctx.ref(), self.optimize, arg.as_ast()),
8154 def minimize(self, arg):
8155 """Add objective function to minimize."""
8156 return OptimizeObjective(
8158 Z3_optimize_minimize(self.ctx.ref(), self.optimize, arg.as_ast()),
8163 """create a backtracking point for added rules, facts and assertions"""
8164 Z3_optimize_push(self.ctx.ref(), self.optimize)
8167 """restore to previously created backtracking point"""
8168 Z3_optimize_pop(self.ctx.ref(), self.optimize)
8170 def check(self, *assumptions):
8171 """Check consistency and produce optimal values."""
8172 assumptions = _get_args(assumptions)
8173 num = len(assumptions)
8174 _assumptions = (Ast * num)()
8175 for i in range(num):
8176 _assumptions[i] = assumptions[i].as_ast()
8177 return CheckSatResult(Z3_optimize_check(self.ctx.ref(), self.optimize, num, _assumptions))
8179 def reason_unknown(self):
8180 """Return a string that describes why the last `check()` returned `unknown`."""
8181 return Z3_optimize_get_reason_unknown(self.ctx.ref(), self.optimize)
8184 """Return a model for the last check()."""
8186 return ModelRef(Z3_optimize_get_model(self.ctx.ref(), self.optimize), self.ctx)
8188 raise Z3Exception("model is not available")
8190 def unsat_core(self):
8191 return AstVector(Z3_optimize_get_unsat_core(self.ctx.ref(), self.optimize), self.ctx)
8193 def lower(self, obj):
8194 if not isinstance(obj, OptimizeObjective):
8195 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8198 def upper(self, obj):
8199 if not isinstance(obj, OptimizeObjective):
8200 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8203 def lower_values(self, obj):
8204 if not isinstance(obj, OptimizeObjective):
8205 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8206 return obj.lower_values()
8208 def upper_values(self, obj):
8209 if not isinstance(obj, OptimizeObjective):
8210 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8211 return obj.upper_values()
8213 def from_file(self, filename):
8214 """Parse assertions and objectives from a file"""
8215 Z3_optimize_from_file(self.ctx.ref(), self.optimize, filename)
8217 def from_string(self, s):
8218 """Parse assertions and objectives from a string"""
8219 Z3_optimize_from_string(self.ctx.ref(), self.optimize, s)
8221 def assertions(self):
8222 """Return an AST vector containing all added constraints."""
8223 return AstVector(Z3_optimize_get_assertions(self.ctx.ref(), self.optimize), self.ctx)
8225 def objectives(self):
8226 """returns set of objective functions"""
8227 return AstVector(Z3_optimize_get_objectives(self.ctx.ref(), self.optimize), self.ctx)
8230 """Return a formatted string with all added rules and constraints."""
8234 """Return a formatted string (in Lisp-like format) with all added constraints.
8235 We say the string is in s-expression format.
8237 return Z3_optimize_to_string(self.ctx.ref(), self.optimize)
8239 def statistics(self):
8240 """Return statistics for the last check`.
8242 return Statistics(Z3_optimize_get_statistics(self.ctx.ref(), self.optimize), self.ctx)
8244 def set_on_model(self, on_model):
8245 """Register a callback that is invoked with every incremental improvement to
8246 objective values. The callback takes a model as argument.
8247 The life-time of the model is limited to the callback so the
8248 model has to be (deep) copied if it is to be used after the callback
8250 id = len(_on_models) + 41
8251 mdl = Model(self.ctx)
8252 _on_models[id] = (on_model, mdl)
8253 self._on_models_id = id
8254 Z3_optimize_register_model_eh(
8255 self.ctx.ref(), self.optimize, mdl.model, ctypes.c_void_p(id), _on_model_eh,
8259#########################################
8263#########################################
8264class ApplyResult(Z3PPObject):
8265 """An ApplyResult object contains the subgoals produced by a tactic when applied to a goal.
8266 It also contains model and proof converters.
8269 def __init__(self, result, ctx):
8270 self.result = result
8272 Z3_apply_result_inc_ref(self.ctx.ref(), self.result)
8274 def __deepcopy__(self, memo={}):
8275 return ApplyResult(self.result, self.ctx)
8278 if self.ctx.ref() is not None and Z3_apply_result_dec_ref is not None:
8279 Z3_apply_result_dec_ref(self.ctx.ref(), self.result)
8282 """Return the number of subgoals in `self`.
8284 >>> a, b = Ints('a b')
8286 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8287 >>> t = Tactic('split-clause')
8291 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'))
8294 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'), Tactic('propagate-values'))
8298 return int(Z3_apply_result_get_num_subgoals(self.ctx.ref(), self.result))
8300 def __getitem__(self, idx):
8301 """Return one of the subgoals stored in ApplyResult object `self`.
8303 >>> a, b = Ints('a b')
8305 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8306 >>> t = Tactic('split-clause')
8309 [a == 0, Or(b == 0, b == 1), a > b]
8311 [a == 1, Or(b == 0, b == 1), a > b]
8313 if idx >= len(self):
8315 return Goal(goal=Z3_apply_result_get_subgoal(self.ctx.ref(), self.result, idx), ctx=self.ctx)
8318 return obj_to_string(self)
8321 """Return a textual representation of the s-expression representing the set of subgoals in `self`."""
8322 return Z3_apply_result_to_string(self.ctx.ref(), self.result)
8325 """Return a Z3 expression consisting of all subgoals.
8330 >>> g.add(Or(x == 2, x == 3))
8331 >>> r = Tactic('simplify')(g)
8333 [[Not(x <= 1), Or(x == 2, x == 3)]]
8335 And(Not(x <= 1), Or(x == 2, x == 3))
8336 >>> r = Tactic('split-clause')(g)
8338 [[x > 1, x == 2], [x > 1, x == 3]]
8340 Or(And(x > 1, x == 2), And(x > 1, x == 3))
8344 return BoolVal(False, self.ctx)
8346 return self[0].as_expr()
8348 return Or([self[i].as_expr() for i in range(len(self))])
8350#########################################
8354#########################################
8357 """Simplifiers act as pre-processing utilities for solvers.
8358 Build a custom simplifier and add it to a solve
r"""
8360 def __init__(self, simplifier, ctx=None):
8361 self.ctx = _get_ctx(ctx)
8362 self.simplifier = None
8363 if isinstance(simplifier, SimplifierObj):
8364 self.simplifier = simplifier
8365 elif isinstance(simplifier, list):
8366 simps = [Simplifier(s, ctx) for s in simplifier]
8367 self.simplifier = simps[0].simplifier
8368 for i in range(1, len(simps)):
8369 self.simplifier = Z3_simplifier_and_then(self.ctx.ref(), self.simplifier, simps[i].simplifier)
8370 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8374 _z3_assert(isinstance(simplifier, str), "simplifier name expected")
8376 self.simplifier = Z3_mk_simplifier(self.ctx.ref(), str(simplifier))
8378 raise Z3Exception("unknown simplifier '%s'" % simplifier)
8379 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8381 def __deepcopy__(self, memo={}):
8382 return Simplifier(self.simplifier, self.ctx)
8385 if self.simplifier is not None and self.ctx.ref() is not None and Z3_simplifier_dec_ref is not None:
8386 Z3_simplifier_dec_ref(self.ctx.ref(), self.simplifier)
8388 def using_params(self, *args, **keys):
8389 """Return a simplifier that uses the given configuration options"""
8390 p = args2params(args, keys, self.ctx)
8391 return Simplifier(Z3_simplifier_using_params(self.ctx.ref(), self.simplifier, p.params), self.ctx)
8393 def add(self, solver):
8394 """Return a solver that applies the simplification pre-processing specified by the simplifie
r"""
8395 return Solver(Z3_solver_add_simplifier(self.ctx.ref(), solver.solver, self.simplifier), self.ctx)
8398 """Display a string containing a description of the available options for the `self` simplifier."""
8399 print(Z3_simplifier_get_help(self.ctx.ref(), self.simplifier))
8401 def param_descrs(self):
8402 """Return the parameter description set."""
8403 return ParamDescrsRef(Z3_simplifier_get_param_descrs(self.ctx.ref(), self.simplifier), self.ctx)
8406#########################################
8410#########################################
8414 """Tactics transform, solver and/or simplify sets of constraints (Goal).
8415 A Tactic can be converted into a Solver using the method solver().
8417 Several combinators are available for creating new tactics using the built-in ones:
8418 Then(), OrElse(), FailIf(), Repeat(), When(), Cond().
8421 def __init__(self, tactic, ctx=None):
8422 self.ctx = _get_ctx(ctx)
8424 if isinstance(tactic, TacticObj):
8425 self.tactic = tactic
8428 _z3_assert(isinstance(tactic, str), "tactic name expected")
8430 self.tactic = Z3_mk_tactic(self.ctx.ref(), str(tactic))
8432 raise Z3Exception("unknown tactic '%s'" % tactic)
8433 Z3_tactic_inc_ref(self.ctx.ref(), self.tactic)
8435 def __deepcopy__(self, memo={}):
8436 return Tactic(self.tactic, self.ctx)
8439 if self.tactic is not None and self.ctx.ref() is not None and Z3_tactic_dec_ref is not None:
8440 Z3_tactic_dec_ref(self.ctx.ref(), self.tactic)
8442 def solver(self, logFile=None):
8443 """Create a solver using the tactic `self`.
8445 The solver supports the methods `push()` and `pop()`, but it
8446 will always solve each `check()` from scratch.
8448 >>> t = Then('simplify', 'nlsat')
8451 >>> s.add(x**2 == 2, x > 0)
8457 return Solver(Z3_mk_solver_from_tactic(self.ctx.ref(), self.tactic), self.ctx, logFile)
8459 def apply(self, goal, *arguments, **keywords):
8460 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8462 >>> x, y = Ints('x y')
8463 >>> t = Tactic('solve-eqs')
8464 >>> t.apply(And(x == 0, y >= x + 1))
8468 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expressions expected")
8469 goal = _to_goal(goal)
8470 if len(arguments) > 0 or len(keywords) > 0:
8471 p = args2params(arguments, keywords, self.ctx)
8472 return ApplyResult(Z3_tactic_apply_ex(self.ctx.ref(), self.tactic, goal.goal, p.params), self.ctx)
8474 return ApplyResult(Z3_tactic_apply(self.ctx.ref(), self.tactic, goal.goal), self.ctx)
8476 def __call__(self, goal, *arguments, **keywords):
8477 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8479 >>> x, y = Ints('x y')
8480 >>> t = Tactic('solve-eqs')
8481 >>> t(And(x == 0, y >= x + 1))
8484 return self.apply(goal, *arguments, **keywords)
8487 """Display a string containing a description of the available options for the `self` tactic."""
8488 print(Z3_tactic_get_help(self.ctx.ref(), self.tactic))
8490 def param_descrs(self):
8491 """Return the parameter description set."""
8492 return ParamDescrsRef(Z3_tactic_get_param_descrs(self.ctx.ref(), self.tactic), self.ctx)
8496 if isinstance(a, BoolRef):
8497 goal = Goal(ctx=a.ctx)
8504def _to_tactic(t, ctx=None):
8505 if isinstance(t, Tactic):
8508 return Tactic(t, ctx)
8511def _and_then(t1, t2, ctx=None):
8512 t1 = _to_tactic(t1, ctx)
8513 t2 = _to_tactic(t2, ctx)
8515 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8516 return Tactic(Z3_tactic_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8519def _or_else(t1, t2, ctx=None):
8520 t1 = _to_tactic(t1, ctx)
8521 t2 = _to_tactic(t2, ctx)
8523 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8524 return Tactic(Z3_tactic_or_else(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8527def AndThen(*ts, **ks):
8528 """Return a tactic that applies the tactics in `*ts` in sequence.
8530 >>> x, y = Ints('x y')
8531 >>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
8532 >>> t(And(x == 0, y > x + 1))
8534 >>> t(And(x == 0, y > x + 1)).as_expr()
8538 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8539 ctx = ks.get("ctx", None)
8542 for i in range(num - 1):
8543 r = _and_then(r, ts[i + 1], ctx)
8548 """Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
8550 >>> x, y = Ints('x y')
8551 >>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
8552 >>> t(And(x == 0, y > x + 1))
8554 >>> t(And(x == 0, y > x + 1)).as_expr()
8557 return AndThen(*ts, **ks)
8560def OrElse(*ts, **ks):
8561 """Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
8564 >>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
8565 >>> # Tactic split-clause fails if there is no clause in the given goal.
8568 >>> t(Or(x == 0, x == 1))
8569 [[x == 0], [x == 1]]
8572 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8573 ctx = ks.get("ctx", None)
8576 for i in range(num - 1):
8577 r = _or_else(r, ts[i + 1], ctx)
8581def ParOr(*ts, **ks):
8582 """Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
8585 >>> t = ParOr(Tactic('simplify'), Tactic('fail'))
8590 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8591 ctx = _get_ctx(ks.get("ctx", None))
8592 ts = [_to_tactic(t, ctx) for t in ts]
8594 _args = (TacticObj * sz)()
8596 _args[i] = ts[i].tactic
8597 return Tactic(Z3_tactic_par_or(ctx.ref(), sz, _args), ctx)
8600def ParThen(t1, t2, ctx=None):
8601 """Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
8602 The subgoals are processed in parallel.
8604 >>> x, y = Ints('x y')
8605 >>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
8606 >>> t(And(Or(x == 1, x == 2), y == x + 1))
8607 [[x == 1, y == 2], [x == 2, y == 3]]
8609 t1 = _to_tactic(t1, ctx)
8610 t2 = _to_tactic(t2, ctx)
8612 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8613 return Tactic(Z3_tactic_par_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8616def ParAndThen(t1, t2, ctx=None):
8617 """Alias for ParThen(t1, t2, ctx)."""
8618 return ParThen(t1, t2, ctx)
8621def With(t, *args, **keys):
8622 """Return a tactic that applies tactic `t` using the given configuration options.
8624 >>> x, y = Ints('x y')
8625 >>> t = With(Tactic('simplify'), som=True)
8626 >>> t((x + 1)*(y + 2) == 0)
8627 [[2*x + y + x*y == -2]]
8629 ctx = keys.pop("ctx", None)
8630 t = _to_tactic(t, ctx)
8631 p = args2params(args, keys, t.ctx)
8632 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8635def WithParams(t, p):
8636 """Return a tactic that applies tactic `t` using the given configuration options.
8638 >>> x, y = Ints('x y')
8640 >>> p.set("som", True)
8641 >>> t = WithParams(Tactic('simplify'), p)
8642 >>> t((x + 1)*(y + 2) == 0)
8643 [[2*x + y + x*y == -2]]
8645 t = _to_tactic(t, None)
8646 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8649def Repeat(t, max=4294967295, ctx=None):
8650 """Return a tactic that keeps applying `t` until the goal is not modified anymore
8651 or the maximum number of iterations `max` is reached.
8653 >>> x, y = Ints('x y')
8654 >>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
8655 >>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
8657 >>> for subgoal in r: print(subgoal)
8658 [x == 0, y == 0, x > y]
8659 [x == 0, y == 1, x > y]
8660 [x == 1, y == 0, x > y]
8661 [x == 1, y == 1, x > y]
8662 >>> t = Then(t, Tactic('propagate-values'))
8666 t = _to_tactic(t, ctx)
8667 return Tactic(Z3_tactic_repeat(t.ctx.ref(), t.tactic, max), t.ctx)
8670def TryFor(t, ms, ctx=None):
8671 """Return a tactic that applies `t` to a given goal for `ms` milliseconds.
8673 If `t` does not terminate in `ms` milliseconds, then it fails.
8675 t = _to_tactic(t, ctx)
8676 return Tactic(Z3_tactic_try_for(t.ctx.ref(), t.tactic, ms), t.ctx)
8679def tactics(ctx=None):
8680 """Return a list of all available tactics in Z3.
8683 >>> l.count('simplify') == 1
8687 return [Z3_get_tactic_name(ctx.ref(), i) for i in range(Z3_get_num_tactics(ctx.ref()))]
8690def tactic_description(name, ctx=None):
8691 """Return a short description for the tactic named `name`.
8693 >>> d = tactic_description('simplify')
8696 return Z3_tactic_get_descr(ctx.ref(), name)
8699def describe_tactics():
8700 """Display a (tabular) description of all available tactics in Z3."""
8703 print('<table border="1" cellpadding="2" cellspacing="0">')
8706 print('<tr style="background-color:#CFCFCF">')
8711 print("<td>%s</td><td>%s</td></tr>" % (t, insert_line_breaks(tactic_description(t), 40)))
8715 print("%s : %s" % (t, tactic_description(t)))
8719 """Probes are used to inspect a goal (aka problem) and collect information that may be used
8720 to decide which solver and/or preprocessing step will be used.
8723 def __init__(self, probe, ctx=None):
8724 self.ctx = _get_ctx(ctx)
8726 if isinstance(probe, ProbeObj):
8728 elif isinstance(probe, float):
8729 self.probe = Z3_probe_const(self.ctx.ref(), probe)
8730 elif _is_int(probe):
8731 self.probe = Z3_probe_const(self.ctx.ref(), float(probe))
8732 elif isinstance(probe, bool):
8734 self.probe = Z3_probe_const(self.ctx.ref(), 1.0)
8736 self.probe = Z3_probe_const(self.ctx.ref(), 0.0)
8739 _z3_assert(isinstance(probe, str), "probe name expected")
8741 self.probe = Z3_mk_probe(self.ctx.ref(), probe)
8743 raise Z3Exception("unknown probe '%s'" % probe)
8744 Z3_probe_inc_ref(self.ctx.ref(), self.probe)
8746 def __deepcopy__(self, memo={}):
8747 return Probe(self.probe, self.ctx)
8750 if self.probe is not None and self.ctx.ref() is not None and Z3_probe_dec_ref is not None:
8751 Z3_probe_dec_ref(self.ctx.ref(), self.probe)
8753 def __lt__(self, other):
8754 """Return a probe that evaluates to "true" when the value returned by `self`
8755 is less than the value returned by `other`.
8757 >>> p = Probe('size') < 10
8765 return Probe(Z3_probe_lt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8767 def __gt__(self, other):
8768 """Return a probe that evaluates to "true" when the value returned by `self`
8769 is greater than the value returned by `other`.
8771 >>> p = Probe('size') > 10
8779 return Probe(Z3_probe_gt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8781 def __le__(self, other):
8782 """Return a probe that evaluates to "true" when the value returned by `self`
8783 is less than or equal to the value returned by `other`.
8785 >>> p = Probe('size') <= 2
8793 return Probe(Z3_probe_le(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8795 def __ge__(self, other):
8796 """Return a probe that evaluates to "true" when the value returned by `self`
8797 is greater than or equal to the value returned by `other`.
8799 >>> p = Probe('size') >= 2
8807 return Probe(Z3_probe_ge(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8809 def __eq__(self, other):
8810 """Return a probe that evaluates to "true" when the value returned by `self`
8811 is equal to the value returned by `other`.
8813 >>> p = Probe('size') == 2
8821 return Probe(Z3_probe_eq(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8823 def __ne__(self, other):
8824 """Return a probe that evaluates to "true" when the value returned by `self`
8825 is not equal to the value returned by `other`.
8827 >>> p = Probe('size') != 2
8835 p = self.__eq__(other)
8836 return Probe(Z3_probe_not(self.ctx.ref(), p.probe), self.ctx)
8838 def __call__(self, goal):
8839 """Evaluate the probe `self` in the given goal.
8841 >>> p = Probe('size')
8851 >>> p = Probe('num-consts')
8854 >>> p = Probe('is-propositional')
8857 >>> p = Probe('is-qflia')
8862 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expression expected")
8863 goal = _to_goal(goal)
8864 return Z3_probe_apply(self.ctx.ref(), self.probe, goal.goal)
8868 """Return `True` if `p` is a Z3 probe.
8870 >>> is_probe(Int('x'))
8872 >>> is_probe(Probe('memory'))
8875 return isinstance(p, Probe)
8878def _to_probe(p, ctx=None):
8882 return Probe(p, ctx)
8885def probes(ctx=None):
8886 """Return a list of all available probes in Z3.
8889 >>> l.count('memory') == 1
8893 return [Z3_get_probe_name(ctx.ref(), i) for i in range(Z3_get_num_probes(ctx.ref()))]
8896def probe_description(name, ctx=None):
8897 """Return a short description for the probe named `name`.
8899 >>> d = probe_description('memory')
8902 return Z3_probe_get_descr(ctx.ref(), name)
8905def describe_probes():
8906 """Display a (tabular) description of all available probes in Z3."""
8909 print('<table border="1" cellpadding="2" cellspacing="0">')
8912 print('<tr style="background-color:#CFCFCF">')
8917 print("<td>%s</td><td>%s</td></tr>" % (p, insert_line_breaks(probe_description(p), 40)))
8921 print("%s : %s" % (p, probe_description(p)))
8924def _probe_nary(f, args, ctx):
8926 _z3_assert(len(args) > 0, "At least one argument expected")
8928 r = _to_probe(args[0], ctx)
8929 for i in range(num - 1):
8930 r = Probe(f(ctx.ref(), r.probe, _to_probe(args[i + 1], ctx).probe), ctx)
8934def _probe_and(args, ctx):
8935 return _probe_nary(Z3_probe_and, args, ctx)
8938def _probe_or(args, ctx):
8939 return _probe_nary(Z3_probe_or, args, ctx)
8942def FailIf(p, ctx=None):
8943 """Return a tactic that fails if the probe `p` evaluates to true.
8944 Otherwise, it returns the input goal unmodified.
8946 In the following example, the tactic applies 'simplify' if and only if there are
8947 more than 2 constraints in the goal.
8949 >>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
8950 >>> x, y = Ints('x y')
8956 >>> g.add(x == y + 1)
8958 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8960 p = _to_probe(p, ctx)
8961 return Tactic(Z3_tactic_fail_if(p.ctx.ref(), p.probe), p.ctx)
8964def When(p, t, ctx=None):
8965 """Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
8966 Otherwise, it returns the input goal unmodified.
8968 >>> t = When(Probe('size') > 2, Tactic('simplify'))
8969 >>> x, y = Ints('x y')
8975 >>> g.add(x == y + 1)
8977 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8979 p = _to_probe(p, ctx)
8980 t = _to_tactic(t, ctx)
8981 return Tactic(Z3_tactic_when(t.ctx.ref(), p.probe, t.tactic), t.ctx)
8984def Cond(p, t1, t2, ctx=None):
8985 """Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
8987 >>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
8989 p = _to_probe(p, ctx)
8990 t1 = _to_tactic(t1, ctx)
8991 t2 = _to_tactic(t2, ctx)
8992 return Tactic(Z3_tactic_cond(t1.ctx.ref(), p.probe, t1.tactic, t2.tactic), t1.ctx)
8994#########################################
8998#########################################
9001def simplify(a, *arguments, **keywords):
9002 """Simplify the expression `a` using the given options.
9004 This function has many options. Use `help_simplify` to obtain the complete list.
9008 >>> simplify(x + 1 + y + x + 1)
9010 >>> simplify((x + 1)*(y + 1), som=True)
9012 >>> simplify(Distinct(x, y, 1), blast_distinct=True)
9013 And(Not(x == y), Not(x == 1), Not(y == 1))
9014 >>> simplify(And(x == 0, y == 1), elim_and=True)
9015 Not(Or(Not(x == 0), Not(y == 1)))
9018 _z3_assert(is_expr(a), "Z3 expression expected")
9019 if len(arguments) > 0 or len(keywords) > 0:
9020 p = args2params(arguments, keywords, a.ctx)
9021 return _to_expr_ref(Z3_simplify_ex(a.ctx_ref(), a.as_ast(), p.params), a.ctx)
9023 return _to_expr_ref(Z3_simplify(a.ctx_ref(), a.as_ast()), a.ctx)
9027 """Return a string describing all options available for Z3 `simplify` procedure."""
9028 print(Z3_simplify_get_help(main_ctx().ref()))
9031def simplify_param_descrs():
9032 """Return the set of parameter descriptions for Z3 `simplify` procedure."""
9033 return ParamDescrsRef(Z3_simplify_get_param_descrs(main_ctx().ref()), main_ctx())
9036def substitute(t, *m):
9037 """Apply substitution m on t, m is a list of pairs of the form (from, to).
9038 Every occurrence in t of from is replaced with to.
9042 >>> substitute(x + 1, (x, y + 1))
9044 >>> f = Function('f', IntSort(), IntSort())
9045 >>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
9048 if isinstance(m, tuple):
9050 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
9053 _z3_assert(is_expr(t), "Z3 expression expected")
9055 all([isinstance(p, tuple) and is_expr(p[0]) and is_expr(p[1]) for p in m]),
9056 "Z3 invalid substitution, expression pairs expected.")
9058 all([p[0].sort().eq(p[1].sort()) for p in m]),
9059 'Z3 invalid substitution, mismatching "from" and "to" sorts.')
9061 _from = (Ast * num)()
9063 for i in range(num):
9064 _from[i] = m[i][0].as_ast()
9065 _to[i] = m[i][1].as_ast()
9066 return _to_expr_ref(Z3_substitute(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
9069def substitute_vars(t, *m):
9070 """Substitute the free variables in t with the expression in m.
9072 >>> v0 = Var(0, IntSort())
9073 >>> v1 = Var(1, IntSort())
9075 >>> f = Function('f', IntSort(), IntSort(), IntSort())
9076 >>> # replace v0 with x+1 and v1 with x
9077 >>> substitute_vars(f(v0, v1), x + 1, x)
9081 _z3_assert(is_expr(t), "Z3 expression expected")
9082 _z3_assert(all([is_expr(n) for n in m]), "Z3 invalid substitution, list of expressions expected.")
9085 for i in range(num):
9086 _to[i] = m[i].as_ast()
9087 return _to_expr_ref(Z3_substitute_vars(t.ctx.ref(), t.as_ast(), num, _to), t.ctx)
9089def substitute_funs(t, *m):
9090 """Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
9091 Every occurrence in to of the function from is replaced with the expression to.
9092 The expression to can have free variables, that refer to the arguments of from.
9095 if isinstance(m, tuple):
9097 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
9100 _z3_assert(is_expr(t), "Z3 expression expected")
9101 _z3_assert(all([isinstance(p, tuple) and is_func_decl(p[0]) and is_expr(p[1]) for p in m]), "Z3 invalid substitution, function pairs expected.")
9103 _from = (FuncDecl * num)()
9105 for i in range(num):
9106 _from[i] = m[i][0].as_func_decl()
9107 _to[i] = m[i][1].as_ast()
9108 return _to_expr_ref(Z3_substitute_funs(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
9112 """Create the sum of the Z3 expressions.
9114 >>> a, b, c = Ints('a b c')
9119 >>> A = IntVector('a', 5)
9121 a__0 + a__1 + a__2 + a__3 + a__4
9123 args = _get_args(args)
9126 ctx = _ctx_from_ast_arg_list(args)
9128 return _reduce(lambda a, b: a + b, args, 0)
9129 args = _coerce_expr_list(args, ctx)
9131 return _reduce(lambda a, b: a + b, args, 0)
9133 _args, sz = _to_ast_array(args)
9134 return ArithRef(Z3_mk_add(ctx.ref(), sz, _args), ctx)
9138 """Create the product of the Z3 expressions.
9140 >>> a, b, c = Ints('a b c')
9141 >>> Product(a, b, c)
9143 >>> Product([a, b, c])
9145 >>> A = IntVector('a', 5)
9147 a__0*a__1*a__2*a__3*a__4
9149 args = _get_args(args)
9152 ctx = _ctx_from_ast_arg_list(args)
9154 return _reduce(lambda a, b: a * b, args, 1)
9155 args = _coerce_expr_list(args, ctx)
9157 return _reduce(lambda a, b: a * b, args, 1)
9159 _args, sz = _to_ast_array(args)
9160 return ArithRef(Z3_mk_mul(ctx.ref(), sz, _args), ctx)
9163 """Create the absolute value of an arithmetic expression"""
9164 return If(arg > 0, arg, -arg)
9168 """Create an at-most Pseudo-Boolean k constraint.
9170 >>> a, b, c = Bools('a b c')
9171 >>> f = AtMost(a, b, c, 2)
9173 args = _get_args(args)
9175 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
9176 ctx = _ctx_from_ast_arg_list(args)
9178 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9179 args1 = _coerce_expr_list(args[:-1], ctx)
9181 _args, sz = _to_ast_array(args1)
9182 return BoolRef(Z3_mk_atmost(ctx.ref(), sz, _args, k), ctx)
9186 """Create an at-least Pseudo-Boolean k constraint.
9188 >>> a, b, c = Bools('a b c')
9189 >>> f = AtLeast(a, b, c, 2)
9191 args = _get_args(args)
9193 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
9194 ctx = _ctx_from_ast_arg_list(args)
9196 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9197 args1 = _coerce_expr_list(args[:-1], ctx)
9199 _args, sz = _to_ast_array(args1)
9200 return BoolRef(Z3_mk_atleast(ctx.ref(), sz, _args, k), ctx)
9203def _reorder_pb_arg(arg):
9205 if not _is_int(b) and _is_int(a):
9210def _pb_args_coeffs(args, default_ctx=None):
9211 args = _get_args_ast_list(args)
9213 return _get_ctx(default_ctx), 0, (Ast * 0)(), (ctypes.c_int * 0)()
9214 args = [_reorder_pb_arg(arg) for arg in args]
9215 args, coeffs = zip(*args)
9217 _z3_assert(len(args) > 0, "Non empty list of arguments expected")
9218 ctx = _ctx_from_ast_arg_list(args)
9220 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9221 args = _coerce_expr_list(args, ctx)
9222 _args, sz = _to_ast_array(args)
9223 _coeffs = (ctypes.c_int * len(coeffs))()
9224 for i in range(len(coeffs)):
9225 _z3_check_cint_overflow(coeffs[i], "coefficient")
9226 _coeffs[i] = coeffs[i]
9227 return ctx, sz, _args, _coeffs, args
9231 """Create a Pseudo-Boolean inequality k constraint.
9233 >>> a, b, c = Bools('a b c')
9234 >>> f = PbLe(((a,1),(b,3),(c,2)), 3)
9236 _z3_check_cint_overflow(k, "k")
9237 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9238 return BoolRef(Z3_mk_pble(ctx.ref(), sz, _args, _coeffs, k), ctx)
9242 """Create a Pseudo-Boolean inequality k constraint.
9244 >>> a, b, c = Bools('a b c')
9245 >>> f = PbGe(((a,1),(b,3),(c,2)), 3)
9247 _z3_check_cint_overflow(k, "k")
9248 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9249 return BoolRef(Z3_mk_pbge(ctx.ref(), sz, _args, _coeffs, k), ctx)
9252def PbEq(args, k, ctx=None):
9253 """Create a Pseudo-Boolean equality k constraint.
9255 >>> a, b, c = Bools('a b c')
9256 >>> f = PbEq(((a,1),(b,3),(c,2)), 3)
9258 _z3_check_cint_overflow(k, "k")
9259 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9260 return BoolRef(Z3_mk_pbeq(ctx.ref(), sz, _args, _coeffs, k), ctx)
9263def solve(*args, **keywords):
9264 """Solve the constraints `*args`.
9266 This is a simple function for creating demonstrations. It creates a solver,
9267 configure it using the options in `keywords`, adds the constraints
9268 in `args`, and invokes check.
9271 >>> solve(a > 0, a < 2)
9274 show = keywords.pop("show", False)
9282 print("no solution")
9284 print("failed to solve")
9293def solve_using(s, *args, **keywords):
9294 """Solve the constraints `*args` using solver `s`.
9296 This is a simple function for creating demonstrations. It is similar to `solve`,
9297 but it uses the given solver `s`.
9298 It configures solver `s` using the options in `keywords`, adds the constraints
9299 in `args`, and invokes check.
9301 show = keywords.pop("show", False)
9303 _z3_assert(isinstance(s, Solver), "Solver object expected")
9311 print("no solution")
9313 print("failed to solve")
9324def prove(claim, show=False, **keywords):
9325 """Try to prove the given claim.
9327 This is a simple function for creating demonstrations. It tries to prove
9328 `claim` by showing the negation is unsatisfiable.
9330 >>> p, q = Bools('p q')
9331 >>> prove(Not(And(p, q)) == Or(Not(p), Not(q)))
9335 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9345 print("failed to prove")
9348 print("counterexample")
9352def _solve_html(*args, **keywords):
9353 """Version of function `solve` that renders HTML output."""
9354 show = keywords.pop("show", False)
9359 print("<b>Problem:</b>")
9363 print("<b>no solution</b>")
9365 print("<b>failed to solve</b>")
9372 print("<b>Solution:</b>")
9376def _solve_using_html(s, *args, **keywords):
9377 """Version of function `solve_using` that renders HTML."""
9378 show = keywords.pop("show", False)
9380 _z3_assert(isinstance(s, Solver), "Solver object expected")
9384 print("<b>Problem:</b>")
9388 print("<b>no solution</b>")
9390 print("<b>failed to solve</b>")
9397 print("<b>Solution:</b>")
9401def _prove_html(claim, show=False, **keywords):
9402 """Version of function `prove` that renders HTML."""
9404 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9412 print("<b>proved</b>")
9414 print("<b>failed to prove</b>")
9417 print("<b>counterexample</b>")
9421def _dict2sarray(sorts, ctx):
9423 _names = (Symbol * sz)()
9424 _sorts = (Sort * sz)()
9429 _z3_assert(isinstance(k, str), "String expected")
9430 _z3_assert(is_sort(v), "Z3 sort expected")
9431 _names[i] = to_symbol(k, ctx)
9434 return sz, _names, _sorts
9437def _dict2darray(decls, ctx):
9439 _names = (Symbol * sz)()
9440 _decls = (FuncDecl * sz)()
9445 _z3_assert(isinstance(k, str), "String expected")
9446 _z3_assert(is_func_decl(v) or is_const(v), "Z3 declaration or constant expected")
9447 _names[i] = to_symbol(k, ctx)
9449 _decls[i] = v.decl().ast
9453 return sz, _names, _decls
9456 def __init__(self, ctx= None):
9457 self.ctx = _get_ctx(ctx)
9458 self.pctx = Z3_mk_parser_context(self.ctx.ref())
9459 Z3_parser_context_inc_ref(self.ctx.ref(), self.pctx)
9462 if self.ctx.ref() is not None and self.pctx is not None and Z3_parser_context_dec_ref is not None:
9463 Z3_parser_context_dec_ref(self.ctx.ref(), self.pctx)
9466 def add_sort(self, sort):
9467 Z3_parser_context_add_sort(self.ctx.ref(), self.pctx, sort.as_ast())
9469 def add_decl(self, decl):
9470 Z3_parser_context_add_decl(self.ctx.ref(), self.pctx, decl.as_ast())
9472 def from_string(self, s):
9473 return AstVector(Z3_parser_context_from_string(self.ctx.ref(), self.pctx, s), self.ctx)
9475def parse_smt2_string(s, sorts={}, decls={}, ctx=None):
9476 """Parse a string in SMT 2.0 format using the given sorts and decls.
9478 The arguments sorts and decls are Python dictionaries used to initialize
9479 the symbol table used for the SMT 2.0 parser.
9481 >>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
9483 >>> x, y = Ints('x y')
9484 >>> f = Function('f', IntSort(), IntSort())
9485 >>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
9487 >>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
9491 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9492 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9493 return AstVector(Z3_parse_smtlib2_string(ctx.ref(), s, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9496def parse_smt2_file(f, sorts={}, decls={}, ctx=None):
9497 """Parse a file in SMT 2.0 format using the given sorts and decls.
9499 This function is similar to parse_smt2_string().
9502 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9503 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9504 return AstVector(Z3_parse_smtlib2_file(ctx.ref(), f, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9507#########################################
9509# Floating-Point Arithmetic
9511#########################################
9514# Global default rounding mode
9515_dflt_rounding_mode = Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN
9516_dflt_fpsort_ebits = 11
9517_dflt_fpsort_sbits = 53
9520def get_default_rounding_mode(ctx=None):
9521 """Retrieves the global default rounding mode."""
9522 global _dflt_rounding_mode
9523 if _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_ZERO:
9525 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_NEGATIVE:
9527 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_POSITIVE:
9529 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN:
9531 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY:
9535_ROUNDING_MODES = frozenset({
9536 Z3_OP_FPA_RM_TOWARD_ZERO,
9537 Z3_OP_FPA_RM_TOWARD_NEGATIVE,
9538 Z3_OP_FPA_RM_TOWARD_POSITIVE,
9539 Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN,
9540 Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY
9544def set_default_rounding_mode(rm, ctx=None):
9545 global _dflt_rounding_mode
9546 if is_fprm_value(rm):
9547 _dflt_rounding_mode = rm.kind()
9549 _z3_assert(_dflt_rounding_mode in _ROUNDING_MODES, "illegal rounding mode")
9550 _dflt_rounding_mode = rm
9553def get_default_fp_sort(ctx=None):
9554 return FPSort(_dflt_fpsort_ebits, _dflt_fpsort_sbits, ctx)
9557def set_default_fp_sort(ebits, sbits, ctx=None):
9558 global _dflt_fpsort_ebits
9559 global _dflt_fpsort_sbits
9560 _dflt_fpsort_ebits = ebits
9561 _dflt_fpsort_sbits = sbits
9564def _dflt_rm(ctx=None):
9565 return get_default_rounding_mode(ctx)
9568def _dflt_fps(ctx=None):
9569 return get_default_fp_sort(ctx)
9572def _coerce_fp_expr_list(alist, ctx):
9573 first_fp_sort = None
9576 if first_fp_sort is None:
9577 first_fp_sort = a.sort()
9578 elif first_fp_sort == a.sort():
9579 pass # OK, same as before
9581 # we saw at least 2 different float sorts; something will
9582 # throw a sort mismatch later, for now assume None.
9583 first_fp_sort = None
9587 for i in range(len(alist)):
9589 is_repr = isinstance(a, str) and a.contains("2**(") and a.endswith(")")
9590 if is_repr or _is_int(a) or isinstance(a, (float, bool)):
9591 r.append(FPVal(a, None, first_fp_sort, ctx))
9594 return _coerce_expr_list(r, ctx)
9599class FPSortRef(SortRef):
9600 """Floating-point sort."""
9603 """Retrieves the number of bits reserved for the exponent in the FloatingPoint sort `self`.
9604 >>> b = FPSort(8, 24)
9608 return int(Z3_fpa_get_ebits(self.ctx_ref(), self.ast))
9611 """Retrieves the number of bits reserved for the significand in the FloatingPoint sort `self`.
9612 >>> b = FPSort(8, 24)
9616 return int(Z3_fpa_get_sbits(self.ctx_ref(), self.ast))
9618 def cast(self, val):
9619 """Try to cast `val` as a floating-point expression.
9620 >>> b = FPSort(8, 24)
9623 >>> b.cast(1.0).sexpr()
9624 '(fp #b0 #x7f #b00000000000000000000000)'
9628 _z3_assert(self.ctx == val.ctx, "Context mismatch")
9631 return FPVal(val, None, self, self.ctx)
9634def Float16(ctx=None):
9635 """Floating-point 16-bit (half) sort."""
9637 return FPSortRef(Z3_mk_fpa_sort_16(ctx.ref()), ctx)
9640def FloatHalf(ctx=None):
9641 """Floating-point 16-bit (half) sort."""
9643 return FPSortRef(Z3_mk_fpa_sort_half(ctx.ref()), ctx)
9646def Float32(ctx=None):
9647 """Floating-point 32-bit (single) sort."""
9649 return FPSortRef(Z3_mk_fpa_sort_32(ctx.ref()), ctx)
9652def FloatSingle(ctx=None):
9653 """Floating-point 32-bit (single) sort."""
9655 return FPSortRef(Z3_mk_fpa_sort_single(ctx.ref()), ctx)
9658def Float64(ctx=None):
9659 """Floating-point 64-bit (double) sort."""
9661 return FPSortRef(Z3_mk_fpa_sort_64(ctx.ref()), ctx)
9664def FloatDouble(ctx=None):
9665 """Floating-point 64-bit (double) sort."""
9667 return FPSortRef(Z3_mk_fpa_sort_double(ctx.ref()), ctx)
9670def Float128(ctx=None):
9671 """Floating-point 128-bit (quadruple) sort."""
9673 return FPSortRef(Z3_mk_fpa_sort_128(ctx.ref()), ctx)
9676def FloatQuadruple(ctx=None):
9677 """Floating-point 128-bit (quadruple) sort."""
9679 return FPSortRef(Z3_mk_fpa_sort_quadruple(ctx.ref()), ctx)
9682class FPRMSortRef(SortRef):
9683 """"Floating-point rounding mode sort."""
9687 """Return True if `s` is a Z3 floating-point sort.
9689 >>> is_fp_sort(FPSort(8, 24))
9691 >>> is_fp_sort(IntSort())
9694 return isinstance(s, FPSortRef)
9698 """Return True if `s` is a Z3 floating-point rounding mode sort.
9700 >>> is_fprm_sort(FPSort(8, 24))
9702 >>> is_fprm_sort(RNE().sort())
9705 return isinstance(s, FPRMSortRef)
9710class FPRef(ExprRef):
9711 """Floating-point expressions."""
9714 """Return the sort of the floating-point expression `self`.
9716 >>> x = FP('1.0', FPSort(8, 24))
9719 >>> x.sort() == FPSort(8, 24)
9722 return FPSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
9725 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9726 >>> b = FPSort(8, 24)
9730 return self.sort().ebits()
9733 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9734 >>> b = FPSort(8, 24)
9738 return self.sort().sbits()
9740 def as_string(self):
9741 """Return a Z3 floating point expression as a Python string."""
9742 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9744 def __le__(self, other):
9745 return fpLEQ(self, other, self.ctx)
9747 def __lt__(self, other):
9748 return fpLT(self, other, self.ctx)
9750 def __ge__(self, other):
9751 return fpGEQ(self, other, self.ctx)
9753 def __gt__(self, other):
9754 return fpGT(self, other, self.ctx)
9756 def __add__(self, other):
9757 """Create the Z3 expression `self + other`.
9759 >>> x = FP('x', FPSort(8, 24))
9760 >>> y = FP('y', FPSort(8, 24))
9766 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9767 return fpAdd(_dflt_rm(), a, b, self.ctx)
9769 def __radd__(self, other):
9770 """Create the Z3 expression `other + self`.
9772 >>> x = FP('x', FPSort(8, 24))
9776 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9777 return fpAdd(_dflt_rm(), a, b, self.ctx)
9779 def __sub__(self, other):
9780 """Create the Z3 expression `self - other`.
9782 >>> x = FP('x', FPSort(8, 24))
9783 >>> y = FP('y', FPSort(8, 24))
9789 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9790 return fpSub(_dflt_rm(), a, b, self.ctx)
9792 def __rsub__(self, other):
9793 """Create the Z3 expression `other - self`.
9795 >>> x = FP('x', FPSort(8, 24))
9799 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9800 return fpSub(_dflt_rm(), a, b, self.ctx)
9802 def __mul__(self, other):
9803 """Create the Z3 expression `self * other`.
9805 >>> x = FP('x', FPSort(8, 24))
9806 >>> y = FP('y', FPSort(8, 24))
9814 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9815 return fpMul(_dflt_rm(), a, b, self.ctx)
9817 def __rmul__(self, other):
9818 """Create the Z3 expression `other * self`.
9820 >>> x = FP('x', FPSort(8, 24))
9821 >>> y = FP('y', FPSort(8, 24))
9827 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9828 return fpMul(_dflt_rm(), a, b, self.ctx)
9831 """Create the Z3 expression `+self`."""
9835 """Create the Z3 expression `-self`.
9837 >>> x = FP('x', Float32())
9843 def __div__(self, other):
9844 """Create the Z3 expression `self / other`.
9846 >>> x = FP('x', FPSort(8, 24))
9847 >>> y = FP('y', FPSort(8, 24))
9855 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9856 return fpDiv(_dflt_rm(), a, b, self.ctx)
9858 def __rdiv__(self, other):
9859 """Create the Z3 expression `other / self`.
9861 >>> x = FP('x', FPSort(8, 24))
9862 >>> y = FP('y', FPSort(8, 24))
9868 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9869 return fpDiv(_dflt_rm(), a, b, self.ctx)
9871 def __truediv__(self, other):
9872 """Create the Z3 expression division `self / other`."""
9873 return self.__div__(other)
9875 def __rtruediv__(self, other):
9876 """Create the Z3 expression division `other / self`."""
9877 return self.__rdiv__(other)
9879 def __mod__(self, other):
9880 """Create the Z3 expression mod `self % other`."""
9881 return fpRem(self, other)
9883 def __rmod__(self, other):
9884 """Create the Z3 expression mod `other % self`."""
9885 return fpRem(other, self)
9888class FPRMRef(ExprRef):
9889 """Floating-point rounding mode expressions"""
9891 def as_string(self):
9892 """Return a Z3 floating point expression as a Python string."""
9893 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9896def RoundNearestTiesToEven(ctx=None):
9898 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9903 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9906def RoundNearestTiesToAway(ctx=None):
9908 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9913 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9916def RoundTowardPositive(ctx=None):
9918 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9923 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9926def RoundTowardNegative(ctx=None):
9928 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9933 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9936def RoundTowardZero(ctx=None):
9938 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9943 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9947 """Return `True` if `a` is a Z3 floating-point rounding mode expression.
9956 return isinstance(a, FPRMRef)
9959def is_fprm_value(a):
9960 """Return `True` if `a` is a Z3 floating-point rounding mode numeral value."""
9961 return is_fprm(a) and _is_numeral(a.ctx, a.ast)
9966class FPNumRef(FPRef):
9967 """The sign of the numeral.
9969 >>> x = FPVal(+1.0, FPSort(8, 24))
9972 >>> x = FPVal(-1.0, FPSort(8, 24))
9978 num = (ctypes.c_int)()
9979 nsign = Z3_fpa_get_numeral_sign(self.ctx.ref(), self.as_ast(), byref(num))
9981 raise Z3Exception("error retrieving the sign of a numeral.")
9982 return num.value != 0
9984 """The sign of a floating-point numeral as a bit-vector expression.
9986 Remark: NaN's are invalid arguments.
9989 def sign_as_bv(self):
9990 return BitVecNumRef(Z3_fpa_get_numeral_sign_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9992 """The significand of the numeral.
9994 >>> x = FPVal(2.5, FPSort(8, 24))
9999 def significand(self):
10000 return Z3_fpa_get_numeral_significand_string(self.ctx.ref(), self.as_ast())
10002 """The significand of the numeral as a long.
10004 >>> x = FPVal(2.5, FPSort(8, 24))
10005 >>> x.significand_as_long()
10009 def significand_as_long(self):
10010 ptr = (ctypes.c_ulonglong * 1)()
10011 if not Z3_fpa_get_numeral_significand_uint64(self.ctx.ref(), self.as_ast(), ptr):
10012 raise Z3Exception("error retrieving the significand of a numeral.")
10015 """The significand of the numeral as a bit-vector expression.
10017 Remark: NaN are invalid arguments.
10020 def significand_as_bv(self):
10021 return BitVecNumRef(Z3_fpa_get_numeral_significand_bv(self.ctx.ref(), self.as_ast()), self.ctx)
10023 """The exponent of the numeral.
10025 >>> x = FPVal(2.5, FPSort(8, 24))
10030 def exponent(self, biased=True):
10031 return Z3_fpa_get_numeral_exponent_string(self.ctx.ref(), self.as_ast(), biased)
10033 """The exponent of the numeral as a long.
10035 >>> x = FPVal(2.5, FPSort(8, 24))
10036 >>> x.exponent_as_long()
10040 def exponent_as_long(self, biased=True):
10041 ptr = (ctypes.c_longlong * 1)()
10042 if not Z3_fpa_get_numeral_exponent_int64(self.ctx.ref(), self.as_ast(), ptr, biased):
10043 raise Z3Exception("error retrieving the exponent of a numeral.")
10046 """The exponent of the numeral as a bit-vector expression.
10048 Remark: NaNs are invalid arguments.
10051 def exponent_as_bv(self, biased=True):
10052 return BitVecNumRef(Z3_fpa_get_numeral_exponent_bv(self.ctx.ref(), self.as_ast(), biased), self.ctx)
10054 """Indicates whether the numeral is a NaN."""
10057 return Z3_fpa_is_numeral_nan(self.ctx.ref(), self.as_ast())
10059 """Indicates whether the numeral is +oo or -oo."""
10062 return Z3_fpa_is_numeral_inf(self.ctx.ref(), self.as_ast())
10064 """Indicates whether the numeral is +zero or -zero."""
10067 return Z3_fpa_is_numeral_zero(self.ctx.ref(), self.as_ast())
10069 """Indicates whether the numeral is normal."""
10071 def isNormal(self):
10072 return Z3_fpa_is_numeral_normal(self.ctx.ref(), self.as_ast())
10074 """Indicates whether the numeral is subnormal."""
10076 def isSubnormal(self):
10077 return Z3_fpa_is_numeral_subnormal(self.ctx.ref(), self.as_ast())
10079 """Indicates whether the numeral is positive."""
10081 def isPositive(self):
10082 return Z3_fpa_is_numeral_positive(self.ctx.ref(), self.as_ast())
10084 """Indicates whether the numeral is negative."""
10086 def isNegative(self):
10087 return Z3_fpa_is_numeral_negative(self.ctx.ref(), self.as_ast())
10090 The string representation of the numeral.
10092 >>> x = FPVal(20, FPSort(8, 24))
10097 def as_string(self):
10098 s = Z3_get_numeral_string(self.ctx.ref(), self.as_ast())
10099 return ("FPVal(%s, %s)" % (s, self.sort()))
10101 def py_value(self):
10102 bv = simplify(fpToIEEEBV(self))
10103 binary = bv.py_value()
10104 if not isinstance(binary, int):
10106 # Decode the IEEE 754 binary representation
10108 bytes_rep = binary.to_bytes(8, byteorder='big')
10109 return struct.unpack('>d', bytes_rep)[0]
10113 """Return `True` if `a` is a Z3 floating-point expression.
10115 >>> b = FP('b', FPSort(8, 24))
10120 >>> is_fp(Int('x'))
10123 return isinstance(a, FPRef)
10127 """Return `True` if `a` is a Z3 floating-point numeral value.
10129 >>> b = FP('b', FPSort(8, 24))
10132 >>> b = FPVal(1.0, FPSort(8, 24))
10138 return is_fp(a) and _is_numeral(a.ctx, a.ast)
10141def FPSort(ebits, sbits, ctx=None):
10142 """Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used.
10144 >>> Single = FPSort(8, 24)
10145 >>> Double = FPSort(11, 53)
10148 >>> x = Const('x', Single)
10149 >>> eq(x, FP('x', FPSort(8, 24)))
10152 ctx = _get_ctx(ctx)
10153 return FPSortRef(Z3_mk_fpa_sort(ctx.ref(), ebits, sbits), ctx)
10156def _to_float_str(val, exp=0):
10157 if isinstance(val, float):
10158 if math.isnan(val):
10161 sone = math.copysign(1.0, val)
10166 elif val == float("+inf"):
10168 elif val == float("-inf"):
10171 v = val.as_integer_ratio()
10174 rvs = str(num) + "/" + str(den)
10175 res = rvs + "p" + _to_int_str(exp)
10176 elif isinstance(val, bool):
10183 elif isinstance(val, str):
10184 inx = val.find("*(2**")
10187 elif val[-1] == ")":
10189 exp = str(int(val[inx + 5:-1]) + int(exp))
10191 _z3_assert(False, "String does not have floating-point numeral form.")
10193 _z3_assert(False, "Python value cannot be used to create floating-point numerals.")
10197 return res + "p" + exp
10201 """Create a Z3 floating-point NaN term.
10203 >>> s = FPSort(8, 24)
10204 >>> set_fpa_pretty(True)
10207 >>> pb = get_fpa_pretty()
10208 >>> set_fpa_pretty(False)
10210 fpNaN(FPSort(8, 24))
10211 >>> set_fpa_pretty(pb)
10213 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10214 return FPNumRef(Z3_mk_fpa_nan(s.ctx_ref(), s.ast), s.ctx)
10217def fpPlusInfinity(s):
10218 """Create a Z3 floating-point +oo term.
10220 >>> s = FPSort(8, 24)
10221 >>> pb = get_fpa_pretty()
10222 >>> set_fpa_pretty(True)
10223 >>> fpPlusInfinity(s)
10225 >>> set_fpa_pretty(False)
10226 >>> fpPlusInfinity(s)
10227 fpPlusInfinity(FPSort(8, 24))
10228 >>> set_fpa_pretty(pb)
10230 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10231 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, False), s.ctx)
10234def fpMinusInfinity(s):
10235 """Create a Z3 floating-point -oo term."""
10236 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10237 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, True), s.ctx)
10240def fpInfinity(s, negative):
10241 """Create a Z3 floating-point +oo or -oo term."""
10242 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10243 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10244 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, negative), s.ctx)
10248 """Create a Z3 floating-point +0.0 term."""
10249 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10250 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, False), s.ctx)
10254 """Create a Z3 floating-point -0.0 term."""
10255 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10256 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, True), s.ctx)
10259def fpZero(s, negative):
10260 """Create a Z3 floating-point +0.0 or -0.0 term."""
10261 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10262 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10263 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, negative), s.ctx)
10266def FPVal(sig, exp=None, fps=None, ctx=None):
10267 """Return a floating-point value of value `val` and sort `fps`.
10268 If `ctx=None`, then the global context is used.
10270 >>> v = FPVal(20.0, FPSort(8, 24))
10273 >>> print("0x%.8x" % v.exponent_as_long(False))
10275 >>> v = FPVal(2.25, FPSort(8, 24))
10278 >>> v = FPVal(-2.25, FPSort(8, 24))
10281 >>> FPVal(-0.0, FPSort(8, 24))
10283 >>> FPVal(0.0, FPSort(8, 24))
10285 >>> FPVal(+0.0, FPSort(8, 24))
10288 ctx = _get_ctx(ctx)
10289 if is_fp_sort(exp):
10293 fps = _dflt_fps(ctx)
10294 _z3_assert(is_fp_sort(fps), "sort mismatch")
10297 val = _to_float_str(sig)
10298 if val == "NaN" or val == "nan":
10300 elif val == "-0.0":
10301 return fpMinusZero(fps)
10302 elif val == "0.0" or val == "+0.0":
10303 return fpPlusZero(fps)
10304 elif val == "+oo" or val == "+inf" or val == "+Inf":
10305 return fpPlusInfinity(fps)
10306 elif val == "-oo" or val == "-inf" or val == "-Inf":
10307 return fpMinusInfinity(fps)
10309 return FPNumRef(Z3_mk_numeral(ctx.ref(), val, fps.ast), ctx)
10312def FP(name, fpsort, ctx=None):
10313 """Return a floating-point constant named `name`.
10314 `fpsort` is the floating-point sort.
10315 If `ctx=None`, then the global context is used.
10317 >>> x = FP('x', FPSort(8, 24))
10324 >>> word = FPSort(8, 24)
10325 >>> x2 = FP('x', word)
10329 if isinstance(fpsort, FPSortRef) and ctx is None:
10332 ctx = _get_ctx(ctx)
10333 return FPRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), fpsort.ast), ctx)
10336def FPs(names, fpsort, ctx=None):
10337 """Return an array of floating-point constants.
10339 >>> x, y, z = FPs('x y z', FPSort(8, 24))
10346 >>> fpMul(RNE(), fpAdd(RNE(), x, y), z)
10349 ctx = _get_ctx(ctx)
10350 if isinstance(names, str):
10351 names = names.split(" ")
10352 return [FP(name, fpsort, ctx) for name in names]
10355def fpAbs(a, ctx=None):
10356 """Create a Z3 floating-point absolute value expression.
10358 >>> s = FPSort(8, 24)
10360 >>> x = FPVal(1.0, s)
10363 >>> y = FPVal(-20.0, s)
10367 fpAbs(-1.25*(2**4))
10368 >>> fpAbs(-1.25*(2**4))
10369 fpAbs(-1.25*(2**4))
10370 >>> fpAbs(x).sort()
10373 ctx = _get_ctx(ctx)
10374 [a] = _coerce_fp_expr_list([a], ctx)
10375 return FPRef(Z3_mk_fpa_abs(ctx.ref(), a.as_ast()), ctx)
10378def fpNeg(a, ctx=None):
10379 """Create a Z3 floating-point addition expression.
10381 >>> s = FPSort(8, 24)
10386 >>> fpNeg(x).sort()
10389 ctx = _get_ctx(ctx)
10390 [a] = _coerce_fp_expr_list([a], ctx)
10391 return FPRef(Z3_mk_fpa_neg(ctx.ref(), a.as_ast()), ctx)
10394def _mk_fp_unary(f, rm, a, ctx):
10395 ctx = _get_ctx(ctx)
10396 [a] = _coerce_fp_expr_list([a], ctx)
10398 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10399 _z3_assert(is_fp(a), "Second argument must be a Z3 floating-point expression")
10400 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast()), ctx)
10403def _mk_fp_unary_pred(f, a, ctx):
10404 ctx = _get_ctx(ctx)
10405 [a] = _coerce_fp_expr_list([a], ctx)
10407 _z3_assert(is_fp(a), "First argument must be a Z3 floating-point expression")
10408 return BoolRef(f(ctx.ref(), a.as_ast()), ctx)
10411def _mk_fp_bin(f, rm, a, b, ctx):
10412 ctx = _get_ctx(ctx)
10413 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10415 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10416 _z3_assert(is_fp(a) or is_fp(b), "Second or third argument must be a Z3 floating-point expression")
10417 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast()), ctx)
10420def _mk_fp_bin_norm(f, a, b, ctx):
10421 ctx = _get_ctx(ctx)
10422 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10424 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10425 return FPRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10428def _mk_fp_bin_pred(f, a, b, ctx):
10429 ctx = _get_ctx(ctx)
10430 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10432 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10433 return BoolRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10436def _mk_fp_tern(f, rm, a, b, c, ctx):
10437 ctx = _get_ctx(ctx)
10438 [a, b, c] = _coerce_fp_expr_list([a, b, c], ctx)
10440 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10441 _z3_assert(is_fp(a) or is_fp(b) or is_fp(
10442 c), "Second, third or fourth argument must be a Z3 floating-point expression")
10443 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
10446def fpAdd(rm, a, b, ctx=None):
10447 """Create a Z3 floating-point addition expression.
10449 >>> s = FPSort(8, 24)
10453 >>> fpAdd(rm, x, y)
10455 >>> fpAdd(RTZ(), x, y) # default rounding mode is RTZ
10457 >>> fpAdd(rm, x, y).sort()
10460 return _mk_fp_bin(Z3_mk_fpa_add, rm, a, b, ctx)
10463def fpSub(rm, a, b, ctx=None):
10464 """Create a Z3 floating-point subtraction expression.
10466 >>> s = FPSort(8, 24)
10470 >>> fpSub(rm, x, y)
10472 >>> fpSub(rm, x, y).sort()
10475 return _mk_fp_bin(Z3_mk_fpa_sub, rm, a, b, ctx)
10478def fpMul(rm, a, b, ctx=None):
10479 """Create a Z3 floating-point multiplication expression.
10481 >>> s = FPSort(8, 24)
10485 >>> fpMul(rm, x, y)
10487 >>> fpMul(rm, x, y).sort()
10490 return _mk_fp_bin(Z3_mk_fpa_mul, rm, a, b, ctx)
10493def fpDiv(rm, a, b, ctx=None):
10494 """Create a Z3 floating-point division expression.
10496 >>> s = FPSort(8, 24)
10500 >>> fpDiv(rm, x, y)
10502 >>> fpDiv(rm, x, y).sort()
10505 return _mk_fp_bin(Z3_mk_fpa_div, rm, a, b, ctx)
10508def fpRem(a, b, ctx=None):
10509 """Create a Z3 floating-point remainder expression.
10511 >>> s = FPSort(8, 24)
10516 >>> fpRem(x, y).sort()
10519 return _mk_fp_bin_norm(Z3_mk_fpa_rem, a, b, ctx)
10522def fpMin(a, b, ctx=None):
10523 """Create a Z3 floating-point minimum expression.
10525 >>> s = FPSort(8, 24)
10531 >>> fpMin(x, y).sort()
10534 return _mk_fp_bin_norm(Z3_mk_fpa_min, a, b, ctx)
10537def fpMax(a, b, ctx=None):
10538 """Create a Z3 floating-point maximum expression.
10540 >>> s = FPSort(8, 24)
10546 >>> fpMax(x, y).sort()
10549 return _mk_fp_bin_norm(Z3_mk_fpa_max, a, b, ctx)
10552def fpFMA(rm, a, b, c, ctx=None):
10553 """Create a Z3 floating-point fused multiply-add expression.
10555 return _mk_fp_tern(Z3_mk_fpa_fma, rm, a, b, c, ctx)
10558def fpSqrt(rm, a, ctx=None):
10559 """Create a Z3 floating-point square root expression.
10561 return _mk_fp_unary(Z3_mk_fpa_sqrt, rm, a, ctx)
10564def fpRoundToIntegral(rm, a, ctx=None):
10565 """Create a Z3 floating-point roundToIntegral expression.
10567 return _mk_fp_unary(Z3_mk_fpa_round_to_integral, rm, a, ctx)
10570def fpIsNaN(a, ctx=None):
10571 """Create a Z3 floating-point isNaN expression.
10573 >>> s = FPSort(8, 24)
10579 return _mk_fp_unary_pred(Z3_mk_fpa_is_nan, a, ctx)
10582def fpIsInf(a, ctx=None):
10583 """Create a Z3 floating-point isInfinite expression.
10585 >>> s = FPSort(8, 24)
10590 return _mk_fp_unary_pred(Z3_mk_fpa_is_infinite, a, ctx)
10593def fpIsZero(a, ctx=None):
10594 """Create a Z3 floating-point isZero expression.
10596 return _mk_fp_unary_pred(Z3_mk_fpa_is_zero, a, ctx)
10599def fpIsNormal(a, ctx=None):
10600 """Create a Z3 floating-point isNormal expression.
10602 return _mk_fp_unary_pred(Z3_mk_fpa_is_normal, a, ctx)
10605def fpIsSubnormal(a, ctx=None):
10606 """Create a Z3 floating-point isSubnormal expression.
10608 return _mk_fp_unary_pred(Z3_mk_fpa_is_subnormal, a, ctx)
10611def fpIsNegative(a, ctx=None):
10612 """Create a Z3 floating-point isNegative expression.
10614 return _mk_fp_unary_pred(Z3_mk_fpa_is_negative, a, ctx)
10617def fpIsPositive(a, ctx=None):
10618 """Create a Z3 floating-point isPositive expression.
10620 return _mk_fp_unary_pred(Z3_mk_fpa_is_positive, a, ctx)
10623def _check_fp_args(a, b):
10625 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10628def fpLT(a, b, ctx=None):
10629 """Create the Z3 floating-point expression `other < self`.
10631 >>> x, y = FPs('x y', FPSort(8, 24))
10634 >>> (x < y).sexpr()
10637 return _mk_fp_bin_pred(Z3_mk_fpa_lt, a, b, ctx)
10640def fpLEQ(a, b, ctx=None):
10641 """Create the Z3 floating-point expression `other <= self`.
10643 >>> x, y = FPs('x y', FPSort(8, 24))
10646 >>> (x <= y).sexpr()
10649 return _mk_fp_bin_pred(Z3_mk_fpa_leq, a, b, ctx)
10652def fpGT(a, b, ctx=None):
10653 """Create the Z3 floating-point expression `other > self`.
10655 >>> x, y = FPs('x y', FPSort(8, 24))
10658 >>> (x > y).sexpr()
10661 return _mk_fp_bin_pred(Z3_mk_fpa_gt, a, b, ctx)
10664def fpGEQ(a, b, ctx=None):
10665 """Create the Z3 floating-point expression `other >= self`.
10667 >>> x, y = FPs('x y', FPSort(8, 24))
10670 >>> (x >= y).sexpr()
10673 return _mk_fp_bin_pred(Z3_mk_fpa_geq, a, b, ctx)
10676def fpEQ(a, b, ctx=None):
10677 """Create the Z3 floating-point expression `fpEQ(other, self)`.
10679 >>> x, y = FPs('x y', FPSort(8, 24))
10682 >>> fpEQ(x, y).sexpr()
10685 return _mk_fp_bin_pred(Z3_mk_fpa_eq, a, b, ctx)
10688def fpNEQ(a, b, ctx=None):
10689 """Create the Z3 floating-point expression `Not(fpEQ(other, self))`.
10691 >>> x, y = FPs('x y', FPSort(8, 24))
10694 >>> (x != y).sexpr()
10697 return Not(fpEQ(a, b, ctx))
10700def fpFP(sgn, exp, sig, ctx=None):
10701 """Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectors sgn, sig, and exp.
10703 >>> s = FPSort(8, 24)
10704 >>> x = fpFP(BitVecVal(1, 1), BitVecVal(2**7-1, 8), BitVecVal(2**22, 23))
10706 fpFP(1, 127, 4194304)
10707 >>> xv = FPVal(-1.5, s)
10710 >>> slvr = Solver()
10711 >>> slvr.add(fpEQ(x, xv))
10714 >>> xv = FPVal(+1.5, s)
10717 >>> slvr = Solver()
10718 >>> slvr.add(fpEQ(x, xv))
10722 _z3_assert(is_bv(sgn) and is_bv(exp) and is_bv(sig), "sort mismatch")
10723 _z3_assert(sgn.sort().size() == 1, "sort mismatch")
10724 ctx = _get_ctx(ctx)
10725 _z3_assert(ctx == sgn.ctx == exp.ctx == sig.ctx, "context mismatch")
10726 return FPRef(Z3_mk_fpa_fp(ctx.ref(), sgn.ast, exp.ast, sig.ast), ctx)
10729def fpToFP(a1, a2=None, a3=None, ctx=None):
10730 """Create a Z3 floating-point conversion expression from other term sorts
10733 From a bit-vector term in IEEE 754-2008 format:
10734 >>> x = FPVal(1.0, Float32())
10735 >>> x_bv = fpToIEEEBV(x)
10736 >>> simplify(fpToFP(x_bv, Float32()))
10739 From a floating-point term with different precision:
10740 >>> x = FPVal(1.0, Float32())
10741 >>> x_db = fpToFP(RNE(), x, Float64())
10746 >>> x_r = RealVal(1.5)
10747 >>> simplify(fpToFP(RNE(), x_r, Float32()))
10750 From a signed bit-vector term:
10751 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10752 >>> simplify(fpToFP(RNE(), x_signed, Float32()))
10755 ctx = _get_ctx(ctx)
10756 if is_bv(a1) and is_fp_sort(a2):
10757 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), a1.ast, a2.ast), ctx)
10758 elif is_fprm(a1) and is_fp(a2) and is_fp_sort(a3):
10759 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10760 elif is_fprm(a1) and is_real(a2) and is_fp_sort(a3):
10761 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10762 elif is_fprm(a1) and is_bv(a2) and is_fp_sort(a3):
10763 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10765 raise Z3Exception("Unsupported combination of arguments for conversion to floating-point term.")
10768def fpBVToFP(v, sort, ctx=None):
10769 """Create a Z3 floating-point conversion expression that represents the
10770 conversion from a bit-vector term to a floating-point term.
10772 >>> x_bv = BitVecVal(0x3F800000, 32)
10773 >>> x_fp = fpBVToFP(x_bv, Float32())
10779 _z3_assert(is_bv(v), "First argument must be a Z3 bit-vector expression")
10780 _z3_assert(is_fp_sort(sort), "Second argument must be a Z3 floating-point sort.")
10781 ctx = _get_ctx(ctx)
10782 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), v.ast, sort.ast), ctx)
10785def fpFPToFP(rm, v, sort, ctx=None):
10786 """Create a Z3 floating-point conversion expression that represents the
10787 conversion from a floating-point term to a floating-point term of different precision.
10789 >>> x_sgl = FPVal(1.0, Float32())
10790 >>> x_dbl = fpFPToFP(RNE(), x_sgl, Float64())
10793 >>> simplify(x_dbl)
10798 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10799 _z3_assert(is_fp(v), "Second argument must be a Z3 floating-point expression.")
10800 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10801 ctx = _get_ctx(ctx)
10802 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10805def fpRealToFP(rm, v, sort, ctx=None):
10806 """Create a Z3 floating-point conversion expression that represents the
10807 conversion from a real term to a floating-point term.
10809 >>> x_r = RealVal(1.5)
10810 >>> x_fp = fpRealToFP(RNE(), x_r, Float32())
10816 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10817 _z3_assert(is_real(v), "Second argument must be a Z3 expression or real sort.")
10818 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10819 ctx = _get_ctx(ctx)
10820 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10823def fpSignedToFP(rm, v, sort, ctx=None):
10824 """Create a Z3 floating-point conversion expression that represents the
10825 conversion from a signed bit-vector term (encoding an integer) to a floating-point term.
10827 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10828 >>> x_fp = fpSignedToFP(RNE(), x_signed, Float32())
10830 fpToFP(RNE(), 4294967291)
10834 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10835 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10836 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10837 ctx = _get_ctx(ctx)
10838 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10841def fpUnsignedToFP(rm, v, sort, ctx=None):
10842 """Create a Z3 floating-point conversion expression that represents the
10843 conversion from an unsigned bit-vector term (encoding an integer) to a floating-point term.
10845 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10846 >>> x_fp = fpUnsignedToFP(RNE(), x_signed, Float32())
10848 fpToFPUnsigned(RNE(), 4294967291)
10852 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10853 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10854 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10855 ctx = _get_ctx(ctx)
10856 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10859def fpToFPUnsigned(rm, x, s, ctx=None):
10860 """Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression."""
10862 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10863 _z3_assert(is_bv(x), "Second argument must be a Z3 bit-vector expression")
10864 _z3_assert(is_fp_sort(s), "Third argument must be Z3 floating-point sort")
10865 ctx = _get_ctx(ctx)
10866 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, x.ast, s.ast), ctx)
10869def fpToSBV(rm, x, s, ctx=None):
10870 """Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector.
10872 >>> x = FP('x', FPSort(8, 24))
10873 >>> y = fpToSBV(RTZ(), x, BitVecSort(32))
10874 >>> print(is_fp(x))
10876 >>> print(is_bv(y))
10878 >>> print(is_fp(y))
10880 >>> print(is_bv(x))
10884 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10885 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10886 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10887 ctx = _get_ctx(ctx)
10888 return BitVecRef(Z3_mk_fpa_to_sbv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10891def fpToUBV(rm, x, s, ctx=None):
10892 """Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector.
10894 >>> x = FP('x', FPSort(8, 24))
10895 >>> y = fpToUBV(RTZ(), x, BitVecSort(32))
10896 >>> print(is_fp(x))
10898 >>> print(is_bv(y))
10900 >>> print(is_fp(y))
10902 >>> print(is_bv(x))
10906 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10907 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10908 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10909 ctx = _get_ctx(ctx)
10910 return BitVecRef(Z3_mk_fpa_to_ubv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10913def fpToReal(x, ctx=None):
10914 """Create a Z3 floating-point conversion expression, from floating-point expression to real.
10916 >>> x = FP('x', FPSort(8, 24))
10917 >>> y = fpToReal(x)
10918 >>> print(is_fp(x))
10920 >>> print(is_real(y))
10922 >>> print(is_fp(y))
10924 >>> print(is_real(x))
10928 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10929 ctx = _get_ctx(ctx)
10930 return ArithRef(Z3_mk_fpa_to_real(ctx.ref(), x.ast), ctx)
10933def fpToIEEEBV(x, ctx=None):
10934 """\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
10936 The size of the resulting bit-vector is automatically determined.
10938 Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
10939 knows only one NaN and it will always produce the same bit-vector representation of
10942 >>> x = FP('x', FPSort(8, 24))
10943 >>> y = fpToIEEEBV(x)
10944 >>> print(is_fp(x))
10946 >>> print(is_bv(y))
10948 >>> print(is_fp(y))
10950 >>> print(is_bv(x))
10954 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10955 ctx = _get_ctx(ctx)
10956 return BitVecRef(Z3_mk_fpa_to_ieee_bv(ctx.ref(), x.ast), ctx)
10959#########################################
10961# Strings, Sequences and Regular expressions
10963#########################################
10965class SeqSortRef(SortRef):
10966 """Sequence sort."""
10968 def is_string(self):
10969 """Determine if sort is a string
10970 >>> s = StringSort()
10973 >>> s = SeqSort(IntSort())
10977 return Z3_is_string_sort(self.ctx_ref(), self.ast)
10980 return _to_sort_ref(Z3_get_seq_sort_basis(self.ctx_ref(), self.ast), self.ctx)
10982class CharSortRef(SortRef):
10983 """Character sort."""
10986def StringSort(ctx=None):
10987 """Create a string sort
10988 >>> s = StringSort()
10992 ctx = _get_ctx(ctx)
10993 return SeqSortRef(Z3_mk_string_sort(ctx.ref()), ctx)
10995def CharSort(ctx=None):
10996 """Create a character sort
10997 >>> ch = CharSort()
11001 ctx = _get_ctx(ctx)
11002 return CharSortRef(Z3_mk_char_sort(ctx.ref()), ctx)
11006 """Create a sequence sort over elements provided in the argument
11007 >>> s = SeqSort(IntSort())
11008 >>> s == Unit(IntVal(1)).sort()
11011 return SeqSortRef(Z3_mk_seq_sort(s.ctx_ref(), s.ast), s.ctx)
11014class SeqRef(ExprRef):
11015 """Sequence expression."""
11018 return SeqSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
11020 def __add__(self, other):
11021 return Concat(self, other)
11023 def __radd__(self, other):
11024 return Concat(other, self)
11026 def __getitem__(self, i):
11028 i = IntVal(i, self.ctx)
11029 return _to_expr_ref(Z3_mk_seq_nth(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
11033 i = IntVal(i, self.ctx)
11034 return SeqRef(Z3_mk_seq_at(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
11036 def is_string(self):
11037 return Z3_is_string_sort(self.ctx_ref(), Z3_get_sort(self.ctx_ref(), self.as_ast()))
11039 def is_string_value(self):
11040 return Z3_is_string(self.ctx_ref(), self.as_ast())
11042 def as_string(self):
11043 """Return a string representation of sequence expression."""
11044 if self.is_string_value():
11045 string_length = ctypes.c_uint()
11046 chars = Z3_get_lstring(self.ctx_ref(), self.as_ast(), byref(string_length))
11047 return string_at(chars, size=string_length.value).decode("latin-1")
11048 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
11050 def py_value(self):
11051 return self.as_string()
11053 def __le__(self, other):
11054 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
11056 def __lt__(self, other):
11057 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
11059 def __ge__(self, other):
11060 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
11062 def __gt__(self, other):
11063 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
11066def _coerce_char(ch, ctx=None):
11067 if isinstance(ch, str):
11068 ctx = _get_ctx(ctx)
11069 ch = CharVal(ch, ctx)
11070 if not is_expr(ch):
11071 raise Z3Exception("Character expression expected")
11074class CharRef(ExprRef):
11075 """Character expression."""
11077 def __le__(self, other):
11078 other = _coerce_char(other, self.ctx)
11079 return _to_expr_ref(Z3_mk_char_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
11082 return _to_expr_ref(Z3_mk_char_to_int(self.ctx_ref(), self.as_ast()), self.ctx)
11085 return _to_expr_ref(Z3_mk_char_to_bv(self.ctx_ref(), self.as_ast()), self.ctx)
11087 def is_digit(self):
11088 return _to_expr_ref(Z3_mk_char_is_digit(self.ctx_ref(), self.as_ast()), self.ctx)
11091def CharVal(ch, ctx=None):
11092 ctx = _get_ctx(ctx)
11093 if isinstance(ch, str):
11095 if not isinstance(ch, int):
11096 raise Z3Exception("character value should be an ordinal")
11097 return _to_expr_ref(Z3_mk_char(ctx.ref(), ch), ctx)
11100 if not is_expr(bv):
11101 raise Z3Exception("Bit-vector expression needed")
11102 return _to_expr_ref(Z3_mk_char_from_bv(bv.ctx_ref(), bv.as_ast()), bv.ctx)
11104def CharToBv(ch, ctx=None):
11105 ch = _coerce_char(ch, ctx)
11108def CharToInt(ch, ctx=None):
11109 ch = _coerce_char(ch, ctx)
11112def CharIsDigit(ch, ctx=None):
11113 ch = _coerce_char(ch, ctx)
11114 return ch.is_digit()
11116def _coerce_seq(s, ctx=None):
11117 if isinstance(s, str):
11118 ctx = _get_ctx(ctx)
11119 s = StringVal(s, ctx)
11121 raise Z3Exception("Non-expression passed as a sequence")
11123 raise Z3Exception("Non-sequence passed as a sequence")
11127def _get_ctx2(a, b, ctx=None):
11138 """Return `True` if `a` is a Z3 sequence expression.
11139 >>> print (is_seq(Unit(IntVal(0))))
11141 >>> print (is_seq(StringVal("abc")))
11144 return isinstance(a, SeqRef)
11147def is_string(a: Any) -> bool:
11148 """Return `True` if `a` is a Z3 string expression.
11149 >>> print (is_string(StringVal("ab")))
11152 return isinstance(a, SeqRef) and a.is_string()
11155def is_string_value(a: Any) -> bool:
11156 """return 'True' if 'a' is a Z3 string constant expression.
11157 >>> print (is_string_value(StringVal("a")))
11159 >>> print (is_string_value(StringVal("a") + StringVal("b")))
11162 return isinstance(a, SeqRef) and a.is_string_value()
11164def StringVal(s, ctx=None):
11165 """create a string expression"""
11166 s = "".join(str(ch) if 32 <= ord(ch) and ord(ch) < 127 else "\\u{%x}" % (ord(ch)) for ch in s)
11167 ctx = _get_ctx(ctx)
11168 return SeqRef(Z3_mk_string(ctx.ref(), s), ctx)
11171def String(name, ctx=None):
11172 """Return a string constant named `name`. If `ctx=None`, then the global context is used.
11174 >>> x = String('x')
11176 ctx = _get_ctx(ctx)
11177 return SeqRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), StringSort(ctx).ast), ctx)
11180def Strings(names, ctx=None):
11181 """Return a tuple of String constants. """
11182 ctx = _get_ctx(ctx)
11183 if isinstance(names, str):
11184 names = names.split(" ")
11185 return [String(name, ctx) for name in names]
11188def SubString(s, offset, length):
11189 """Extract substring or subsequence starting at offset"""
11190 return Extract(s, offset, length)
11193def SubSeq(s, offset, length):
11194 """Extract substring or subsequence starting at offset"""
11195 return Extract(s, offset, length)
11199 """Create the empty sequence of the given sort
11200 >>> e = Empty(StringSort())
11201 >>> e2 = StringVal("")
11202 >>> print(e.eq(e2))
11204 >>> e3 = Empty(SeqSort(IntSort()))
11207 >>> e4 = Empty(ReSort(SeqSort(IntSort())))
11209 Empty(ReSort(Seq(Int)))
11211 if isinstance(s, SeqSortRef):
11212 return SeqRef(Z3_mk_seq_empty(s.ctx_ref(), s.ast), s.ctx)
11213 if isinstance(s, ReSortRef):
11214 return ReRef(Z3_mk_re_empty(s.ctx_ref(), s.ast), s.ctx)
11215 raise Z3Exception("Non-sequence, non-regular expression sort passed to Empty")
11219 """Create the regular expression that accepts the universal language
11220 >>> e = Full(ReSort(SeqSort(IntSort())))
11222 Full(ReSort(Seq(Int)))
11223 >>> e1 = Full(ReSort(StringSort()))
11225 Full(ReSort(String))
11227 if isinstance(s, ReSortRef):
11228 return ReRef(Z3_mk_re_full(s.ctx_ref(), s.ast), s.ctx)
11229 raise Z3Exception("Non-sequence, non-regular expression sort passed to Full")
11234 """Create a singleton sequence"""
11235 return SeqRef(Z3_mk_seq_unit(a.ctx_ref(), a.as_ast()), a.ctx)
11239 """Check if 'a' is a prefix of 'b'
11240 >>> s1 = PrefixOf("ab", "abc")
11243 >>> s2 = PrefixOf("bc", "abc")
11247 ctx = _get_ctx2(a, b)
11248 a = _coerce_seq(a, ctx)
11249 b = _coerce_seq(b, ctx)
11250 return BoolRef(Z3_mk_seq_prefix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11254 """Check if 'a' is a suffix of 'b'
11255 >>> s1 = SuffixOf("ab", "abc")
11258 >>> s2 = SuffixOf("bc", "abc")
11262 ctx = _get_ctx2(a, b)
11263 a = _coerce_seq(a, ctx)
11264 b = _coerce_seq(b, ctx)
11265 return BoolRef(Z3_mk_seq_suffix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11269 """Check if 'a' contains 'b'
11270 >>> s1 = Contains("abc", "ab")
11273 >>> s2 = Contains("abc", "bc")
11276 >>> x, y, z = Strings('x y z')
11277 >>> s3 = Contains(Concat(x,y,z), y)
11281 ctx = _get_ctx2(a, b)
11282 a = _coerce_seq(a, ctx)
11283 b = _coerce_seq(b, ctx)
11284 return BoolRef(Z3_mk_seq_contains(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11287def Replace(s, src, dst):
11288 """Replace the first occurrence of 'src' by 'dst' in 's'
11289 >>> r = Replace("aaa", "a", "b")
11293 ctx = _get_ctx2(dst, s)
11294 if ctx is None and is_expr(src):
11296 src = _coerce_seq(src, ctx)
11297 dst = _coerce_seq(dst, ctx)
11298 s = _coerce_seq(s, ctx)
11299 return SeqRef(Z3_mk_seq_replace(src.ctx_ref(), s.as_ast(), src.as_ast(), dst.as_ast()), s.ctx)
11302def IndexOf(s, substr, offset=None):
11303 """Retrieve the index of substring within a string starting at a specified offset.
11304 >>> simplify(IndexOf("abcabc", "bc", 0))
11306 >>> simplify(IndexOf("abcabc", "bc", 2))
11312 if is_expr(offset):
11314 ctx = _get_ctx2(s, substr, ctx)
11315 s = _coerce_seq(s, ctx)
11316 substr = _coerce_seq(substr, ctx)
11317 if _is_int(offset):
11318 offset = IntVal(offset, ctx)
11319 return ArithRef(Z3_mk_seq_index(s.ctx_ref(), s.as_ast(), substr.as_ast(), offset.as_ast()), s.ctx)
11322def LastIndexOf(s, substr):
11323 """Retrieve the last index of substring within a string"""
11325 ctx = _get_ctx2(s, substr, ctx)
11326 s = _coerce_seq(s, ctx)
11327 substr = _coerce_seq(substr, ctx)
11328 return ArithRef(Z3_mk_seq_last_index(s.ctx_ref(), s.as_ast(), substr.as_ast()), s.ctx)
11332 """Obtain the length of a sequence 's'
11333 >>> l = Length(StringVal("abc"))
11338 return ArithRef(Z3_mk_seq_length(s.ctx_ref(), s.as_ast()), s.ctx)
11341 """Map function 'f' over sequence 's'"""
11342 ctx = _get_ctx2(f, s)
11343 s = _coerce_seq(s, ctx)
11344 return _to_expr_ref(Z3_mk_seq_map(s.ctx_ref(), f.as_ast(), s.as_ast()), ctx)
11346def SeqMapI(f, i, s):
11347 """Map function 'f' over sequence 's' at index 'i'"""
11348 ctx = _get_ctx2(f, s)
11349 s = _coerce_seq(s, ctx)
11352 return _to_expr_ref(Z3_mk_seq_mapi(s.ctx_ref(), f.as_ast(), i.as_ast(), s.as_ast()), ctx)
11354def SeqFoldLeft(f, a, s):
11355 ctx = _get_ctx2(f, s)
11356 s = _coerce_seq(s, ctx)
11358 return _to_expr_ref(Z3_mk_seq_foldl(s.ctx_ref(), f.as_ast(), a.as_ast(), s.as_ast()), ctx)
11360def SeqFoldLeftI(f, i, a, s):
11361 ctx = _get_ctx2(f, s)
11362 s = _coerce_seq(s, ctx)
11365 return _to_expr_ref(Z3_mk_seq_foldli(s.ctx_ref(), f.as_ast(), i.as_ast(), a.as_ast(), s.as_ast()), ctx)
11368 """Convert string expression to integer
11369 >>> a = StrToInt("1")
11370 >>> simplify(1 == a)
11372 >>> b = StrToInt("2")
11373 >>> simplify(1 == b)
11375 >>> c = StrToInt(IntToStr(2))
11376 >>> simplify(1 == c)
11380 return ArithRef(Z3_mk_str_to_int(s.ctx_ref(), s.as_ast()), s.ctx)
11384 """Convert integer expression to string"""
11387 return SeqRef(Z3_mk_int_to_str(s.ctx_ref(), s.as_ast()), s.ctx)
11391 """Convert a unit length string to integer code"""
11394 return ArithRef(Z3_mk_string_to_code(s.ctx_ref(), s.as_ast()), s.ctx)
11397 """Convert code to a string"""
11400 return SeqRef(Z3_mk_string_from_code(c.ctx_ref(), c.as_ast()), c.ctx)
11402def Re(s, ctx=None):
11403 """The regular expression that accepts sequence 's'
11405 >>> s2 = Re(StringVal("ab"))
11406 >>> s3 = Re(Unit(BoolVal(True)))
11408 s = _coerce_seq(s, ctx)
11409 return ReRef(Z3_mk_seq_to_re(s.ctx_ref(), s.as_ast()), s.ctx)
11412# Regular expressions
11414class ReSortRef(SortRef):
11415 """Regular expression sort."""
11418 return _to_sort_ref(Z3_get_re_sort_basis(self.ctx_ref(), self.ast), self.ctx)
11423 return ReSortRef(Z3_mk_re_sort(s.ctx.ref(), s.ast), s.ctx)
11424 if s is None or isinstance(s, Context):
11426 return ReSortRef(Z3_mk_re_sort(ctx.ref(), Z3_mk_string_sort(ctx.ref())), s.ctx)
11427 raise Z3Exception("Regular expression sort constructor expects either a string or a context or no argument")
11430class ReRef(ExprRef):
11431 """Regular expressions."""
11433 def __add__(self, other):
11434 return Union(self, other)
11438 return isinstance(s, ReRef)
11442 """Create regular expression membership test
11443 >>> re = Union(Re("a"),Re("b"))
11444 >>> print (simplify(InRe("a", re)))
11446 >>> print (simplify(InRe("b", re)))
11448 >>> print (simplify(InRe("c", re)))
11451 s = _coerce_seq(s, re.ctx)
11452 return BoolRef(Z3_mk_seq_in_re(s.ctx_ref(), s.as_ast(), re.as_ast()), s.ctx)
11456 """Create union of regular expressions.
11457 >>> re = Union(Re("a"), Re("b"), Re("c"))
11458 >>> print (simplify(InRe("d", re)))
11461 args = _get_args(args)
11464 _z3_assert(sz > 0, "At least one argument expected.")
11465 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11470 for i in range(sz):
11471 v[i] = args[i].as_ast()
11472 return ReRef(Z3_mk_re_union(ctx.ref(), sz, v), ctx)
11475def Intersect(*args):
11476 """Create intersection of regular expressions.
11477 >>> re = Intersect(Re("a"), Re("b"), Re("c"))
11479 args = _get_args(args)
11482 _z3_assert(sz > 0, "At least one argument expected.")
11483 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11488 for i in range(sz):
11489 v[i] = args[i].as_ast()
11490 return ReRef(Z3_mk_re_intersect(ctx.ref(), sz, v), ctx)
11494 """Create the regular expression accepting one or more repetitions of argument.
11495 >>> re = Plus(Re("a"))
11496 >>> print(simplify(InRe("aa", re)))
11498 >>> print(simplify(InRe("ab", re)))
11500 >>> print(simplify(InRe("", re)))
11504 _z3_assert(is_expr(re), "expression expected")
11505 return ReRef(Z3_mk_re_plus(re.ctx_ref(), re.as_ast()), re.ctx)
11509 """Create the regular expression that optionally accepts the argument.
11510 >>> re = Option(Re("a"))
11511 >>> print(simplify(InRe("a", re)))
11513 >>> print(simplify(InRe("", re)))
11515 >>> print(simplify(InRe("aa", re)))
11519 _z3_assert(is_expr(re), "expression expected")
11520 return ReRef(Z3_mk_re_option(re.ctx_ref(), re.as_ast()), re.ctx)
11524 """Create the complement regular expression."""
11525 return ReRef(Z3_mk_re_complement(re.ctx_ref(), re.as_ast()), re.ctx)
11529 """Create the regular expression accepting zero or more repetitions of argument.
11530 >>> re = Star(Re("a"))
11531 >>> print(simplify(InRe("aa", re)))
11533 >>> print(simplify(InRe("ab", re)))
11535 >>> print(simplify(InRe("", re)))
11539 _z3_assert(is_expr(re), "expression expected")
11540 return ReRef(Z3_mk_re_star(re.ctx_ref(), re.as_ast()), re.ctx)
11543def Loop(re, lo, hi=0):
11544 """Create the regular expression accepting between a lower and upper bound repetitions
11545 >>> re = Loop(Re("a"), 1, 3)
11546 >>> print(simplify(InRe("aa", re)))
11548 >>> print(simplify(InRe("aaaa", re)))
11550 >>> print(simplify(InRe("", re)))
11554 _z3_assert(is_expr(re), "expression expected")
11555 return ReRef(Z3_mk_re_loop(re.ctx_ref(), re.as_ast(), lo, hi), re.ctx)
11558def Range(lo, hi, ctx=None):
11559 """Create the range regular expression over two sequences of length 1
11560 >>> range = Range("a","z")
11561 >>> print(simplify(InRe("b", range)))
11563 >>> print(simplify(InRe("bb", range)))
11566 lo = _coerce_seq(lo, ctx)
11567 hi = _coerce_seq(hi, ctx)
11569 _z3_assert(is_expr(lo), "expression expected")
11570 _z3_assert(is_expr(hi), "expression expected")
11571 return ReRef(Z3_mk_re_range(lo.ctx_ref(), lo.ast, hi.ast), lo.ctx)
11573def Diff(a, b, ctx=None):
11574 """Create the difference regular expression
11577 _z3_assert(is_expr(a), "expression expected")
11578 _z3_assert(is_expr(b), "expression expected")
11579 return ReRef(Z3_mk_re_diff(a.ctx_ref(), a.ast, b.ast), a.ctx)
11581def AllChar(regex_sort, ctx=None):
11582 """Create a regular expression that accepts all single character strings
11584 return ReRef(Z3_mk_re_allchar(regex_sort.ctx_ref(), regex_sort.ast), regex_sort.ctx)
11589def PartialOrder(a, index):
11590 return FuncDeclRef(Z3_mk_partial_order(a.ctx_ref(), a.ast, index), a.ctx)
11593def LinearOrder(a, index):
11594 return FuncDeclRef(Z3_mk_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11597def TreeOrder(a, index):
11598 return FuncDeclRef(Z3_mk_tree_order(a.ctx_ref(), a.ast, index), a.ctx)
11601def PiecewiseLinearOrder(a, index):
11602 return FuncDeclRef(Z3_mk_piecewise_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11605def TransitiveClosure(f):
11606 """Given a binary relation R, such that the two arguments have the same sort
11607 create the transitive closure relation R+.
11608 The transitive closure R+ is a new relation.
11610 return FuncDeclRef(Z3_mk_transitive_closure(f.ctx_ref(), f.ast), f.ctx)
11614 super(ctypes.c_void_p, ast).__init__(ptr)
11617def to_ContextObj(ptr,):
11618 ctx = ContextObj(ptr)
11619 super(ctypes.c_void_p, ctx).__init__(ptr)
11622def to_AstVectorObj(ptr,):
11623 v = AstVectorObj(ptr)
11624 super(ctypes.c_void_p, v).__init__(ptr)
11627# NB. my-hacky-class only works for a single instance of OnClause
11628# it should be replaced with a proper correlation between OnClause
11629# and object references that can be passed over the FFI.
11630# for UserPropagator we use a global dictionary, which isn't great code.
11632_my_hacky_class = None
11633def on_clause_eh(ctx, p, n, dep, clause):
11634 onc = _my_hacky_class
11635 p = _to_expr_ref(to_Ast(p), onc.ctx)
11636 clause = AstVector(to_AstVectorObj(clause), onc.ctx)
11637 deps = [dep[i] for i in range(n)]
11638 onc.on_clause(p, deps, clause)
11640_on_clause_eh = Z3_on_clause_eh(on_clause_eh)
11643 def __init__(self, s, on_clause):
11646 self.on_clause = on_clause
11648 global _my_hacky_class
11649 _my_hacky_class = self
11650 Z3_solver_register_on_clause(self.ctx.ref(), self.s.solver, self.idx, _on_clause_eh)
11654 def __init__(self):
11658 def set_threaded(self):
11659 if self.lock is None:
11661 self.lock = threading.Lock()
11663 def get(self, ctx):
11666 r = self.bases[ctx]
11668 r = self.bases[ctx]
11671 def set(self, ctx, r):
11674 self.bases[ctx] = r
11676 self.bases[ctx] = r
11678 def insert(self, r):
11681 id = len(self.bases) + 3
11684 id = len(self.bases) + 3
11689_prop_closures = None
11692def ensure_prop_closures():
11693 global _prop_closures
11694 if _prop_closures is None:
11695 _prop_closures = PropClosures()
11698def user_prop_push(ctx, cb):
11699 prop = _prop_closures.get(ctx)
11704def user_prop_pop(ctx, cb, num_scopes):
11705 prop = _prop_closures.get(ctx)
11707 prop.pop(num_scopes)
11710def user_prop_fresh(ctx, _new_ctx):
11711 _prop_closures.set_threaded()
11712 prop = _prop_closures.get(ctx)
11714 Z3_del_context(nctx.ctx)
11715 new_ctx = to_ContextObj(_new_ctx)
11717 nctx.eh = Z3_set_error_handler(new_ctx, z3_error_handler)
11719 new_prop = prop.fresh(nctx)
11720 _prop_closures.set(new_prop.id, new_prop)
11724def user_prop_fixed(ctx, cb, id, value):
11725 prop = _prop_closures.get(ctx)
11728 id = _to_expr_ref(to_Ast(id), prop.ctx())
11729 value = _to_expr_ref(to_Ast(value), prop.ctx())
11730 prop.fixed(id, value)
11733def user_prop_created(ctx, cb, id):
11734 prop = _prop_closures.get(ctx)
11737 id = _to_expr_ref(to_Ast(id), prop.ctx())
11742def user_prop_final(ctx, cb):
11743 prop = _prop_closures.get(ctx)
11749def user_prop_eq(ctx, cb, x, y):
11750 prop = _prop_closures.get(ctx)
11753 x = _to_expr_ref(to_Ast(x), prop.ctx())
11754 y = _to_expr_ref(to_Ast(y), prop.ctx())
11758def user_prop_diseq(ctx, cb, x, y):
11759 prop = _prop_closures.get(ctx)
11762 x = _to_expr_ref(to_Ast(x), prop.ctx())
11763 y = _to_expr_ref(to_Ast(y), prop.ctx())
11767def user_prop_decide(ctx, cb, t_ref, idx, phase):
11768 prop = _prop_closures.get(ctx)
11771 t = _to_expr_ref(to_Ast(t_ref), prop.ctx())
11772 prop.decide(t, idx, phase)
11776_user_prop_push = Z3_push_eh(user_prop_push)
11777_user_prop_pop = Z3_pop_eh(user_prop_pop)
11778_user_prop_fresh = Z3_fresh_eh(user_prop_fresh)
11779_user_prop_fixed = Z3_fixed_eh(user_prop_fixed)
11780_user_prop_created = Z3_created_eh(user_prop_created)
11781_user_prop_final = Z3_final_eh(user_prop_final)
11782_user_prop_eq = Z3_eq_eh(user_prop_eq)
11783_user_prop_diseq = Z3_eq_eh(user_prop_diseq)
11784_user_prop_decide = Z3_decide_eh(user_prop_decide)
11787def PropagateFunction(name, *sig):
11788 """Create a function that gets tracked by user propagator.
11789 Every term headed by this function symbol is tracked.
11790 If a term is fixed and the fixed callback is registered a
11791 callback is invoked that the term headed by this function is fixed.
11793 sig = _get_args(sig)
11795 _z3_assert(len(sig) > 0, "At least two arguments expected")
11796 arity = len(sig) - 1
11799 _z3_assert(is_sort(rng), "Z3 sort expected")
11800 dom = (Sort * arity)()
11801 for i in range(arity):
11803 _z3_assert(is_sort(sig[i]), "Z3 sort expected")
11804 dom[i] = sig[i].ast
11806 return FuncDeclRef(Z3_solver_propagate_declare(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
11810class UserPropagateBase:
11813 # Either solver is set or ctx is set.
11814 # Propagators that are created through callbacks
11815 # to "fresh" inherit the context of that is supplied
11816 # as argument to the callback.
11817 # This context should not be deleted. It is owned by the solver.
11819 def __init__(self, s, ctx=None):
11820 assert s is None or ctx is None
11821 ensure_prop_closures()
11824 self.fresh_ctx = None
11826 self.id = _prop_closures.insert(self)
11832 self.created = None
11834 self.fresh_ctx = ctx
11836 Z3_solver_propagate_init(self.ctx_ref(),
11838 ctypes.c_void_p(self.id),
11845 self._ctx.ctx = None
11849 return self.fresh_ctx
11851 return self.solver.ctx
11854 return self.ctx().ref()
11856 def add_fixed(self, fixed):
11857 assert not self.fixed
11858 assert not self._ctx
11860 Z3_solver_propagate_fixed(self.ctx_ref(), self.solver.solver, _user_prop_fixed)
11863 def add_created(self, created):
11864 assert not self.created
11865 assert not self._ctx
11867 Z3_solver_propagate_created(self.ctx_ref(), self.solver.solver, _user_prop_created)
11868 self.created = created
11870 def add_final(self, final):
11871 assert not self.final
11872 assert not self._ctx
11874 Z3_solver_propagate_final(self.ctx_ref(), self.solver.solver, _user_prop_final)
11877 def add_eq(self, eq):
11879 assert not self._ctx
11881 Z3_solver_propagate_eq(self.ctx_ref(), self.solver.solver, _user_prop_eq)
11884 def add_diseq(self, diseq):
11885 assert not self.diseq
11886 assert not self._ctx
11888 Z3_solver_propagate_diseq(self.ctx_ref(), self.solver.solver, _user_prop_diseq)
11891 def add_decide(self, decide):
11892 assert not self.decide
11893 assert not self._ctx
11895 Z3_solver_propagate_decide(self.ctx_ref(), self.solver.solver, _user_prop_decide)
11896 self.decide = decide
11899 raise Z3Exception("push needs to be overwritten")
11901 def pop(self, num_scopes):
11902 raise Z3Exception("pop needs to be overwritten")
11904 def fresh(self, new_ctx):
11905 raise Z3Exception("fresh needs to be overwritten")
11908 assert not self._ctx
11910 Z3_solver_propagate_register(self.ctx_ref(), self.solver.solver, e.ast)
11912 Z3_solver_propagate_register_cb(self.ctx_ref(), ctypes.c_void_p(self.cb), e.ast)
11915 # Tell the solver to perform the next split on a given term
11916 # If the term is a bit-vector the index idx specifies the index of the Boolean variable being
11917 # split on. A phase of true = 1/false = -1/undef = 0 = let solver decide is the last argument.
11919 def next_split(self, t, idx, phase):
11920 return Z3_solver_next_split(self.ctx_ref(), ctypes.c_void_p(self.cb), t.ast, idx, phase)
11923 # Propagation can only be invoked as during a fixed or final callback.
11925 def propagate(self, e, ids, eqs=[]):
11926 _ids, num_fixed = _to_ast_array(ids)
11928 _lhs, _num_lhs = _to_ast_array([x for x, y in eqs])
11929 _rhs, _num_rhs = _to_ast_array([y for x, y in eqs])
11930 return Z3_solver_propagate_consequence(e.ctx.ref(), ctypes.c_void_p(
11931 self.cb), num_fixed, _ids, num_eqs, _lhs, _rhs, e.ast)
11933 def conflict(self, deps = [], eqs = []):
11934 self.propagate(BoolVal(False, self.ctx()), deps, eqs)
approx(self, precision=10)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, m=None, ctx=None)
__deepcopy__(self, memo={})
__init__(self, ast, ctx=None)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__init__(self, v=None, ctx=None)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, *args, **kws)
__deepcopy__(self, memo={})
__init__(self, name, ctx=None)
declare(self, name, *args)
declare_core(self, name, rec_name, *args)
__deepcopy__(self, memo={})
__init__(self, entry, ctx)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__deepcopy__(self, memo={})
assert_exprs(self, *args)
dimacs(self, include_names=True)
simplify(self, *arguments, **keywords)
convert_model(self, model)
__init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None)
__deepcopy__(self, memo={})
eval(self, t, model_completion=False)
project_with_witness(self, vars, fml)
update_value(self, x, value)
evaluate(self, t, model_completion=False)
__deepcopy__(self, memo={})
__init__(self, descr, ctx=None)
get_documentation(self, n)
__deepcopy__(self, memo={})
__init__(self, ctx=None, params=None)
denominator_as_long(self)
Strings, Sequences and Regular expressions.
__init__(self, solver=None, ctx=None, logFile=None)
assert_and_track(self, a, p)
import_model_converter(self, other)
assert_exprs(self, *args)
check(self, *assumptions)
__exit__(self, *exc_info)
__deepcopy__(self, memo={})
__init__(self, stats, ctx)
Z3_ast Z3_API Z3_model_get_const_interp(Z3_context c, Z3_model m, Z3_func_decl a)
Return the interpretation (i.e., assignment) of constant a in the model m. Return NULL,...
Z3_sort Z3_API Z3_mk_int_sort(Z3_context c)
Create the integer type.
Z3_sort Z3_API Z3_mk_array_sort_n(Z3_context c, unsigned n, Z3_sort const *domain, Z3_sort range)
Create an array type with N arguments.
bool Z3_API Z3_open_log(Z3_string filename)
Log interaction to a file.
Z3_parameter_kind Z3_API Z3_get_decl_parameter_kind(Z3_context c, Z3_func_decl d, unsigned idx)
Return the parameter type associated with a declaration.
Z3_ast Z3_API Z3_get_denominator(Z3_context c, Z3_ast a)
Return the denominator (as a numeral AST) of a numeral AST of sort Real.
Z3_probe Z3_API Z3_probe_not(Z3_context x, Z3_probe p)
Return a probe that evaluates to "true" when p does not evaluate to true.
Z3_decl_kind Z3_API Z3_get_decl_kind(Z3_context c, Z3_func_decl d)
Return declaration kind corresponding to declaration.
void Z3_API Z3_solver_assert_and_track(Z3_context c, Z3_solver s, Z3_ast a, Z3_ast p)
Assert a constraint a into the solver, and track it (in the unsat) core using the Boolean constant p.
Z3_ast Z3_API Z3_func_interp_get_else(Z3_context c, Z3_func_interp f)
Return the 'else' value of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsge(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than or equal to.
void Z3_API Z3_ast_map_inc_ref(Z3_context c, Z3_ast_map m)
Increment the reference counter of the given AST map.
Z3_ast Z3_API Z3_mk_const_array(Z3_context c, Z3_sort domain, Z3_ast v)
Create the constant array.
Z3_ast Z3_API Z3_mk_bvsle(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than or equal to.
Z3_func_decl Z3_API Z3_get_app_decl(Z3_context c, Z3_app a)
Return the declaration of a constant or function application.
void Z3_API Z3_del_context(Z3_context c)
Delete the given logical context.
Z3_func_decl Z3_API Z3_get_decl_func_decl_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_ast Z3_API Z3_ast_map_find(Z3_context c, Z3_ast_map m, Z3_ast k)
Return the value associated with the key k.
Z3_string Z3_API Z3_ast_map_to_string(Z3_context c, Z3_ast_map m)
Convert the given map into a string.
Z3_string Z3_API Z3_param_descrs_to_string(Z3_context c, Z3_param_descrs p)
Convert a parameter description set into a string. This function is mainly used for printing the cont...
Z3_ast Z3_API Z3_mk_zero_ext(Z3_context c, unsigned i, Z3_ast t1)
Extend the given bit-vector with zeros to the (unsigned) equivalent bit-vector of size m+i,...
void Z3_API Z3_solver_set_params(Z3_context c, Z3_solver s, Z3_params p)
Set the given solver using the given parameters.
Z3_ast Z3_API Z3_mk_set_intersect(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the intersection of a list of sets.
Z3_params Z3_API Z3_mk_params(Z3_context c)
Create a Z3 (empty) parameter set. Starting at Z3 4.0, parameter sets are used to configure many comp...
unsigned Z3_API Z3_get_decl_num_parameters(Z3_context c, Z3_func_decl d)
Return the number of parameters associated with a declaration.
Z3_ast Z3_API Z3_mk_set_subset(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Check for subsetness of sets.
Z3_ast Z3_API Z3_mk_bvule(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than or equal to.
Z3_ast Z3_API Z3_mk_full_set(Z3_context c, Z3_sort domain)
Create the full set.
Z3_param_kind Z3_API Z3_param_descrs_get_kind(Z3_context c, Z3_param_descrs p, Z3_symbol n)
Return the kind associated with the given parameter name n.
void Z3_API Z3_add_rec_def(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast args[], Z3_ast body)
Define the body of a recursive function.
Z3_ast Z3_API Z3_mk_true(Z3_context c)
Create an AST node representing true.
Z3_ast Z3_API Z3_mk_set_union(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the union of a list of sets.
Z3_func_interp Z3_API Z3_add_func_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast default_value)
Create a fresh func_interp object, add it to a model for a specified function. It has reference count...
Z3_ast Z3_API Z3_mk_bvsdiv_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed division of t1 and t2 does not overflow.
unsigned Z3_API Z3_get_arity(Z3_context c, Z3_func_decl d)
Alias for Z3_get_domain_size.
void Z3_API Z3_ast_vector_set(Z3_context c, Z3_ast_vector v, unsigned i, Z3_ast a)
Update position i of the AST vector v with the AST a.
Z3_ast Z3_API Z3_mk_bvxor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise exclusive-or.
Z3_string Z3_API Z3_stats_to_string(Z3_context c, Z3_stats s)
Convert a statistics into a string.
Z3_sort Z3_API Z3_mk_real_sort(Z3_context c)
Create the real type.
Z3_ast Z3_API Z3_mk_le(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than or equal to.
bool Z3_API Z3_global_param_get(Z3_string param_id, Z3_string_ptr param_value)
Get a global (or module) parameter.
bool Z3_API Z3_goal_inconsistent(Z3_context c, Z3_goal g)
Return true if the given goal contains the formula false.
Z3_ast Z3_API Z3_mk_lambda_const(Z3_context c, unsigned num_bound, Z3_app const bound[], Z3_ast body)
Create a lambda expression using a list of constants that form the set of bound variables.
void Z3_API Z3_solver_dec_ref(Z3_context c, Z3_solver s)
Decrement the reference counter of the given solver.
Z3_ast Z3_API Z3_mk_bvslt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than.
Z3_func_decl Z3_API Z3_model_get_func_decl(Z3_context c, Z3_model m, unsigned i)
Return the declaration of the i-th function in the given model.
bool Z3_API Z3_ast_map_contains(Z3_context c, Z3_ast_map m, Z3_ast k)
Return true if the map m contains the AST key k.
Z3_ast Z3_API Z3_mk_numeral(Z3_context c, Z3_string numeral, Z3_sort ty)
Create a numeral of a given sort.
unsigned Z3_API Z3_func_entry_get_num_args(Z3_context c, Z3_func_entry e)
Return the number of arguments in a Z3_func_entry object.
Z3_symbol Z3_API Z3_get_decl_symbol_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
Z3_symbol Z3_API Z3_get_quantifier_skolem_id(Z3_context c, Z3_ast a)
Obtain skolem id of quantifier.
Z3_ast Z3_API Z3_get_numerator(Z3_context c, Z3_ast a)
Return the numerator (as a numeral AST) of a numeral AST of sort Real.
Z3_ast Z3_API Z3_mk_unary_minus(Z3_context c, Z3_ast arg)
Create an AST node representing - arg.
Z3_ast Z3_API Z3_mk_and(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] and ... and args[num_args-1].
void Z3_API Z3_interrupt(Z3_context c)
Interrupt the execution of a Z3 procedure. This procedure can be used to interrupt: solvers,...
void Z3_API Z3_goal_assert(Z3_context c, Z3_goal g, Z3_ast a)
Add a new formula a to the given goal. The formula is split according to the following procedure that...
Z3_symbol Z3_API Z3_param_descrs_get_name(Z3_context c, Z3_param_descrs p, unsigned i)
Return the name of the parameter at given index i.
Z3_ast Z3_API Z3_func_entry_get_value(Z3_context c, Z3_func_entry e)
Return the value of this point.
bool Z3_API Z3_is_quantifier_exists(Z3_context c, Z3_ast a)
Determine if ast is an existential quantifier.
Z3_sort Z3_API Z3_mk_uninterpreted_sort(Z3_context c, Z3_symbol s)
Create a free (uninterpreted) type using the given name (symbol).
Z3_ast Z3_API Z3_mk_false(Z3_context c)
Create an AST node representing false.
Z3_ast_vector Z3_API Z3_ast_map_keys(Z3_context c, Z3_ast_map m)
Return the keys stored in the given map.
Z3_ast Z3_API Z3_mk_bvmul(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement multiplication.
Z3_model Z3_API Z3_goal_convert_model(Z3_context c, Z3_goal g, Z3_model m)
Convert a model of the formulas of a goal to a model of an original goal. The model may be null,...
void Z3_API Z3_del_constructor(Z3_context c, Z3_constructor constr)
Reclaim memory allocated to constructor.
Z3_ast Z3_API Z3_mk_bvsgt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than.
Z3_string Z3_API Z3_ast_to_string(Z3_context c, Z3_ast a)
Convert the given AST node into a string.
Z3_context Z3_API Z3_mk_context_rc(Z3_config c)
Create a context using the given configuration. This function is similar to Z3_mk_context....
Z3_string Z3_API Z3_get_full_version(void)
Return a string that fully describes the version of Z3 in use.
void Z3_API Z3_enable_trace(Z3_string tag)
Enable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_mk_set_complement(Z3_context c, Z3_ast arg)
Take the complement of a set.
unsigned Z3_API Z3_get_quantifier_num_patterns(Z3_context c, Z3_ast a)
Return number of patterns used in quantifier.
Z3_symbol Z3_API Z3_get_quantifier_bound_name(Z3_context c, Z3_ast a, unsigned i)
Return symbol of the i'th bound variable.
bool Z3_API Z3_stats_is_uint(Z3_context c, Z3_stats s, unsigned idx)
Return true if the given statistical data is a unsigned integer.
unsigned Z3_API Z3_model_get_num_consts(Z3_context c, Z3_model m)
Return the number of constants assigned by the given model.
Z3_ast Z3_API Z3_mk_extract(Z3_context c, unsigned high, unsigned low, Z3_ast t1)
Extract the bits high down to low from a bit-vector of size m to yield a new bit-vector of size n,...
Z3_ast Z3_API Z3_mk_mod(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 mod arg2.
Z3_ast Z3_API Z3_mk_bvredand(Z3_context c, Z3_ast t1)
Take conjunction of bits in vector, return vector of length 1.
Z3_ast Z3_API Z3_mk_set_add(Z3_context c, Z3_ast set, Z3_ast elem)
Add an element to a set.
Z3_ast Z3_API Z3_mk_ge(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than or equal to.
Z3_ast Z3_API Z3_mk_bvadd_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed addition of t1 and t2 does not underflow.
Z3_ast Z3_API Z3_mk_bvadd_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise addition of t1 and t2 does not overflow.
void Z3_API Z3_set_ast_print_mode(Z3_context c, Z3_ast_print_mode mode)
Select mode for the format used for pretty-printing AST nodes.
Z3_ast Z3_API Z3_mk_array_default(Z3_context c, Z3_ast array)
Access the array default value. Produces the default range value, for arrays that can be represented ...
unsigned Z3_API Z3_model_get_num_sorts(Z3_context c, Z3_model m)
Return the number of uninterpreted sorts that m assigns an interpretation to.
Z3_ast_vector Z3_API Z3_ast_vector_translate(Z3_context s, Z3_ast_vector v, Z3_context t)
Translate the AST vector v from context s into an AST vector in context t.
void Z3_API Z3_func_entry_inc_ref(Z3_context c, Z3_func_entry e)
Increment the reference counter of the given Z3_func_entry object.
Z3_ast Z3_API Z3_mk_fresh_const(Z3_context c, Z3_string prefix, Z3_sort ty)
Declare and create a fresh constant.
Z3_ast Z3_API Z3_mk_bvsub_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed subtraction of t1 and t2 does not overflow.
void Z3_API Z3_solver_push(Z3_context c, Z3_solver s)
Create a backtracking point.
Z3_ast Z3_API Z3_mk_bvsub_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise subtraction of t1 and t2 does not underflow.
Z3_goal Z3_API Z3_goal_translate(Z3_context source, Z3_goal g, Z3_context target)
Copy a goal g from the context source to the context target.
Z3_ast Z3_API Z3_mk_bvudiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned division.
Z3_string Z3_API Z3_ast_vector_to_string(Z3_context c, Z3_ast_vector v)
Convert AST vector into a string.
Z3_ast Z3_API Z3_mk_bvshl(Z3_context c, Z3_ast t1, Z3_ast t2)
Shift left.
bool Z3_API Z3_is_numeral_ast(Z3_context c, Z3_ast a)
Z3_ast Z3_API Z3_mk_bvsrem(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows dividend).
bool Z3_API Z3_is_as_array(Z3_context c, Z3_ast a)
The (_ as-array f) AST node is a construct for assigning interpretations for arrays in Z3....
Z3_func_decl Z3_API Z3_mk_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a constant or function.
Z3_ast Z3_API Z3_mk_is_int(Z3_context c, Z3_ast t1)
Check if a real number is an integer.
void Z3_API Z3_params_set_bool(Z3_context c, Z3_params p, Z3_symbol k, bool v)
Add a Boolean parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_mk_ite(Z3_context c, Z3_ast t1, Z3_ast t2, Z3_ast t3)
Create an AST node representing an if-then-else: ite(t1, t2, t3).
Z3_ast Z3_API Z3_mk_select(Z3_context c, Z3_ast a, Z3_ast i)
Array read. The argument a is the array and i is the index of the array that gets read.
Z3_ast Z3_API Z3_mk_sign_ext(Z3_context c, unsigned i, Z3_ast t1)
Sign-extend of the given bit-vector to the (signed) equivalent bit-vector of size m+i,...
unsigned Z3_API Z3_goal_size(Z3_context c, Z3_goal g)
Return the number of formulas in the given goal.
void Z3_API Z3_stats_inc_ref(Z3_context c, Z3_stats s)
Increment the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_select_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs)
n-ary Array read. The argument a is the array and idxs are the indices of the array that gets read.
Z3_ast_vector Z3_API Z3_algebraic_get_poly(Z3_context c, Z3_ast a)
Return the coefficients of the defining polynomial.
Z3_ast Z3_API Z3_mk_div(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 div arg2.
void Z3_API Z3_model_dec_ref(Z3_context c, Z3_model m)
Decrement the reference counter of the given model.
void Z3_API Z3_func_interp_inc_ref(Z3_context c, Z3_func_interp f)
Increment the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_set_double(Z3_context c, Z3_params p, Z3_symbol k, double v)
Add a double parameter k with value v to the parameter set p.
Z3_string Z3_API Z3_param_descrs_get_documentation(Z3_context c, Z3_param_descrs p, Z3_symbol s)
Retrieve documentation string corresponding to parameter name s.
Z3_sort Z3_API Z3_mk_datatype_sort(Z3_context c, Z3_symbol name)
create a forward reference to a recursive datatype being declared. The forward reference can be used ...
Z3_solver Z3_API Z3_mk_solver(Z3_context c)
Create a new solver. This solver is a "combined solver" (see combined_solver module) that internally ...
Z3_model Z3_API Z3_solver_get_model(Z3_context c, Z3_solver s)
Retrieve the model for the last Z3_solver_check or Z3_solver_check_assumptions.
int Z3_API Z3_get_symbol_int(Z3_context c, Z3_symbol s)
Return the symbol int value.
Z3_func_decl Z3_API Z3_get_as_array_func_decl(Z3_context c, Z3_ast a)
Return the function declaration f associated with a (_ as_array f) node.
Z3_ast Z3_API Z3_mk_ext_rotate_left(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the left t2 times.
void Z3_API Z3_goal_inc_ref(Z3_context c, Z3_goal g)
Increment the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_implies(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 implies t2.
unsigned Z3_API Z3_get_datatype_sort_num_constructors(Z3_context c, Z3_sort t)
Return number of constructors for datatype.
void Z3_API Z3_params_set_uint(Z3_context c, Z3_params p, Z3_symbol k, unsigned v)
Add a unsigned parameter k with value v to the parameter set p.
Z3_lbool Z3_API Z3_solver_check_assumptions(Z3_context c, Z3_solver s, unsigned num_assumptions, Z3_ast const assumptions[])
Check whether the assertions in the given solver and optional assumptions are consistent or not.
Z3_sort Z3_API Z3_model_get_sort(Z3_context c, Z3_model m, unsigned i)
Return a uninterpreted sort that m assigns an interpretation.
Z3_ast Z3_API Z3_mk_bvashr(Z3_context c, Z3_ast t1, Z3_ast t2)
Arithmetic shift right.
Z3_ast Z3_API Z3_mk_bv2int(Z3_context c, Z3_ast t1, bool is_signed)
Create an integer from the bit-vector argument t1. If is_signed is false, then the bit-vector t1 is t...
Z3_sort Z3_API Z3_get_array_sort_domain_n(Z3_context c, Z3_sort t, unsigned idx)
Return the i'th domain sort of an n-dimensional array.
Z3_ast Z3_API Z3_mk_set_del(Z3_context c, Z3_ast set, Z3_ast elem)
Remove an element to a set.
Z3_ast Z3_API Z3_mk_bvmul_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise multiplication of t1 and t2 does not overflow.
Z3_ast Z3_API Z3_mk_bvor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise or.
int Z3_API Z3_get_decl_int_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the integer value associated with an integer parameter.
unsigned Z3_API Z3_get_quantifier_num_no_patterns(Z3_context c, Z3_ast a)
Return number of no_patterns used in quantifier.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th constructor.
void Z3_API Z3_ast_vector_resize(Z3_context c, Z3_ast_vector v, unsigned n)
Resize the AST vector v.
Z3_ast Z3_API Z3_mk_quantifier_const_ex(Z3_context c, bool is_forall, unsigned weight, Z3_symbol quantifier_id, Z3_symbol skolem_id, unsigned num_bound, Z3_app const bound[], unsigned num_patterns, Z3_pattern const patterns[], unsigned num_no_patterns, Z3_ast const no_patterns[], Z3_ast body)
Create a universal or existential quantifier using a list of constants that will form the set of boun...
Z3_pattern Z3_API Z3_mk_pattern(Z3_context c, unsigned num_patterns, Z3_ast const terms[])
Create a pattern for quantifier instantiation.
Z3_symbol_kind Z3_API Z3_get_symbol_kind(Z3_context c, Z3_symbol s)
Return Z3_INT_SYMBOL if the symbol was constructed using Z3_mk_int_symbol, and Z3_STRING_SYMBOL if th...
bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a)
Determine if ast is a lambda expression.
unsigned Z3_API Z3_stats_get_uint_value(Z3_context c, Z3_stats s, unsigned idx)
Return the unsigned value of the given statistical data.
Z3_sort Z3_API Z3_get_array_sort_domain(Z3_context c, Z3_sort t)
Return the domain of the given array sort. In the case of a multi-dimensional array,...
Z3_ast Z3_API Z3_mk_bvmul_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed multiplication of t1 and t2 does not underflo...
Z3_ast Z3_API Z3_func_decl_to_ast(Z3_context c, Z3_func_decl f)
Convert a Z3_func_decl into Z3_ast. This is just type casting.
void Z3_API Z3_add_const_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast a)
Add a constant interpretation.
Z3_ast Z3_API Z3_mk_bvadd(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement addition.
unsigned Z3_API Z3_algebraic_get_i(Z3_context c, Z3_ast a)
Return which root of the polynomial the algebraic number represents.
void Z3_API Z3_params_dec_ref(Z3_context c, Z3_params p)
Decrement the reference counter of the given parameter set.
Z3_ast Z3_API Z3_get_app_arg(Z3_context c, Z3_app a, unsigned i)
Return the i-th argument of the given application.
Z3_string Z3_API Z3_model_to_string(Z3_context c, Z3_model m)
Convert the given model into a string.
Z3_func_decl Z3_API Z3_mk_fresh_func_decl(Z3_context c, Z3_string prefix, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a fresh constant or function.
unsigned Z3_API Z3_ast_map_size(Z3_context c, Z3_ast_map m)
Return the size of the given map.
unsigned Z3_API Z3_param_descrs_size(Z3_context c, Z3_param_descrs p)
Return the number of parameters in the given parameter description set.
Z3_string Z3_API Z3_goal_to_dimacs_string(Z3_context c, Z3_goal g, bool include_names)
Convert a goal into a DIMACS formatted string. The goal must be in CNF. You can convert a goal to CNF...
Z3_ast Z3_API Z3_mk_lt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than.
Z3_ast Z3_API Z3_get_quantifier_no_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th no_pattern.
double Z3_API Z3_stats_get_double_value(Z3_context c, Z3_stats s, unsigned idx)
Return the double value of the given statistical data.
Z3_ast Z3_API Z3_mk_bvugt(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than.
unsigned Z3_API Z3_goal_depth(Z3_context c, Z3_goal g)
Return the depth of the given goal. It tracks how many transformations were applied to it.
Z3_string Z3_API Z3_get_symbol_string(Z3_context c, Z3_symbol s)
Return the symbol name.
Z3_ast Z3_API Z3_pattern_to_ast(Z3_context c, Z3_pattern p)
Convert a Z3_pattern into Z3_ast. This is just type casting.
Z3_ast Z3_API Z3_mk_bvnot(Z3_context c, Z3_ast t1)
Bitwise negation.
Z3_ast Z3_API Z3_mk_bvurem(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned remainder.
void Z3_API Z3_mk_datatypes(Z3_context c, unsigned num_sorts, Z3_symbol const sort_names[], Z3_sort sorts[], Z3_constructor_list constructor_lists[])
Create mutually recursive datatypes.
unsigned Z3_API Z3_func_interp_get_arity(Z3_context c, Z3_func_interp f)
Return the arity (number of arguments) of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsub(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement subtraction.
Z3_ast Z3_API Z3_get_algebraic_number_upper(Z3_context c, Z3_ast a, unsigned precision)
Return a upper bound for the given real algebraic number. The interval isolating the number is smalle...
Z3_ast Z3_API Z3_mk_power(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 ^ arg2.
Z3_ast Z3_API Z3_mk_seq_concat(Z3_context c, unsigned n, Z3_ast const args[])
Concatenate sequences.
Z3_sort Z3_API Z3_mk_enumeration_sort(Z3_context c, Z3_symbol name, unsigned n, Z3_symbol const enum_names[], Z3_func_decl enum_consts[], Z3_func_decl enum_testers[])
Create a enumeration sort.
unsigned Z3_API Z3_get_bv_sort_size(Z3_context c, Z3_sort t)
Return the size of the given bit-vector sort.
Z3_ast Z3_API Z3_mk_set_member(Z3_context c, Z3_ast elem, Z3_ast set)
Check for set membership.
void Z3_API Z3_ast_vector_dec_ref(Z3_context c, Z3_ast_vector v)
Decrement the reference counter of the given AST vector.
void Z3_API Z3_func_interp_dec_ref(Z3_context c, Z3_func_interp f)
Decrement the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_inc_ref(Z3_context c, Z3_params p)
Increment the reference counter of the given parameter set.
void Z3_API Z3_set_error_handler(Z3_context c, Z3_error_handler h)
Register a Z3 error handler.
Z3_ast Z3_API Z3_mk_distinct(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing distinct(args[0], ..., args[num_args-1]).
Z3_config Z3_API Z3_mk_config(void)
Create a configuration object for the Z3 context object.
void Z3_API Z3_set_param_value(Z3_config c, Z3_string param_id, Z3_string param_value)
Set a configuration parameter.
Z3_sort Z3_API Z3_mk_bv_sort(Z3_context c, unsigned sz)
Create a bit-vector type of the given size.
Z3_ast Z3_API Z3_mk_bvult(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than.
void Z3_API Z3_ast_map_dec_ref(Z3_context c, Z3_ast_map m)
Decrement the reference counter of the given AST map.
Z3_string Z3_API Z3_params_to_string(Z3_context c, Z3_params p)
Convert a parameter set into a string. This function is mainly used for printing the contents of a pa...
Z3_param_descrs Z3_API Z3_get_global_param_descrs(Z3_context c)
Retrieve description of global parameters.
Z3_func_decl Z3_API Z3_model_get_const_decl(Z3_context c, Z3_model m, unsigned i)
Return the i-th constant in the given model.
Z3_ast Z3_API Z3_translate(Z3_context source, Z3_ast a, Z3_context target)
Translate/Copy the AST a from context source to context target. AST a must have been created using co...
Z3_sort Z3_API Z3_get_range(Z3_context c, Z3_func_decl d)
Return the range of the given declaration.
void Z3_API Z3_global_param_set(Z3_string param_id, Z3_string param_value)
Set a global (or module) parameter. This setting is shared by all Z3 contexts.
Z3_ast_vector Z3_API Z3_model_get_sort_universe(Z3_context c, Z3_model m, Z3_sort s)
Return the finite set of distinct values that represent the interpretation for sort s.
void Z3_API Z3_func_entry_dec_ref(Z3_context c, Z3_func_entry e)
Decrement the reference counter of the given Z3_func_entry object.
unsigned Z3_API Z3_stats_size(Z3_context c, Z3_stats s)
Return the number of statistical data in s.
void Z3_API Z3_append_log(Z3_string string)
Append user-defined string to interaction log.
Z3_ast Z3_API Z3_get_quantifier_body(Z3_context c, Z3_ast a)
Return body of quantifier.
void Z3_API Z3_param_descrs_dec_ref(Z3_context c, Z3_param_descrs p)
Decrement the reference counter of the given parameter description set.
Z3_model Z3_API Z3_mk_model(Z3_context c)
Create a fresh model object. It has reference count 0.
Z3_symbol Z3_API Z3_get_decl_name(Z3_context c, Z3_func_decl d)
Return the constant declaration name as a symbol.
Z3_ast Z3_API Z3_mk_bvneg_no_overflow(Z3_context c, Z3_ast t1)
Check that bit-wise negation does not overflow when t1 is interpreted as a signed bit-vector.
Z3_string Z3_API Z3_stats_get_key(Z3_context c, Z3_stats s, unsigned idx)
Return the key (a string) for a particular statistical data.
Z3_ast Z3_API Z3_mk_bvand(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise and.
Z3_ast_kind Z3_API Z3_get_ast_kind(Z3_context c, Z3_ast a)
Return the kind of the given AST.
Z3_ast Z3_API Z3_mk_bvsmod(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows divisor).
Z3_model Z3_API Z3_model_translate(Z3_context c, Z3_model m, Z3_context dst)
translate model from context c to context dst.
void Z3_API Z3_get_version(unsigned *major, unsigned *minor, unsigned *build_number, unsigned *revision_number)
Return Z3 version number information.
Z3_ast Z3_API Z3_mk_int2bv(Z3_context c, unsigned n, Z3_ast t1)
Create an n bit bit-vector from the integer argument t1.
void Z3_API Z3_solver_assert(Z3_context c, Z3_solver s, Z3_ast a)
Assert a constraint into the solver.
unsigned Z3_API Z3_ast_vector_size(Z3_context c, Z3_ast_vector v)
Return the size of the given AST vector.
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.
bool Z3_API Z3_model_eval(Z3_context c, Z3_model m, Z3_ast t, bool model_completion, Z3_ast *v)
Evaluate the AST node t in the given model. Return true if succeeded, and store the result in v.
unsigned Z3_API Z3_solver_get_num_scopes(Z3_context c, Z3_solver s)
Return the number of backtracking points.
Z3_sort Z3_API Z3_get_array_sort_range(Z3_context c, Z3_sort t)
Return the range of the given array sort.
void Z3_API Z3_del_constructor_list(Z3_context c, Z3_constructor_list clist)
Reclaim memory allocated for constructor list.
Z3_ast Z3_API Z3_mk_bound(Z3_context c, unsigned index, Z3_sort ty)
Create a variable.
unsigned Z3_API Z3_get_app_num_args(Z3_context c, Z3_app a)
Return the number of argument of an application. If t is an constant, then the number of arguments is...
Z3_ast Z3_API Z3_func_entry_get_arg(Z3_context c, Z3_func_entry e, unsigned i)
Return an argument of a Z3_func_entry object.
Z3_ast Z3_API Z3_mk_eq(Z3_context c, Z3_ast l, Z3_ast r)
Create an AST node representing l = r.
void Z3_API Z3_ast_vector_inc_ref(Z3_context c, Z3_ast_vector v)
Increment the reference counter of the given AST vector.
unsigned Z3_API Z3_model_get_num_funcs(Z3_context c, Z3_model m)
Return the number of function interpretations in the given model.
void Z3_API Z3_dec_ref(Z3_context c, Z3_ast a)
Decrement the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast_vector Z3_API Z3_mk_ast_vector(Z3_context c)
Return an empty AST vector.
Z3_ast Z3_API Z3_mk_empty_set(Z3_context c, Z3_sort domain)
Create the empty set.
Z3_ast Z3_API Z3_mk_set_has_size(Z3_context c, Z3_ast set, Z3_ast k)
Create predicate that holds if Boolean array set has k elements set to true.
Z3_ast Z3_API Z3_mk_repeat(Z3_context c, unsigned i, Z3_ast t1)
Repeat the given bit-vector up length i.
Z3_goal_prec Z3_API Z3_goal_precision(Z3_context c, Z3_goal g)
Return the "precision" of the given goal. Goals can be transformed using over and under approximation...
void Z3_API Z3_solver_pop(Z3_context c, Z3_solver s, unsigned n)
Backtrack n backtracking points.
void Z3_API Z3_ast_map_erase(Z3_context c, Z3_ast_map m, Z3_ast k)
Erase a key from the map.
Z3_ast Z3_API Z3_mk_int2real(Z3_context c, Z3_ast t1)
Coerce an integer to a real.
unsigned Z3_API Z3_get_index_value(Z3_context c, Z3_ast a)
Return index of de-Bruijn bound variable.
Z3_goal Z3_API Z3_mk_goal(Z3_context c, bool models, bool unsat_cores, bool proofs)
Create a goal (aka problem). A goal is essentially a set of formulas, that can be solved and/or trans...
double Z3_API Z3_get_decl_double_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
unsigned Z3_API Z3_get_ast_hash(Z3_context c, Z3_ast a)
Return a hash code for the given AST. The hash code is structural but two different AST objects can m...
Z3_symbol Z3_API Z3_get_sort_name(Z3_context c, Z3_sort d)
Return the sort name as a symbol.
void Z3_API Z3_params_validate(Z3_context c, Z3_params p, Z3_param_descrs d)
Validate the parameter set p against the parameter description set d.
Z3_func_decl Z3_API Z3_get_datatype_sort_recognizer(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th recognizer.
void Z3_API Z3_global_param_reset_all(void)
Restore the value of all global (and module) parameters. This command will not affect already created...
Z3_ast Z3_API Z3_mk_gt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than.
Z3_ast Z3_API Z3_mk_store(Z3_context c, Z3_ast a, Z3_ast i, Z3_ast v)
Array update.
Z3_string Z3_API Z3_get_decl_rational_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the rational value, as a string, associated with a rational parameter.
void Z3_API Z3_ast_vector_push(Z3_context c, Z3_ast_vector v, Z3_ast a)
Add the AST a in the end of the AST vector v. The size of v is increased by one.
bool Z3_API Z3_is_eq_ast(Z3_context c, Z3_ast t1, Z3_ast t2)
Compare terms.
bool Z3_API Z3_is_quantifier_forall(Z3_context c, Z3_ast a)
Determine if an ast is a universal quantifier.
Z3_ast_map Z3_API Z3_mk_ast_map(Z3_context c)
Return an empty mapping from AST to AST.
Z3_ast Z3_API Z3_mk_xor(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 xor t2.
Z3_ast Z3_API Z3_mk_map(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast const *args)
Map f on the argument arrays.
Z3_ast Z3_API Z3_mk_const(Z3_context c, Z3_symbol s, Z3_sort ty)
Declare and create a constant.
Z3_symbol Z3_API Z3_mk_string_symbol(Z3_context c, Z3_string s)
Create a Z3 symbol using a C string.
void Z3_API Z3_param_descrs_inc_ref(Z3_context c, Z3_param_descrs p)
Increment the reference counter of the given parameter description set.
void Z3_API Z3_stats_dec_ref(Z3_context c, Z3_stats s)
Decrement the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_array_ext(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create array extensionality index given two arrays with the same sort. The meaning is given by the ax...
Z3_ast Z3_API Z3_mk_re_concat(Z3_context c, unsigned n, Z3_ast const args[])
Create the concatenation of the regular languages.
Z3_ast Z3_API Z3_sort_to_ast(Z3_context c, Z3_sort s)
Convert a Z3_sort into Z3_ast. This is just type casting.
Z3_func_entry Z3_API Z3_func_interp_get_entry(Z3_context c, Z3_func_interp f, unsigned i)
Return a "point" of the given function interpretation. It represents the value of f in a particular p...
Z3_func_decl Z3_API Z3_mk_rec_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a recursive function.
unsigned Z3_API Z3_get_ast_id(Z3_context c, Z3_ast t)
Return a unique identifier for t. The identifier is unique up to structural equality....
Z3_ast Z3_API Z3_mk_concat(Z3_context c, Z3_ast t1, Z3_ast t2)
Concatenate the given bit-vectors.
unsigned Z3_API Z3_get_quantifier_num_bound(Z3_context c, Z3_ast a)
Return number of bound variables of quantifier.
Z3_sort Z3_API Z3_get_decl_sort_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the sort value associated with a sort parameter.
Z3_constructor_list Z3_API Z3_mk_constructor_list(Z3_context c, unsigned num_constructors, Z3_constructor const constructors[])
Create list of constructors.
Z3_ast Z3_API Z3_mk_app(Z3_context c, Z3_func_decl d, unsigned num_args, Z3_ast const args[])
Create a constant or function application.
Z3_sort_kind Z3_API Z3_get_sort_kind(Z3_context c, Z3_sort t)
Return the sort kind (e.g., array, tuple, int, bool, etc).
Z3_ast Z3_API Z3_mk_bvneg(Z3_context c, Z3_ast t1)
Standard two's complement unary minus.
Z3_ast Z3_API Z3_mk_store_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs, Z3_ast v)
n-ary Array update.
Z3_sort Z3_API Z3_get_domain(Z3_context c, Z3_func_decl d, unsigned i)
Return the sort of the i-th parameter of the given function declaration.
Z3_sort Z3_API Z3_mk_bool_sort(Z3_context c)
Create the Boolean type.
void Z3_API Z3_params_set_symbol(Z3_context c, Z3_params p, Z3_symbol k, Z3_symbol v)
Add a symbol parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_ast_vector_get(Z3_context c, Z3_ast_vector v, unsigned i)
Return the AST at position i in the AST vector v.
Z3_func_decl Z3_API Z3_to_func_decl(Z3_context c, Z3_ast a)
Convert an AST into a FUNC_DECL_AST. This is just type casting.
Z3_ast Z3_API Z3_mk_set_difference(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Take the set difference between two sets.
Z3_ast Z3_API Z3_mk_bvsdiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed division.
Z3_ast Z3_API Z3_mk_bvlshr(Z3_context c, Z3_ast t1, Z3_ast t2)
Logical shift right.
Z3_ast Z3_API Z3_get_decl_ast_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_pattern Z3_API Z3_get_quantifier_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th pattern.
void Z3_API Z3_goal_dec_ref(Z3_context c, Z3_goal g)
Decrement the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_not(Z3_context c, Z3_ast a)
Create an AST node representing not(a).
Z3_ast Z3_API Z3_mk_or(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] or ... or args[num_args-1].
Z3_sort Z3_API Z3_mk_array_sort(Z3_context c, Z3_sort domain, Z3_sort range)
Create an array type.
void Z3_API Z3_model_inc_ref(Z3_context c, Z3_model m)
Increment the reference counter of the given model.
Z3_ast Z3_API Z3_mk_seq_extract(Z3_context c, Z3_ast s, Z3_ast offset, Z3_ast length)
Extract subsequence starting at offset of length.
Z3_sort Z3_API Z3_mk_type_variable(Z3_context c, Z3_symbol s)
Create a type variable.
Z3_string Z3_API Z3_get_numeral_string(Z3_context c, Z3_ast a)
Return numeral value, as a decimal string of a numeric constant term.
void Z3_API Z3_func_interp_add_entry(Z3_context c, Z3_func_interp fi, Z3_ast_vector args, Z3_ast value)
add a function entry to a function interpretation.
Z3_ast Z3_API Z3_mk_bvuge(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than or equal to.
Z3_string Z3_API Z3_get_numeral_binary_string(Z3_context c, Z3_ast a)
Return numeral value, as a binary string of a numeric constant term.
Z3_sort Z3_API Z3_get_quantifier_bound_sort(Z3_context c, Z3_ast a, unsigned i)
Return sort of the i'th bound variable.
void Z3_API Z3_disable_trace(Z3_string tag)
Disable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_goal_formula(Z3_context c, Z3_goal g, unsigned idx)
Return a formula from the given goal.
Z3_symbol Z3_API Z3_mk_int_symbol(Z3_context c, int i)
Create a Z3 symbol using an integer.
unsigned Z3_API Z3_func_interp_get_num_entries(Z3_context c, Z3_func_interp f)
Return the number of entries in the given function interpretation.
void Z3_API Z3_ast_map_insert(Z3_context c, Z3_ast_map m, Z3_ast k, Z3_ast v)
Store/Replace a new key, value pair in the given map.
Z3_constructor Z3_API Z3_mk_constructor(Z3_context c, Z3_symbol name, Z3_symbol recognizer, unsigned num_fields, Z3_symbol const field_names[], Z3_sort const sorts[], unsigned sort_refs[])
Create a constructor.
Z3_string Z3_API Z3_goal_to_string(Z3_context c, Z3_goal g)
Convert a goal into a string.
bool Z3_API Z3_is_eq_sort(Z3_context c, Z3_sort s1, Z3_sort s2)
compare sorts.
void Z3_API Z3_del_config(Z3_config c)
Delete the given configuration object.
double Z3_API Z3_get_numeral_double(Z3_context c, Z3_ast a)
Return numeral as a double.
void Z3_API Z3_inc_ref(Z3_context c, Z3_ast a)
Increment the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast Z3_API Z3_mk_real2int(Z3_context c, Z3_ast t1)
Coerce a real to an integer.
Z3_func_interp Z3_API Z3_model_get_func_interp(Z3_context c, Z3_model m, Z3_func_decl f)
Return the interpretation of the function f in the model m. Return NULL, if the model does not assign...
void Z3_API Z3_solver_inc_ref(Z3_context c, Z3_solver s)
Increment the reference counter of the given solver.
Z3_symbol Z3_API Z3_get_quantifier_id(Z3_context c, Z3_ast a)
Obtain id of quantifier.
Z3_ast Z3_API Z3_mk_ext_rotate_right(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the right t2 times.
Z3_string Z3_API Z3_get_numeral_decimal_string(Z3_context c, Z3_ast a, unsigned precision)
Return numeral as a string in decimal notation. The result has at most precision decimal places.
Z3_sort Z3_API Z3_get_sort(Z3_context c, Z3_ast a)
Return the sort of an AST node.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor_accessor(Z3_context c, Z3_sort t, unsigned idx_c, unsigned idx_a)
Return idx_a'th accessor for the idx_c'th constructor.
Z3_ast Z3_API Z3_mk_bvredor(Z3_context c, Z3_ast t1)
Take disjunction of bits in vector, return vector of length 1.
void Z3_API Z3_ast_map_reset(Z3_context c, Z3_ast_map m)
Remove all keys from the given map.
void Z3_API Z3_solver_reset(Z3_context c, Z3_solver s)
Remove all assertions from the solver.
bool Z3_API Z3_is_algebraic_number(Z3_context c, Z3_ast a)
Return true if the given AST is a real algebraic number.
BitVecVal(val, bv, ctx=None)
_coerce_exprs(a, b, ctx=None)
_ctx_from_ast_args(*args)
_to_func_decl_ref(a, ctx)
_valid_accessor(acc)
Datatypes.
BitVec(name, bv, ctx=None)
RecAddDefinition(f, args, body)
DeclareTypeVar(name, ctx=None)
_z3_check_cint_overflow(n, name)
TupleSort(name, sorts, ctx=None)
_coerce_expr_list(alist, ctx=None)
RealVector(prefix, sz, ctx=None)
SortRef _sort(Context ctx, Any a)
ExprRef RealVar(int idx, ctx=None)
bool is_arith_sort(Any s)
BitVecs(names, bv, ctx=None)
BoolVector(prefix, sz, ctx=None)
FreshConst(sort, prefix="c")
EnumSort(name, values, ctx=None)
simplify(a, *arguments, **keywords)
Utils.
BV2Int(a, is_signed=False)
FreshInt(prefix="x", ctx=None)
_to_func_decl_array(args)
args2params(arguments, keywords, ctx=None)
Cond(p, t1, t2, ctx=None)
RealVarVector(int n, ctx=None)
bool eq(AstRef a, AstRef b)
FreshReal(prefix="b", ctx=None)
_reduce(func, sequence, initial)
ExprRef Var(int idx, SortRef s)
BVAddNoOverflow(a, b, signed)
FreshBool(prefix="b", ctx=None)
_ctx_from_ast_arg_list(args, default_ctx=None)
IntVector(prefix, sz, ctx=None)
DisjointSum(name, sorts, ctx=None)
Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
int _ast_kind(Context ctx, Any a)
BVSubNoUnderflow(a, b, signed)
DatatypeSort(name, ctx=None)
SortRef DeclareSort(name, ctx=None)
BVMulNoOverflow(a, b, signed)
_mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])