Functions | |
def | enable_trace (msg) |
def | disable_trace (msg) |
def | get_version_string () |
def | get_version () |
def | open_log (fname) |
def | append_log (s) |
def | to_symbol |
def | main_ctx () |
def | set_param (args, kws) |
def | reset_params () |
def | set_option (args, kws) |
def | get_param (name) |
def | is_ast (a) |
def | eq (a, b) |
def | is_sort (s) |
def | DeclareSort |
def | is_func_decl (a) |
def | Function (name, sig) |
def | is_expr (a) |
def | is_app (a) |
def | is_const (a) |
def | is_var (a) |
def | get_var_index (a) |
def | is_app_of (a, k) |
def | If |
def | Distinct (args) |
def | Const (name, sort) |
def | Consts (names, sort) |
def | Var (idx, s) |
def | RealVar |
def | RealVarVector |
def | is_bool (a) |
def | is_true (a) |
def | is_false (a) |
def | is_and (a) |
def | is_or (a) |
def | is_not (a) |
def | is_eq (a) |
def | is_distinct (a) |
def | BoolSort |
def | BoolVal |
def | Bool |
def | Bools |
def | BoolVector |
def | FreshBool |
def | Implies |
def | Xor |
def | Not |
def | And (args) |
def | Or (args) |
def | is_pattern (a) |
def | MultiPattern (args) |
def | is_quantifier (a) |
def | ForAll |
def | Exists |
def | is_arith_sort (s) |
def | is_arith (a) |
def | is_int (a) |
def | is_real (a) |
def | is_int_value (a) |
def | is_rational_value (a) |
def | is_algebraic_value (a) |
def | is_add (a) |
def | is_mul (a) |
def | is_sub (a) |
def | is_div (a) |
def | is_idiv (a) |
def | is_mod (a) |
def | is_le (a) |
def | is_lt (a) |
def | is_ge (a) |
def | is_gt (a) |
def | is_is_int (a) |
def | is_to_real (a) |
def | is_to_int (a) |
def | IntSort |
def | RealSort |
def | IntVal |
def | RealVal |
def | RatVal |
def | Q |
def | Int |
def | Ints |
def | IntVector |
def | FreshInt |
def | Real |
def | Reals |
def | RealVector |
def | FreshReal |
def | ToReal (a) |
def | ToInt (a) |
def | IsInt (a) |
def | Sqrt |
def | Cbrt |
def | is_bv_sort (s) |
def | is_bv (a) |
def | is_bv_value (a) |
def | BV2Int (a) |
def | BitVecSort |
def | BitVecVal |
def | BitVec |
def | BitVecs |
def | Concat (args) |
def | Extract (high, low, a) |
def | ULE (a, b) |
def | ULT (a, b) |
def | UGE (a, b) |
def | UGT (a, b) |
def | UDiv (a, b) |
def | URem (a, b) |
def | SRem (a, b) |
def | LShR (a, b) |
def | RotateLeft (a, b) |
def | RotateRight (a, b) |
def | SignExt (n, a) |
def | ZeroExt (n, a) |
def | RepeatBitVec (n, a) |
def | BVRedAnd (a) |
def | BVRedOr (a) |
def | is_array (a) |
def | is_const_array (a) |
def | is_K (a) |
def | is_map (a) |
def | get_map_func (a) |
def | ArraySort (d, r) |
def | Array (name, dom, rng) |
def | Update (a, i, v) |
def | Store (a, i, v) |
def | Select (a, i) |
def | Map (f, args) |
def | K (dom, v) |
def | is_select (a) |
def | is_store (a) |
def | CreateDatatypes (ds) |
def | EnumSort |
def | args2params |
def | is_as_array (n) |
def | get_as_array_func (n) |
def | SolverFor |
def | SimpleSolver |
def | AndThen (ts, ks) |
def | Then (ts, ks) |
def | OrElse (ts, ks) |
def | ParOr (ts, ks) |
def | ParThen |
def | ParAndThen |
def | With (t, args, keys) |
def | Repeat |
def | TryFor |
def | tactics |
def | tactic_description |
def | describe_tactics () |
def | is_probe (p) |
def | probes |
def | probe_description |
def | describe_probes () |
def | FailIf |
def | When |
def | Cond |
def | simplify (a, arguments, keywords) |
Utils. More... | |
def | help_simplify () |
def | simplify_param_descrs () |
def | substitute (t, m) |
def | substitute_vars (t, m) |
def | Sum (args) |
def | Product (args) |
def | solve (args, keywords) |
def | solve_using (s, args, keywords) |
def | prove (claim, keywords) |
def | parse_smt2_string |
def | parse_smt2_file |
def | Interpolant |
def | tree_interpolant |
def | binary_interpolant |
def | sequence_interpolant |
def | get_default_rounding_mode |
def | set_default_rounding_mode |
def | get_default_fp_sort |
def | set_default_fp_sort |
def | Float16 |
def | FloatHalf |
def | Float32 |
def | FloatSingle |
def | Float64 |
def | Float128 |
def | is_fp_sort (s) |
def | is_fprm_sort (s) |
def | RoundNearestTiesToEven |
def | RNE |
def | RoundNearestTiesToAway |
def | RNA |
def | RoundTowardPositive |
def | RTP |
def | RoundTowardNegative |
def | RTN |
def | RoundTowardZero |
def | RTZ |
def | is_fprm (a) |
def | is_fprm_value (a) |
def | is_fp (a) |
def | is_fp_value (a) |
def | FPSort |
def | fpNaN (s) |
def | fpPlusInfinity (s) |
def | fpMinusInfinity (s) |
def | fpInfinity (s, negative) |
def | fpPlusZero (s) |
def | fpMinusZero (s) |
def | fpZero (s, negative) |
def | FPVal |
def | FP |
def | FPs |
def | fpAbs (a) |
def | fpNeg (a) |
def | fpAdd (rm, a, b) |
def | fpSub (rm, a, b) |
def | fpMul (rm, a, b) |
def | fpDiv (rm, a, b) |
def | fpRem (a, b) |
def | fpMin (a, b) |
def | fpMax (a, b) |
def | fpFMA (rm, a, b, c) |
def | fpSqrt (rm, a) |
def | fpRoundToIntegral (rm, a) |
def | fpIsNaN (a) |
def | fpIsInfinite (a) |
def | fpIsZero (a) |
def | fpIsNormal (a) |
def | fpIsSubnormal (a) |
def | fpIsNegative (a) |
def | fpIsPositive (a) |
def | fpLT (a, b) |
def | fpLEQ (a, b) |
def | fpGT (a, b) |
def | fpGEQ (a, b) |
def | fpEQ (a, b) |
def | fpNEQ (a, b) |
def | fpFP (sgn, exp, sig) |
def | fpToFP |
def | fpToFPUnsigned (rm, x, s) |
def | fpToSBV (rm, x, s) |
def | fpToUBV (rm, x, s) |
def | fpToReal (x) |
def | fpToIEEEBV (x) |
Variables | |
tuple | _error_handler_fptr = ctypes.CFUNCTYPE(None, ctypes.c_void_p, ctypes.c_uint) |
tuple | _Z3Python_error_handler = _error_handler_fptr(_Z3python_error_handler_core) |
_main_ctx = None | |
tuple | sat = CheckSatResult(Z3_L_TRUE) |
tuple | unsat = CheckSatResult(Z3_L_FALSE) |
tuple | unknown = CheckSatResult(Z3_L_UNDEF) |
_dflt_rounding_mode = Z3_OP_FPA_RM_TOWARD_ZERO | |
Floating-Point Arithmetic. More... | |
int | _dflt_fpsort_ebits = 11 |
int | _dflt_fpsort_sbits = 53 |
def z3py.And | ( | args | ) |
Create a Z3 and-expression or and-probe. >>> p, q, r = Bools('p q r') >>> And(p, q, r) And(p, q, r) >>> P = BoolVector('p', 5) >>> And(P) And(p__0, p__1, p__2, p__3, p__4)
Definition at line 1479 of file z3py.py.
Referenced by Fixedpoint.add_rule(), Goal.as_expr(), Bool(), Bools(), BoolVector(), Fixedpoint.query(), tree_interpolant(), and Fixedpoint.update_rule().
def z3py.AndThen | ( | ts, | |
ks | |||
) |
Return a tactic that applies the tactics in `*ts` in sequence. >>> x, y = Ints('x y') >>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs')) >>> t(And(x == 0, y > x + 1)) [[Not(y <= 1)]] >>> t(And(x == 0, y > x + 1)).as_expr() Not(y <= 1)
Definition at line 6560 of file z3py.py.
Referenced by Context.Then(), and Then().
def z3py.append_log | ( | s | ) |
def z3py.args2params | ( | arguments, | |
keywords, | |||
ctx = None |
|||
) |
Convert python arguments into a Z3_params object. A ':' is added to the keywords, and '_' is replaced with '-' >>> args2params(['model', True, 'relevancy', 2], {'elim_and' : True}) (params model true relevancy 2 elim_and true)
Definition at line 4490 of file z3py.py.
Referenced by Tactic.apply(), Fixedpoint.set(), simplify(), and With().
def z3py.Array | ( | name, | |
dom, | |||
rng | |||
) |
Return an array constant named `name` with the given domain and range sorts. >>> a = Array('a', IntSort(), IntSort()) >>> a.sort() Array(Int, Int) >>> a[0] a[0]
Definition at line 3999 of file z3py.py.
Referenced by ArrayRef.__getitem__(), ArraySort(), ArrayRef.domain(), get_map_func(), is_array(), is_const_array(), is_K(), is_map(), is_select(), is_store(), K(), Map(), ArrayRef.range(), Select(), ArrayRef.sort(), Store(), and Update().
def z3py.ArraySort | ( | d, | |
r | |||
) |
Return the Z3 array sort with the given domain and range sorts. >>> A = ArraySort(IntSort(), BoolSort()) >>> A Array(Int, Bool) >>> A.domain() Int >>> A.range() Bool >>> AA = ArraySort(IntSort(), A) >>> AA Array(Int, Array(Int, Bool))
Definition at line 3978 of file z3py.py.
Referenced by Array(), ArraySortRef.domain(), Context.mkArraySort(), Context.MkArraySort(), and ArraySortRef.range().
def z3py.binary_interpolant | ( | a, | |
b, | |||
p = None , |
|||
ctx = None |
|||
) |
Compute an interpolant for a binary conjunction. If a & b is unsatisfiable, returns an interpolant for a & b. This is a formula phi such that 1) a implies phi 2) b implies not phi 3) All the uninterpreted symbols of phi occur in both a and b. If a & b is satisfiable, raises an object of class ModelRef that represents a model of a &b. If parameters p are supplied, these are used in creating the solver that determines satisfiability. x = Int('x') print binary_interpolant(x<0,x>2) Not(x >= 0)
Definition at line 7391 of file z3py.py.
def z3py.BitVec | ( | name, | |
bv, | |||
ctx = None |
|||
) |
Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort. If `ctx=None`, then the global context is used. >>> x = BitVec('x', 16) >>> is_bv(x) True >>> x.size() 16 >>> x.sort() BitVec(16) >>> word = BitVecSort(16) >>> x2 = BitVec('x', word) >>> eq(x, x2) True
Definition at line 3476 of file z3py.py.
Referenced by BitVecRef.__add__(), BitVecRef.__and__(), BitVecRef.__div__(), BitVecRef.__invert__(), BitVecRef.__mod__(), BitVecRef.__mul__(), BitVecRef.__neg__(), BitVecRef.__or__(), BitVecRef.__pos__(), BitVecRef.__radd__(), BitVecRef.__rand__(), BitVecRef.__rdiv__(), BitVecRef.__rlshift__(), BitVecRef.__rmod__(), BitVecRef.__rmul__(), BitVecRef.__ror__(), BitVecRef.__rrshift__(), BitVecRef.__rsub__(), BitVecRef.__rxor__(), BitVecRef.__sub__(), BitVecRef.__xor__(), BitVecs(), BitVecSort(), BV2Int(), Extract(), FPs(), is_bv(), is_bv_value(), RepeatBitVec(), SignExt(), BitVecRef.size(), BitVecRef.sort(), SRem(), UDiv(), URem(), and ZeroExt().
def z3py.BitVecs | ( | names, | |
bv, | |||
ctx = None |
|||
) |
Return a tuple of bit-vector constants of size bv. >>> x, y, z = BitVecs('x y z', 16) >>> x.size() 16 >>> x.sort() BitVec(16) >>> Sum(x, y, z) 0 + x + y + z >>> Product(x, y, z) 1*x*y*z >>> simplify(Product(x, y, z)) x*y*z
Definition at line 3499 of file z3py.py.
Referenced by BitVecRef.__ge__(), BitVecRef.__gt__(), BitVecRef.__le__(), BitVecRef.__lshift__(), BitVecRef.__lt__(), BitVecRef.__rshift__(), FPs(), LShR(), RotateLeft(), RotateRight(), UGE(), UGT(), ULE(), and ULT().
def z3py.BitVecSort | ( | sz, | |
ctx = None |
|||
) |
Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used. >>> Byte = BitVecSort(8) >>> Word = BitVecSort(16) >>> Byte BitVec(8) >>> x = Const('x', Byte) >>> eq(x, BitVec('x', 8)) True
Definition at line 3446 of file z3py.py.
Referenced by BitVec(), BitVecSortRef.cast(), fpToSBV(), fpToUBV(), is_bv_sort(), Context.mkBitVecSort(), Context.MkBitVecSort(), BitVecSortRef.size(), and BitVecRef.sort().
def z3py.BitVecVal | ( | val, | |
bv, | |||
ctx = None |
|||
) |
Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used. >>> v = BitVecVal(10, 32) >>> v 10 >>> print("0x%.8x" % v.as_long()) 0x0000000a
Definition at line 3460 of file z3py.py.
Referenced by BitVecRef.__lshift__(), BitVecRef.__rshift__(), BitVecNumRef.as_long(), BitVecNumRef.as_signed_long(), Concat(), is_bv_value(), LShR(), RepeatBitVec(), SignExt(), and ZeroExt().
def z3py.Bool | ( | name, | |
ctx = None |
|||
) |
Return a Boolean constant named `name`. If `ctx=None`, then the global context is used. >>> p = Bool('p') >>> q = Bool('q') >>> And(p, q) And(p, q)
Definition at line 1371 of file z3py.py.
Referenced by Solver.assert_and_track(), and Not().
def z3py.Bools | ( | names, | |
ctx = None |
|||
) |
Return a tuple of Boolean constants. `names` is a single string containing all names separated by blank spaces. If `ctx=None`, then the global context is used. >>> p, q, r = Bools('p q r') >>> And(p, Or(q, r)) And(p, Or(q, r))
Definition at line 1382 of file z3py.py.
Referenced by And(), Implies(), Or(), Solver.unsat_core(), and Xor().
def z3py.BoolSort | ( | ctx = None | ) |
Return the Boolean Z3 sort. If `ctx=None`, then the global context is used. >>> BoolSort() Bool >>> p = Const('p', BoolSort()) >>> is_bool(p) True >>> r = Function('r', IntSort(), IntSort(), BoolSort()) >>> r(0, 1) r(0, 1) >>> is_bool(r(0, 1)) True
Definition at line 1336 of file z3py.py.
Referenced by ArrayRef.__getitem__(), ArraySort(), Fixedpoint.assert_exprs(), Bool(), ArraySortRef.domain(), ArrayRef.domain(), Context.getBoolSort(), If(), IntSort(), is_arith_sort(), Context.mkBoolSort(), Context.MkBoolSort(), ArraySortRef.range(), ArrayRef.range(), and ArrayRef.sort().
def z3py.BoolVal | ( | val, | |
ctx = None |
|||
) |
Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used. >>> BoolVal(True) True >>> is_true(BoolVal(True)) True >>> is_true(True) False >>> is_false(BoolVal(False)) True
Definition at line 1353 of file z3py.py.
Referenced by ApplyResult.as_expr(), BoolSortRef.cast(), and Solver.to_smt2().
def z3py.BoolVector | ( | prefix, | |
sz, | |||
ctx = None |
|||
) |
Return a list of Boolean constants of size `sz`. The constants are named using the given prefix. If `ctx=None`, then the global context is used. >>> P = BoolVector('p', 3) >>> P [p__0, p__1, p__2] >>> And(P) And(p__0, p__1, p__2)
Definition at line 1397 of file z3py.py.
Referenced by And(), and Or().
def z3py.BV2Int | ( | a | ) |
Return the Z3 expression BV2Int(a). >>> b = BitVec('b', 3) >>> BV2Int(b).sort() Int >>> x = Int('x') >>> x > BV2Int(b) x > BV2Int(b) >>> solve(x > BV2Int(b), b == 1, x < 3) [b = 1, x = 2]
Definition at line 3428 of file z3py.py.
def z3py.BVRedAnd | ( | a | ) |
Return the reduction-and expression of `a`.
Definition at line 3827 of file z3py.py.
def z3py.BVRedOr | ( | a | ) |
Return the reduction-or expression of `a`.
Definition at line 3833 of file z3py.py.
def z3py.Cbrt | ( | a, | |
ctx = None |
|||
) |
def z3py.Concat | ( | args | ) |
Create a Z3 bit-vector concatenation expression. >>> v = BitVecVal(1, 4) >>> Concat(v, v+1, v) Concat(Concat(1, 1 + 1), 1) >>> simplify(Concat(v, v+1, v)) 289 >>> print("%.3x" % simplify(Concat(v, v+1, v)).as_long()) 121
Definition at line 3519 of file z3py.py.
Referenced by BitVecRef.size().
def z3py.Cond | ( | p, | |
t1, | |||
t2, | |||
ctx = None |
|||
) |
Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise. >>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
Definition at line 6963 of file z3py.py.
Referenced by If().
def z3py.Const | ( | name, | |
sort | |||
) |
Create a constant of the given sort. >>> Const('x', IntSort()) x
Definition at line 1145 of file z3py.py.
Referenced by BitVecSort(), Consts(), FPSort(), IntSort(), RealSort(), and DatatypeSortRef.recognizer().
def z3py.Consts | ( | names, | |
sort | |||
) |
Create a several constants of the given sort. `names` is a string containing the names of all constants to be created. Blank spaces separate the names of different constants. >>> x, y, z = Consts('x y z', IntSort()) >>> x + y + z x + y + z
Definition at line 1156 of file z3py.py.
Referenced by ModelRef.get_sort(), ModelRef.get_universe(), ModelRef.num_sorts(), and ModelRef.sorts().
def z3py.CreateDatatypes | ( | ds | ) |
Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects. In the following example we define a Tree-List using two mutually recursive datatypes. >>> TreeList = Datatype('TreeList') >>> Tree = Datatype('Tree') >>> # Tree has two constructors: leaf and node >>> Tree.declare('leaf', ('val', IntSort())) >>> # a node contains a list of trees >>> Tree.declare('node', ('children', TreeList)) >>> TreeList.declare('nil') >>> TreeList.declare('cons', ('car', Tree), ('cdr', TreeList)) >>> Tree, TreeList = CreateDatatypes(Tree, TreeList) >>> Tree.val(Tree.leaf(10)) val(leaf(10)) >>> simplify(Tree.val(Tree.leaf(10))) 10 >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil))) >>> n1 node(cons(leaf(10), cons(leaf(20), nil))) >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil)) >>> simplify(n2 == n1) False >>> simplify(TreeList.car(Tree.children(n2)) == n1) True
Definition at line 4232 of file z3py.py.
Referenced by Datatype.create().
def z3py.DeclareSort | ( | name, | |
ctx = None |
|||
) |
Create a new uninterpred sort named `name`. If `ctx=None`, then the new sort is declared in the global Z3Py context. >>> A = DeclareSort('A') >>> a = Const('a', A) >>> b = Const('b', A) >>> a.sort() == A True >>> b.sort() == A True >>> a == b a == b
Definition at line 567 of file z3py.py.
Referenced by ModelRef.get_sort(), ModelRef.get_universe(), ModelRef.num_sorts(), and ModelRef.sorts().
def z3py.describe_probes | ( | ) |
def z3py.describe_tactics | ( | ) |
def z3py.disable_trace | ( | msg | ) |
def z3py.Distinct | ( | args | ) |
Create a Z3 distinct expression. >>> x = Int('x') >>> y = Int('y') >>> Distinct(x, y) x != y >>> z = Int('z') >>> Distinct(x, y, z) Distinct(x, y, z) >>> simplify(Distinct(x, y, z)) Distinct(x, y, z) >>> simplify(Distinct(x, y, z), blast_distinct=True) And(Not(x == y), Not(x == z), Not(y == z))
Definition at line 1114 of file z3py.py.
def z3py.enable_trace | ( | msg | ) |
def z3py.EnumSort | ( | name, | |
values, | |||
ctx = None |
|||
) |
Return a new enumeration sort named `name` containing the given values. The result is a pair (sort, list of constants). Example: >>> Color, (red, green, blue) = EnumSort('Color', ['red', 'green', 'blue'])
Definition at line 4421 of file z3py.py.
Referenced by Context.mkEnumSort(), and Context.MkEnumSort().
def z3py.eq | ( | a, | |
b | |||
) |
Return `True` if `a` and `b` are structurally identical AST nodes. >>> x = Int('x') >>> y = Int('y') >>> eq(x, y) False >>> eq(x + 1, x + 1) True >>> eq(x + 1, 1 + x) False >>> eq(simplify(x + 1), simplify(1 + x)) True
Definition at line 372 of file z3py.py.
Referenced by BitVec(), BitVecSort(), FP(), FPSort(), FreshBool(), FreshInt(), FreshReal(), get_map_func(), Select(), and substitute().
def z3py.Exists | ( | vs, | |
body, | |||
weight = 1 , |
|||
qid = "" , |
|||
skid = "" , |
|||
patterns = [] , |
|||
no_patterns = [] |
|||
) |
Create a Z3 exists formula. The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations. See http://rise4fun.com/Z3Py/tutorial/advanced for more details. >>> f = Function('f', IntSort(), IntSort(), IntSort()) >>> x = Int('x') >>> y = Int('y') >>> q = Exists([x, y], f(x, y) >= x, skid="foo") >>> q Exists([x, y], f(x, y) >= x) >>> is_quantifier(q) True >>> r = Tactic('nnf')(q).as_expr() >>> is_quantifier(r) False
Definition at line 1819 of file z3py.py.
Referenced by Fixedpoint.abstract(), and QuantifierRef.is_forall().
def z3py.Extract | ( | high, | |
low, | |||
a | |||
) |
Create a Z3 bit-vector extraction expression. >>> x = BitVec('x', 8) >>> Extract(6, 2, x) Extract(6, 2, x) >>> Extract(6, 2, x).sort() BitVec(5)
Definition at line 3540 of file z3py.py.
def z3py.FailIf | ( | p, | |
ctx = None |
|||
) |
Return a tactic that fails if the probe `p` evaluates to true. Otherwise, it returns the input goal unmodified. In the following example, the tactic applies 'simplify' if and only if there are more than 2 constraints in the goal. >>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify')) >>> x, y = Ints('x y') >>> g = Goal() >>> g.add(x > 0) >>> g.add(y > 0) >>> t(g) [[x > 0, y > 0]] >>> g.add(x == y + 1) >>> t(g) [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
Definition at line 6926 of file z3py.py.
def z3py.Float128 | ( | ctx = None | ) |
def z3py.Float16 | ( | ctx = None | ) |
def z3py.Float32 | ( | ctx = None | ) |
def z3py.Float64 | ( | ctx = None | ) |
def z3py.FloatHalf | ( | ctx = None | ) |
def FloatSingle | ( | ctx = None | ) |
def z3py.ForAll | ( | vs, | |
body, | |||
weight = 1 , |
|||
qid = "" , |
|||
skid = "" , |
|||
patterns = [] , |
|||
no_patterns = [] |
|||
) |
Create a Z3 forall formula. The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations. See http://rise4fun.com/Z3Py/tutorial/advanced for more details. >>> f = Function('f', IntSort(), IntSort(), IntSort()) >>> x = Int('x') >>> y = Int('y') >>> ForAll([x, y], f(x, y) >= x) ForAll([x, y], f(x, y) >= x) >>> ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ]) ForAll([x, y], f(x, y) >= x) >>> ForAll([x, y], f(x, y) >= x, weight=10) ForAll([x, y], f(x, y) >= x)
Definition at line 1800 of file z3py.py.
Referenced by Fixedpoint.abstract(), QuantifierRef.body(), QuantifierRef.children(), QuantifierRef.is_forall(), is_pattern(), is_quantifier(), MultiPattern(), QuantifierRef.num_patterns(), QuantifierRef.num_vars(), QuantifierRef.pattern(), QuantifierRef.var_name(), QuantifierRef.var_sort(), and QuantifierRef.weight().
def z3py.FP | ( | name, | |
fpsort, | |||
ctx = None |
|||
) |
Return a floating-point constant named `name`. `fpsort` is the floating-point sort. If `ctx=None`, then the global context is used. >>> x = FP('x', FPSort(8, 24)) >>> is_fp(x) True >>> x.ebits() 8 >>> x.sort() FPSort(8, 24) >>> word = FPSort(8, 24) >>> x2 = FP('x', word) >>> eq(x, x2) True
Definition at line 8008 of file z3py.py.
Referenced by FPRef.__add__(), FPRef.__mul__(), FPRef.__radd__(), FPRef.__rmul__(), FPRef.__rsub__(), FPRef.__sub__(), fpAdd(), fpDiv(), fpMax(), fpMin(), fpMul(), fpNeg(), fpRem(), FPSort(), fpSub(), fpToIEEEBV(), fpToReal(), fpToSBV(), fpToUBV(), is_fp(), is_fp_value(), and FPRef.sort().
def z3py.fpAbs | ( | a | ) |
Create a Z3 floating-point absolute value expression. >>> s = FPSort(8, 24) >>> rm = RNE() >>> x = FPVal(1.0, s) >>> fpAbs(x) fpAbs(1) >>> y = FPVal(-20.0, s) >>> y -1.25*(2**4) >>> fpAbs(y) fpAbs(-1.25*(2**4)) >>> fpAbs(-1.25*(2**4)) fpAbs(-1.25*(2**4)) >>> fpAbs(x).sort() FPSort(8, 24)
Definition at line 8048 of file z3py.py.
def z3py.fpAdd | ( | rm, | |
a, | |||
b | |||
) |
Create a Z3 floating-point addition expression. >>> s = FPSort(8, 24) >>> rm = RNE() >>> x = FP('x', s) >>> y = FP('y', s) >>> fpAdd(rm, x, y) fpAdd(RNE(), x, y) >>> fpAdd(rm, x, y).sort() FPSort(8, 24)
def z3py.fpDiv | ( | rm, | |
a, | |||
b | |||
) |
Create a Z3 floating-point divison expression. >>> s = FPSort(8, 24) >>> rm = RNE() >>> x = FP('x', s) >>> y = FP('y', s) >>> fpDiv(rm, x, y) fpDiv(RNE(), x, y) >>> fpDiv(rm, x, y).sort() FPSort(8, 24)
def z3py.fpEQ | ( | a, | |
b | |||
) |
Create the Z3 floating-point expression `other <= self`. >>> x, y = FPs('x y', FPSort(8, 24)) >>> fpEQ(x, y) fpEQ(x, y) >>> fpEQ(x, y).sexpr() '(fp.eq x y)'
Definition at line 8368 of file z3py.py.
Referenced by fpNEQ().
def z3py.fpFMA | ( | rm, | |
a, | |||
b, | |||
c | |||
) |
Create a Z3 floating-point fused multiply-add expression.
Definition at line 8221 of file z3py.py.
def z3py.fpFP | ( | sgn, | |
exp, | |||
sig | |||
) |
Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectorssgn, sig, and exp.
def z3py.fpGEQ | ( | a, | |
b | |||
) |
Create the Z3 floating-point expression `other <= self`. >>> x, y = FPs('x y', FPSort(8, 24)) >>> x + y x + y >>> fpGEQ(x, y) x >= y >>> (x >= y).sexpr() '(fp.geq x y)'
Definition at line 8353 of file z3py.py.
def z3py.fpGT | ( | a, | |
b | |||
) |
Create the Z3 floating-point expression `other <= self`. >>> x, y = FPs('x y', FPSort(8, 24)) >>> fpGT(x, y) x > y >>> (x > y).sexpr() '(fp.gt x y)'
Definition at line 8339 of file z3py.py.
def z3py.fpInfinity | ( | s, | |
negative | |||
) |
def z3py.fpIsInfinite | ( | a | ) |
def z3py.fpIsNaN | ( | a | ) |
def z3py.fpIsNegative | ( | a | ) |
def z3py.fpIsNormal | ( | a | ) |
def z3py.fpIsPositive | ( | a | ) |
def z3py.fpIsSubnormal | ( | a | ) |
def z3py.fpIsZero | ( | a | ) |
def z3py.fpLEQ | ( | a, | |
b | |||
) |
Create the Z3 floating-point expression `other <= self`. >>> x, y = FPs('x y', FPSort(8, 24)) >>> fpLEQ(x, y) x <= y >>> (x <= y).sexpr() '(fp.leq x y)'
Definition at line 8326 of file z3py.py.
def z3py.fpLT | ( | a, | |
b | |||
) |
Create the Z3 floating-point expression `other <= self`. >>> x, y = FPs('x y', FPSort(8, 24)) >>> fpLT(x, y) x < y >>> (x <= y).sexpr() '(fp.leq x y)'
Definition at line 8313 of file z3py.py.
def z3py.fpMax | ( | a, | |
b | |||
) |
Create a Z3 floating-point maximum expression. >>> s = FPSort(8, 24) >>> rm = RNE() >>> x = FP('x', s) >>> y = FP('y', s) >>> fpMax(x, y) fpMax(x, y) >>> fpMax(x, y).sort() FPSort(8, 24)
def z3py.fpMin | ( | a, | |
b | |||
) |
Create a Z3 floating-point minimium expression. >>> s = FPSort(8, 24) >>> rm = RNE() >>> x = FP('x', s) >>> y = FP('y', s) >>> fpMin(x, y) fpMin(x, y) >>> fpMin(x, y).sort() FPSort(8, 24)
def z3py.fpMinusInfinity | ( | s | ) |
def z3py.fpMinusZero | ( | s | ) |
def z3py.fpMul | ( | rm, | |
a, | |||
b | |||
) |
Create a Z3 floating-point multiplication expression. >>> s = FPSort(8, 24) >>> rm = RNE() >>> x = FP('x', s) >>> y = FP('y', s) >>> fpMul(rm, x, y) fpMul(RNE(), x, y) >>> fpMul(rm, x, y).sort() FPSort(8, 24)
def z3py.fpNaN | ( | s | ) |
def z3py.fpNeg | ( | a | ) |
def z3py.fpNEQ | ( | a, | |
b | |||
) |
Create the Z3 floating-point expression `other <= self`. >>> x, y = FPs('x y', FPSort(8, 24)) >>> fpNEQ(x, y) Not(fpEQ(x, y)) >>> (x != y).sexpr() '(not (fp.eq x y))'
Definition at line 8381 of file z3py.py.
def z3py.fpPlusInfinity | ( | s | ) |
def z3py.fpPlusZero | ( | s | ) |
def z3py.fpRem | ( | a, | |
b | |||
) |
Create a Z3 floating-point remainder expression. >>> s = FPSort(8, 24) >>> x = FP('x', s) >>> y = FP('y', s) >>> fpRem(x, y) fpRem(x, y) >>> fpRem(x, y).sort() FPSort(8, 24)
def z3py.fpRoundToIntegral | ( | rm, | |
a | |||
) |
Create a Z3 floating-point roundToIntegral expression.
Definition at line 8245 of file z3py.py.
def z3py.FPs | ( | names, | |
fpsort, | |||
ctx = None |
|||
) |
Return an array of floating-point constants. >>> x, y, z = BitVecs('x y z', 16) >>> x.size() 16 >>> x.sort() BitVec(16) >>> Sum(x, y, z) 0 + x + y + z >>> Product(x, y, z) 1*x*y*z >>> simplify(Product(x, y, z)) x*y*z
Definition at line 8028 of file z3py.py.
Referenced by fpEQ(), fpGEQ(), fpGT(), fpLEQ(), fpLT(), and fpNEQ().
def z3py.FPSort | ( | ebits, | |
sbits, | |||
ctx = None |
|||
) |
Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used. >>> Single = FPSort(8, 24) >>> Double = FPSort(11, 53) >>> Single FPSort(8, 24) >>> x = Const('x', Single) >>> eq(x, FP('x', FPSort(8, 24))) True
Definition at line 7920 of file z3py.py.
Referenced by FPRef.__add__(), FPRef.__mul__(), FPRef.__radd__(), FPRef.__rmul__(), FPRef.__rsub__(), FPRef.__sub__(), FPSortRef.cast(), FPSortRef.ebits(), FPRef.ebits(), FPNumRef.exponent(), FPNumRef.exponent_as_long(), FP(), fpAbs(), fpAdd(), fpDiv(), fpEQ(), fpGEQ(), fpGT(), fpLEQ(), fpLT(), fpMax(), fpMin(), fpMul(), fpNeg(), fpNEQ(), fpRem(), fpSub(), fpToIEEEBV(), fpToReal(), fpToSBV(), fpToUBV(), FPVal(), is_fp(), is_fp_sort(), is_fp_value(), is_fprm_sort(), FPNumRef.isNegative(), Context.mkFPSort(), Context.mkFPSort128(), Context.MkFPSort128(), Context.mkFPSort16(), Context.MkFPSort16(), Context.mkFPSort32(), Context.MkFPSort32(), Context.mkFPSort64(), Context.MkFPSort64(), Context.mkFPSortDouble(), Context.MkFPSortDouble(), Context.mkFPSortHalf(), Context.MkFPSortHalf(), Context.mkFPSortQuadruple(), Context.MkFPSortQuadruple(), Context.mkFPSortSingle(), Context.MkFPSortSingle(), FPSortRef.sbits(), FPRef.sbits(), FPNumRef.sign(), FPNumRef.significand(), and FPRef.sort().
def z3py.fpSqrt | ( | rm, | |
a | |||
) |
def z3py.fpSub | ( | rm, | |
a, | |||
b | |||
) |
Create a Z3 floating-point subtraction expression. >>> s = FPSort(8, 24) >>> rm = RNE() >>> x = FP('x', s) >>> y = FP('y', s) >>> fpSub(rm, x, y) fpSub(RNE(), x, y) >>> fpSub(rm, x, y).sort() FPSort(8, 24)
def z3py.fpToFP | ( | a1, | |
a2 = None , |
|||
a3 = None |
|||
) |
Create a Z3 floating-point conversion expression from other terms.
Definition at line 8403 of file z3py.py.
def z3py.fpToFPUnsigned | ( | rm, | |
x, | |||
s | |||
) |
Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression.
Definition at line 8416 of file z3py.py.
def z3py.fpToIEEEBV | ( | x | ) |
\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format. The size of the resulting bit-vector is automatically determined. Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion knows only one NaN and it will always produce the same bit-vector represenatation of that NaN. >>> x = FP('x', FPSort(8, 24)) >>> y = fpToIEEEBV(x) >>> print is_fp(x) True >>> print is_bv(y) True >>> print is_fp(y) False >>> print is_bv(x) False
Definition at line 8482 of file z3py.py.
def z3py.fpToReal | ( | x | ) |
Create a Z3 floating-point conversion expression, from floating-point expression to real. >>> x = FP('x', FPSort(8, 24)) >>> y = fpToReal(x) >>> print is_fp(x) True >>> print is_real(y) True >>> print is_fp(y) False >>> print is_real(x) False
Definition at line 8464 of file z3py.py.
def z3py.fpToSBV | ( | rm, | |
x, | |||
s | |||
) |
Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector. >>> x = FP('x', FPSort(8, 24)) >>> y = fpToSBV(RTZ(), x, BitVecSort(32)) >>> print is_fp(x) True >>> print is_bv(y) True >>> print is_fp(y) False >>> print is_bv(x) False
Definition at line 8424 of file z3py.py.
def z3py.fpToUBV | ( | rm, | |
x, | |||
s | |||
) |
Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector. >>> x = FP('x', FPSort(8, 24)) >>> y = fpToUBV(RTZ(), x, BitVecSort(32)) >>> print is_fp(x) True >>> print is_bv(y) True >>> print is_fp(y) False >>> print is_bv(x) False
Definition at line 8444 of file z3py.py.
def z3py.FPVal | ( | sig, | |
exp = None , |
|||
fps = None , |
|||
ctx = None |
|||
) |
Return a floating-point value of value `val` and sort `fps`. If `ctx=None`, then the global context is used. >>> v = FPVal(20.0, FPSort(8, 24)) >>> v 1.25*(2**4) >>> print("0x%.8x" % v.exponent_as_long()) 0x00000004 >>> v = FPVal(2.25, FPSort(8, 24)) >>> v 1.125*(2**1) >>> v = FPVal(-2.25, FPSort(8, 24)) >>> v -1.125*(2**1)
Definition at line 7979 of file z3py.py.
Referenced by fpAbs(), fpNeg(), fpRoundToIntegral(), fpSqrt(), and is_fp_value().
def z3py.fpZero | ( | s, | |
negative | |||
) |
def z3py.FreshBool | ( | prefix = 'b' , |
|
ctx = None |
|||
) |
Return a fresh Boolean constant in the given context using the given prefix. If `ctx=None`, then the global context is used. >>> b1 = FreshBool() >>> b2 = FreshBool() >>> eq(b1, b2) False
Definition at line 1411 of file z3py.py.
def z3py.FreshInt | ( | prefix = 'x' , |
|
ctx = None |
|||
) |
Return a fresh integer constant in the given context using the given prefix. >>> x = FreshInt() >>> y = FreshInt() >>> eq(x, y) False >>> x.sort() Int
Definition at line 2763 of file z3py.py.
def z3py.FreshReal | ( | prefix = 'b' , |
|
ctx = None |
|||
) |
Return a fresh real constant in the given context using the given prefix. >>> x = FreshReal() >>> y = FreshReal() >>> eq(x, y) False >>> x.sort() Real
Definition at line 2815 of file z3py.py.
def z3py.Function | ( | name, | |
sig | |||
) |
Create a new Z3 uninterpreted function with the given sorts. >>> f = Function('f', IntSort(), IntSort()) >>> f(f(0)) f(f(0))
Definition at line 705 of file z3py.py.
Referenced by ModelRef.__getitem__(), ModelRef.__len__(), FuncEntry.arg_value(), FuncInterp.arity(), FuncEntry.as_list(), FuncInterp.as_list(), QuantifierRef.body(), QuantifierRef.children(), ModelRef.decls(), FuncInterp.else_value(), FuncInterp.entry(), Exists(), ForAll(), ModelRef.get_interp(), get_map_func(), QuantifierRef.is_forall(), is_map(), is_pattern(), is_quantifier(), Map(), MultiPattern(), FuncEntry.num_args(), FuncInterp.num_entries(), QuantifierRef.num_patterns(), QuantifierRef.num_vars(), QuantifierRef.pattern(), FuncEntry.value(), QuantifierRef.var_name(), QuantifierRef.var_sort(), and QuantifierRef.weight().
def z3py.get_as_array_func | ( | n | ) |
Return the function declaration f associated with a Z3 expression of the form (_ as-array f).
def z3py.get_default_fp_sort | ( | ctx = None | ) |
def z3py.get_default_rounding_mode | ( | ctx = None | ) |
def z3py.get_map_func | ( | a | ) |
Return the function declaration associated with a Z3 map array expression. >>> f = Function('f', IntSort(), IntSort()) >>> b = Array('b', IntSort(), IntSort()) >>> a = Map(f, b) >>> eq(f, get_map_func(a)) True >>> get_map_func(a) f >>> get_map_func(a)(0) f(0)
Definition at line 3961 of file z3py.py.
def z3py.get_param | ( | name | ) |
def z3py.get_var_index | ( | a | ) |
Return the de-Bruijn index of the Z3 bounded variable `a`. >>> x = Int('x') >>> y = Int('y') >>> is_var(x) False >>> is_const(x) True >>> f = Function('f', IntSort(), IntSort(), IntSort()) >>> # Z3 replaces x and y with bound variables when ForAll is executed. >>> q = ForAll([x, y], f(x, y) == x + y) >>> q.body() f(Var(1), Var(0)) == Var(1) + Var(0) >>> b = q.body() >>> b.arg(0) f(Var(1), Var(0)) >>> v1 = b.arg(0).arg(0) >>> v2 = b.arg(0).arg(1) >>> v1 Var(1) >>> v2 Var(0) >>> get_var_index(v1) 1 >>> get_var_index(v2) 0
Definition at line 1048 of file z3py.py.
def z3py.get_version | ( | ) |
def z3py.get_version_string | ( | ) |
def z3py.help_simplify | ( | ) |
def z3py.If | ( | a, | |
b, | |||
c, | |||
ctx = None |
|||
) |
Create a Z3 if-then-else expression. >>> x = Int('x') >>> y = Int('y') >>> max = If(x > y, x, y) >>> max If(x > y, x, y) >>> simplify(max) If(x <= y, y, x)
Definition at line 1092 of file z3py.py.
def z3py.Implies | ( | a, | |
b, | |||
ctx = None |
|||
) |
Create a Z3 implies expression. >>> p, q = Bools('p q') >>> Implies(p, q) Implies(p, q) >>> simplify(Implies(p, q)) Or(Not(p), q)
Definition at line 1424 of file z3py.py.
Referenced by Fixedpoint.add_rule(), Store(), Solver.unsat_core(), Update(), and Fixedpoint.update_rule().
def z3py.Int | ( | name, | |
ctx = None |
|||
) |
Return an integer constant named `name`. If `ctx=None`, then the global context is used. >>> x = Int('x') >>> is_int(x) True >>> is_int(x + 1) True
Definition at line 2728 of file z3py.py.
Referenced by ArithRef.__add__(), AstVector.__contains__(), AstMap.__contains__(), ArithRef.__div__(), Statistics.__getattr__(), ArrayRef.__getitem__(), AstVector.__getitem__(), AstMap.__getitem__(), ModelRef.__getitem__(), Statistics.__getitem__(), AstVector.__len__(), AstMap.__len__(), ModelRef.__len__(), Statistics.__len__(), ArithRef.__mod__(), ArithRef.__neg__(), ArithRef.__pos__(), ArithRef.__radd__(), ArithRef.__rdiv__(), ArithRef.__rmod__(), ArithRef.__rsub__(), AstVector.__setitem__(), AstMap.__setitem__(), ArithRef.__sub__(), Goal.add(), Solver.add(), Goal.append(), Solver.append(), Goal.as_expr(), Solver.assert_and_track(), Goal.assert_exprs(), Solver.assert_exprs(), Solver.assertions(), binary_interpolant(), QuantifierRef.body(), BV2Int(), Solver.check(), QuantifierRef.children(), ModelRef.decls(), AstMap.erase(), ModelRef.eval(), ModelRef.evaluate(), Exists(), ForAll(), ModelRef.get_interp(), Statistics.get_key_value(), Goal.insert(), Solver.insert(), Interpolant(), is_arith(), is_arith_sort(), is_bv(), QuantifierRef.is_forall(), is_fp(), ArithSortRef.is_int(), ArithRef.is_int(), is_int(), is_int_value(), is_pattern(), is_quantifier(), ArithSortRef.is_real(), is_real(), is_select(), is_to_real(), K(), AstMap.keys(), Statistics.keys(), Solver.model(), MultiPattern(), QuantifierRef.num_patterns(), QuantifierRef.num_vars(), QuantifierRef.pattern(), Solver.pop(), AstVector.push(), Solver.push(), Solver.reason_unknown(), AstMap.reset(), Solver.reset(), AstVector.resize(), Select(), sequence_interpolant(), Solver.sexpr(), Goal.simplify(), ArithRef.sort(), Solver.statistics(), Store(), ToReal(), Goal.translate(), AstVector.translate(), tree_interpolant(), Update(), QuantifierRef.var_name(), QuantifierRef.var_sort(), and QuantifierRef.weight().
def z3py.Interpolant | ( | a, | |
ctx = None |
|||
) |
Create an interpolation operator. The argument is an interpolation pattern (see tree_interpolant). >>> x = Int('x') >>> print Interpolant(x>0) interp(x > 0)
Definition at line 7318 of file z3py.py.
Referenced by binary_interpolant(), and tree_interpolant().
def z3py.Ints | ( | names, | |
ctx = None |
|||
) |
Return a tuple of Integer constants. >>> x, y, z = Ints('x y z') >>> Sum(x, y, z) x + y + z
Definition at line 2740 of file z3py.py.
Referenced by ArithRef.__ge__(), Goal.__getitem__(), ArithRef.__gt__(), ArithRef.__le__(), Goal.__len__(), ArithRef.__lt__(), Goal.depth(), Goal.get(), Goal.inconsistent(), is_add(), is_div(), is_ge(), is_gt(), is_idiv(), is_le(), is_lt(), is_mod(), is_mul(), is_sub(), Goal.prec(), Goal.size(), Store(), Solver.unsat_core(), and Update().
def z3py.IntSort | ( | ctx = None | ) |
Return the interger sort in the given context. If `ctx=None`, then the global context is used. >>> IntSort() Int >>> x = Const('x', IntSort()) >>> is_int(x) True >>> x.sort() == IntSort() True >>> x.sort() == BoolSort() False
Definition at line 2625 of file z3py.py.
Referenced by ArrayRef.__getitem__(), ModelRef.__getitem__(), ModelRef.__len__(), DatatypeSortRef.accessor(), FuncEntry.arg_value(), FuncInterp.arity(), Array(), ArraySort(), FuncEntry.as_list(), FuncInterp.as_list(), QuantifierRef.body(), ArithSortRef.cast(), QuantifierRef.children(), DatatypeSortRef.constructor(), Datatype.create(), CreateDatatypes(), Datatype.declare(), ModelRef.decls(), ArraySortRef.domain(), ArrayRef.domain(), FuncInterp.else_value(), FuncInterp.entry(), Exists(), ForAll(), FreshInt(), ModelRef.get_interp(), get_map_func(), Context.getIntSort(), Int(), is_arith_sort(), is_array(), is_bv_sort(), is_const_array(), QuantifierRef.is_forall(), is_fp_sort(), is_K(), is_map(), is_pattern(), is_quantifier(), is_select(), is_store(), K(), Map(), Context.mkIntSort(), Context.MkIntSort(), MultiPattern(), FuncEntry.num_args(), DatatypeSortRef.num_constructors(), FuncInterp.num_entries(), QuantifierRef.num_patterns(), QuantifierRef.num_vars(), QuantifierRef.pattern(), ArraySortRef.range(), ArrayRef.range(), DatatypeSortRef.recognizer(), Select(), ArrayRef.sort(), Store(), Update(), FuncEntry.value(), QuantifierRef.var_name(), QuantifierRef.var_sort(), and QuantifierRef.weight().
def z3py.IntVal | ( | val, | |
ctx = None |
|||
) |
Return a Z3 integer value. If `ctx=None`, then the global context is used. >>> IntVal(1) 1 >>> IntVal("100") 100
Definition at line 2672 of file z3py.py.
Referenced by AstMap.__len__(), ArithRef.__mod__(), ArithRef.__pow__(), ArithRef.__rpow__(), AstMap.__setitem__(), IntNumRef.as_long(), IntNumRef.as_string(), is_arith(), is_int(), is_int_value(), is_rational_value(), AstMap.keys(), and AstMap.reset().
def z3py.IntVector | ( | prefix, | |
sz, | |||
ctx = None |
|||
) |
def z3py.is_add | ( | a | ) |
def z3py.is_algebraic_value | ( | a | ) |
def z3py.is_and | ( | a | ) |
def z3py.is_app | ( | a | ) |
Return `True` if `a` is a Z3 function application. Note that, constants are function applications with 0 arguments. >>> a = Int('a') >>> is_app(a) True >>> is_app(a + 1) True >>> is_app(IntSort()) False >>> is_app(1) False >>> is_app(IntVal(1)) True >>> x = Int('x') >>> is_app(ForAll(x, x >= 0)) False
Definition at line 981 of file z3py.py.
Referenced by ExprRef.arg(), ExprRef.children(), ExprRef.decl(), is_app_of(), is_const(), and ExprRef.num_args().
def z3py.is_app_of | ( | a, | |
k | |||
) |
Return `True` if `a` is an application of the given kind `k`. >>> x = Int('x') >>> n = x + 1 >>> is_app_of(n, Z3_OP_ADD) True >>> is_app_of(n, Z3_OP_MUL) False
Definition at line 1080 of file z3py.py.
Referenced by is_add(), is_and(), is_distinct(), is_eq(), is_false(), is_not(), is_or(), and is_true().
def z3py.is_arith | ( | a | ) |
Return `True` if `a` is an arithmetical expression. >>> x = Int('x') >>> is_arith(x) True >>> is_arith(x + 1) True >>> is_arith(1) False >>> is_arith(IntVal(1)) True >>> y = Real('y') >>> is_arith(y) True >>> is_arith(y + 1) True
Definition at line 2210 of file z3py.py.
Referenced by is_algebraic_value().
def z3py.is_arith_sort | ( | s | ) |
def z3py.is_array | ( | a | ) |
def z3py.is_as_array | ( | n | ) |
Return true if n is a Z3 expression of the form (_ as-array f).
Definition at line 5552 of file z3py.py.
Referenced by get_as_array_func().
def z3py.is_ast | ( | a | ) |
Return `True` if `a` is an AST node. >>> is_ast(10) False >>> is_ast(IntVal(10)) True >>> is_ast(Int('x')) True >>> is_ast(BoolSort()) True >>> is_ast(Function('f', IntSort(), IntSort())) True >>> is_ast("x") False >>> is_ast(Solver()) False
Definition at line 352 of file z3py.py.
Referenced by AstRef.eq(), and eq().
def z3py.is_bool | ( | a | ) |
Return `True` if `a` is a Z3 Boolean expression. >>> p = Bool('p') >>> is_bool(p) True >>> q = Bool('q') >>> is_bool(And(p, q)) True >>> x = Real('x') >>> is_bool(x) False >>> is_bool(x == 0) True
Definition at line 1236 of file z3py.py.
Referenced by BoolSort(), and prove().
def z3py.is_bv | ( | a | ) |
Return `True` if `a` is a Z3 bit-vector expression. >>> b = BitVec('b', 32) >>> is_bv(b) True >>> is_bv(b + 10) True >>> is_bv(Int('x')) False
Definition at line 3401 of file z3py.py.
Referenced by BitVec(), BV2Int(), BVRedAnd(), BVRedOr(), Concat(), Extract(), fpFP(), fpToFP(), fpToFPUnsigned(), fpToIEEEBV(), fpToSBV(), fpToUBV(), Product(), and Sum().
def z3py.is_bv_sort | ( | s | ) |
Return True if `s` is a Z3 bit-vector sort. >>> is_bv_sort(BitVecSort(32)) True >>> is_bv_sort(IntSort()) False
Definition at line 2940 of file z3py.py.
Referenced by BitVecVal(), fpToSBV(), and fpToUBV().
def z3py.is_bv_value | ( | a | ) |
def z3py.is_const | ( | a | ) |
def z3py.is_const_array | ( | a | ) |
def z3py.is_distinct | ( | a | ) |
def z3py.is_div | ( | a | ) |
def z3py.is_eq | ( | a | ) |
def z3py.is_expr | ( | a | ) |
Return `True` if `a` is a Z3 expression. >>> a = Int('a') >>> is_expr(a) True >>> is_expr(a + 1) True >>> is_expr(IntSort()) False >>> is_expr(1) False >>> is_expr(IntVal(1)) True >>> x = Int('x') >>> is_expr(ForAll(x, x >= 0)) True
Definition at line 961 of file z3py.py.
Referenced by SortRef.cast(), BoolSortRef.cast(), Cbrt(), ExprRef.children(), fpAbs(), fpNeg(), fpRoundToIntegral(), fpSqrt(), is_var(), simplify(), substitute(), and substitute_vars().
def z3py.is_false | ( | a | ) |
def z3py.is_fp | ( | a | ) |
Return `True` if `a` is a Z3 floating-point expression. >>> b = FP('b', FPSort(8, 24)) >>> is_fp(b) True >>> is_fp(b + 1.0) True >>> is_fp(Int('x')) False
Definition at line 7893 of file z3py.py.
Referenced by FP(), fpAbs(), fpAdd(), fpDiv(), fpFMA(), fpIsInfinite(), fpIsNaN(), fpIsNegative(), fpIsNormal(), fpIsPositive(), fpIsSubnormal(), fpIsZero(), fpMax(), fpMin(), fpMul(), fpNeg(), fpRem(), fpRoundToIntegral(), fpSqrt(), fpSub(), fpToFP(), fpToIEEEBV(), fpToReal(), fpToSBV(), and fpToUBV().
def z3py.is_fp_sort | ( | s | ) |
Return True if `s` is a Z3 floating-point sort. >>> is_fp_sort(FPSort(8, 24)) True >>> is_fp_sort(IntSort()) False
Definition at line 7579 of file z3py.py.
Referenced by fpToFP(), fpToFPUnsigned(), and FPVal().
def z3py.is_fp_value | ( | a | ) |
def z3py.is_fprm | ( | a | ) |
Return `True` if `a` is a Z3 floating-point rounding mode expression. >>> rm = RNE() >>> is_fprm(rm) True >>> rm = 1.0 >>> is_fprm(rm) False
Definition at line 7797 of file z3py.py.
Referenced by fpAdd(), fpDiv(), fpFMA(), fpMul(), fpRoundToIntegral(), fpSqrt(), fpSub(), fpToFP(), fpToFPUnsigned(), fpToSBV(), and fpToUBV().
def z3py.is_fprm_sort | ( | s | ) |
def z3py.is_fprm_value | ( | a | ) |
def z3py.is_func_decl | ( | a | ) |
def z3py.is_ge | ( | a | ) |
def z3py.is_gt | ( | a | ) |
def z3py.is_idiv | ( | a | ) |
def z3py.is_int | ( | a | ) |
Return `True` if `a` is an integer expression. >>> x = Int('x') >>> is_int(x + 1) True >>> is_int(1) False >>> is_int(IntVal(1)) True >>> y = Real('y') >>> is_int(y) False >>> is_int(y + 1) False
Definition at line 2230 of file z3py.py.
Referenced by Int(), IntSort(), and RealSort().
def z3py.is_int_value | ( | a | ) |
Return `True` if `a` is an integer value of sort Int. >>> is_int_value(IntVal(1)) True >>> is_int_value(1) False >>> is_int_value(Int('x')) False >>> n = Int('x') + 1 >>> n x + 1 >>> n.arg(1) 1 >>> is_int_value(n.arg(1)) True >>> is_int_value(RealVal("1/3")) False >>> is_int_value(RealVal(1)) False
Definition at line 2272 of file z3py.py.
def z3py.is_is_int | ( | a | ) |
def z3py.is_K | ( | a | ) |
def z3py.is_le | ( | a | ) |
def z3py.is_lt | ( | a | ) |
def z3py.is_map | ( | a | ) |
Return `True` if `a` is a Z3 map array expression. >>> f = Function('f', IntSort(), IntSort()) >>> b = Array('b', IntSort(), IntSort()) >>> a = Map(f, b) >>> a Map(f, b) >>> is_map(a) True >>> is_map(b) False
Definition at line 3946 of file z3py.py.
Referenced by get_map_func().
def z3py.is_mod | ( | a | ) |
def z3py.is_mul | ( | a | ) |
def z3py.is_not | ( | a | ) |
def z3py.is_or | ( | a | ) |
def z3py.is_pattern | ( | a | ) |
Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation. See http://rise4fun.com/Z3Py/tutorial/advanced for more details. >>> f = Function('f', IntSort(), IntSort()) >>> x = Int('x') >>> q = ForAll(x, f(x) == 0, patterns = [ f(x) ]) >>> q ForAll(x, f(x) == 0) >>> q.num_patterns() 1 >>> is_pattern(q.pattern(0)) True >>> q.pattern(0) f(Var(0))
Definition at line 1556 of file z3py.py.
Referenced by MultiPattern().
def z3py.is_probe | ( | p | ) |
def z3py.is_quantifier | ( | a | ) |
def z3py.is_rational_value | ( | a | ) |
Return `True` if `a` is rational value of sort Real. >>> is_rational_value(RealVal(1)) True >>> is_rational_value(RealVal("3/5")) True >>> is_rational_value(IntVal(1)) False >>> is_rational_value(1) False >>> n = Real('x') + 1 >>> n.arg(1) 1 >>> is_rational_value(n.arg(1)) True >>> is_rational_value(Real('x')) False
Definition at line 2295 of file z3py.py.
Referenced by RatNumRef.denominator(), and RatNumRef.numerator().
def z3py.is_real | ( | a | ) |
Return `True` if `a` is a real expression. >>> x = Int('x') >>> is_real(x + 1) False >>> y = Real('y') >>> is_real(y) True >>> is_real(y + 1) True >>> is_real(1) False >>> is_real(RealVal(1)) True
Definition at line 2248 of file z3py.py.
Referenced by fpToFP(), fpToReal(), Real(), and RealSort().
def z3py.is_select | ( | a | ) |
def z3py.is_sort | ( | s | ) |
Return `True` if `s` is a Z3 sort. >>> is_sort(IntSort()) True >>> is_sort(Int('x')) False >>> is_expr(Int('x')) True
Definition at line 532 of file z3py.py.
Referenced by ArraySort(), CreateDatatypes(), Function(), prove(), and Var().
def z3py.is_store | ( | a | ) |
def z3py.is_sub | ( | a | ) |
def z3py.is_to_int | ( | a | ) |
def z3py.is_to_real | ( | a | ) |
def z3py.is_true | ( | a | ) |
def z3py.is_var | ( | a | ) |
Return `True` if `a` is variable. Z3 uses de-Bruijn indices for representing bound variables in quantifiers. >>> x = Int('x') >>> is_var(x) False >>> is_const(x) True >>> f = Function('f', IntSort(), IntSort()) >>> # Z3 replaces x with bound variables when ForAll is executed. >>> q = ForAll(x, f(x) == x) >>> b = q.body() >>> b f(Var(0)) == Var(0) >>> b.arg(1) Var(0) >>> is_var(b.arg(1)) True
Definition at line 1024 of file z3py.py.
Referenced by get_var_index().
def z3py.IsInt | ( | a | ) |
Return the Z3 predicate IsInt(a). >>> x = Real('x') >>> IsInt(x + "1/2") IsInt(x + 1/2) >>> solve(IsInt(x + "1/2"), x > 0, x < 1) [x = 1/2] >>> solve(IsInt(x + "1/2"), x > 0, x < 1, x != "1/2") no solution
Definition at line 2862 of file z3py.py.
Referenced by is_is_int().
def z3py.K | ( | dom, | |
v | |||
) |
Return a Z3 constant array expression. >>> a = K(IntSort(), 10) >>> a K(Int, 10) >>> a.sort() Array(Int, Int) >>> i = Int('i') >>> a[i] K(Int, 10)[i] >>> simplify(a[i]) 10
Definition at line 4085 of file z3py.py.
Referenced by is_const_array(), and is_K().
def z3py.LShR | ( | a, | |
b | |||
) |
Create the Z3 expression logical right shift. Use the operator >> for the arithmetical right shift. >>> x, y = BitVecs('x y', 32) >>> LShR(x, y) LShR(x, y) >>> (x >> y).sexpr() '(bvashr x y)' >>> LShR(x, y).sexpr() '(bvlshr x y)' >>> BitVecVal(4, 3) 4 >>> BitVecVal(4, 3).as_signed_long() -4 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long() -2 >>> simplify(BitVecVal(4, 3) >> 1) 6 >>> simplify(LShR(BitVecVal(4, 3), 1)) 2 >>> simplify(BitVecVal(2, 3) >> 1) 1 >>> simplify(LShR(BitVecVal(2, 3), 1)) 1
Definition at line 3687 of file z3py.py.
Referenced by BitVecRef.__rlshift__(), BitVecRef.__rrshift__(), and BitVecRef.__rshift__().
def z3py.main_ctx | ( | ) |
Return a reference to the global Z3 context. >>> x = Real('x') >>> x.ctx == main_ctx() True >>> c = Context() >>> c == main_ctx() False >>> x2 = Real('x', c) >>> x2.ctx == c True >>> eq(x, x2) False
Definition at line 188 of file z3py.py.
Referenced by And(), help_simplify(), simplify_param_descrs(), and Goal.translate().
def z3py.Map | ( | f, | |
args | |||
) |
Return a Z3 map array expression. >>> f = Function('f', IntSort(), IntSort(), IntSort()) >>> a1 = Array('a1', IntSort(), IntSort()) >>> a2 = Array('a2', IntSort(), IntSort()) >>> b = Map(f, a1, a2) >>> b Map(f, a1, a2) >>> prove(b[0] == f(a1[0], a2[0])) proved
Definition at line 4063 of file z3py.py.
Referenced by Context.Context(), get_map_func(), InterpolationContext.InterpolationContext(), and is_map().
def z3py.MultiPattern | ( | args | ) |
Create a Z3 multi-pattern using the given expressions `*args` See http://rise4fun.com/Z3Py/tutorial/advanced for more details. >>> f = Function('f', IntSort(), IntSort()) >>> g = Function('g', IntSort(), IntSort()) >>> x = Int('x') >>> q = ForAll(x, f(x) != g(x), patterns = [ MultiPattern(f(x), g(x)) ]) >>> q ForAll(x, f(x) != g(x)) >>> q.num_patterns() 1 >>> is_pattern(q.pattern(0)) True >>> q.pattern(0) MultiPattern(f(Var(0)), g(Var(0)))
Definition at line 1575 of file z3py.py.
def z3py.Not | ( | a, | |
ctx = None |
|||
) |
Create a Z3 not expression or probe. >>> p = Bool('p') >>> Not(Not(p)) Not(Not(p)) >>> simplify(Not(Not(p))) p
Definition at line 1454 of file z3py.py.
Referenced by binary_interpolant(), fpNEQ(), Implies(), prove(), sequence_interpolant(), tree_interpolant(), and Xor().
def z3py.open_log | ( | fname | ) |
def z3py.Or | ( | args | ) |
Create a Z3 or-expression or or-probe. >>> p, q, r = Bools('p q r') >>> Or(p, q, r) Or(p, q, r) >>> P = BoolVector('p', 5) >>> Or(P) Or(p__0, p__1, p__2, p__3, p__4)
Definition at line 1509 of file z3py.py.
Referenced by ApplyResult.as_expr(), Bools(), and Implies().
def z3py.OrElse | ( | ts, | |
ks | |||
) |
Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail). >>> x = Int('x') >>> t = OrElse(Tactic('split-clause'), Tactic('skip')) >>> # Tactic split-clause fails if there is no clause in the given goal. >>> t(x == 0) [[x == 0]] >>> t(Or(x == 0, x == 1)) [[x == 0], [x == 1]]
def z3py.ParAndThen | ( | t1, | |
t2, | |||
ctx = None |
|||
) |
def z3py.ParOr | ( | ts, | |
ks | |||
) |
Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail). >>> x = Int('x') >>> t = ParOr(Tactic('simplify'), Tactic('fail')) >>> t(x + 1 == 2) [[x == 1]]
Definition at line 6611 of file z3py.py.
def z3py.parse_smt2_file | ( | f, | |
sorts = {} , |
|||
decls = {} , |
|||
ctx = None |
|||
) |
Parse a file in SMT 2.0 format using the given sorts and decls. This function is similar to parse_smt2_string().
Definition at line 7308 of file z3py.py.
def z3py.parse_smt2_string | ( | s, | |
sorts = {} , |
|||
decls = {} , |
|||
ctx = None |
|||
) |
Parse a string in SMT 2.0 format using the given sorts and decls. The arguments sorts and decls are Python dictionaries used to initialize the symbol table used for the SMT 2.0 parser. >>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))') And(x > 0, x < 10) >>> x, y = Ints('x y') >>> f = Function('f', IntSort(), IntSort()) >>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f}) x + f(y) > 0 >>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() }) a > 0
Definition at line 7288 of file z3py.py.
Referenced by parse_smt2_file().
def z3py.ParThen | ( | t1, | |
t2, | |||
ctx = None |
|||
) |
Return a tactic that applies t1 and then t2 to every subgoal produced by t1. The subgoals are processed in parallel. >>> x, y = Ints('x y') >>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values')) >>> t(And(Or(x == 1, x == 2), y == x + 1)) [[x == 1, y == 2], [x == 2, y == 3]]
Definition at line 6629 of file z3py.py.
Referenced by ParAndThen().
def z3py.probe_description | ( | name, | |
ctx = None |
|||
) |
Return a short description for the probe named `name`. >>> d = probe_description('memory')
Definition at line 6885 of file z3py.py.
Referenced by describe_probes().
def z3py.probes | ( | ctx = None | ) |
Return a list of all available probes in Z3. >>> l = probes() >>> l.count('memory') == 1 True
Definition at line 6875 of file z3py.py.
Referenced by describe_probes().
def z3py.Product | ( | args | ) |
Create the product of the Z3 expressions. >>> a, b, c = Ints('a b c') >>> Product(a, b, c) a*b*c >>> Product([a, b, c]) a*b*c >>> A = IntVector('a', 5) >>> Product(A) a__0*a__1*a__2*a__3*a__4
Definition at line 7082 of file z3py.py.
Referenced by BitVecs(), and FPs().
def z3py.prove | ( | claim, | |
keywords | |||
) |
Try to prove the given claim. This is a simple function for creating demonstrations. It tries to prove `claim` by showing the negation is unsatisfiable. >>> p, q = Bools('p q') >>> prove(Not(And(p, q)) == Or(Not(p), Not(q))) proved
Definition at line 7164 of file z3py.py.
Referenced by Map(), Store(), and Update().
def z3py.Q | ( | a, | |
b, | |||
ctx = None |
|||
) |
Return a Z3 rational a/b. If `ctx=None`, then the global context is used. >>> Q(3,5) 3/5 >>> Q(3,5).sort() Real
Definition at line 2716 of file z3py.py.
Referenced by RatNumRef.as_string(), RatNumRef.denominator(), and RatNumRef.numerator().
def z3py.RatVal | ( | a, | |
b, | |||
ctx = None |
|||
) |
Return a Z3 rational a/b. If `ctx=None`, then the global context is used. >>> RatVal(3,5) 3/5 >>> RatVal(3,5).sort() Real
Definition at line 2701 of file z3py.py.
Referenced by Q().
def z3py.Real | ( | name, | |
ctx = None |
|||
) |
Return a real constant named `name`. If `ctx=None`, then the global context is used. >>> x = Real('x') >>> is_real(x) True >>> is_real(x + 1) True
Definition at line 2776 of file z3py.py.
Referenced by ArithRef.__div__(), ArithRef.__ge__(), ArithRef.__gt__(), ArithRef.__le__(), ArithRef.__lt__(), ArithRef.__mul__(), ArithRef.__pow__(), ArithRef.__rdiv__(), ArithRef.__rmul__(), ArithRef.__rpow__(), Cbrt(), is_arith(), ArithSortRef.is_int(), ArithRef.is_int(), is_int(), is_is_int(), is_rational_value(), ArithSortRef.is_real(), ArithRef.is_real(), is_real(), is_to_int(), IsInt(), ArithRef.sort(), Sqrt(), ToInt(), and QuantifierRef.var_sort().
def z3py.Reals | ( | names, | |
ctx = None |
|||
) |
def z3py.RealSort | ( | ctx = None | ) |
Return the real sort in the given context. If `ctx=None`, then the global context is used. >>> RealSort() Real >>> x = Const('x', RealSort()) >>> is_real(x) True >>> is_int(x) False >>> x.sort() == RealSort() True
Definition at line 2641 of file z3py.py.
Referenced by ArithSortRef.cast(), FreshReal(), Context.getRealSort(), is_arith_sort(), Context.mkRealSort(), Context.MkRealSort(), Real(), RealVar(), and QuantifierRef.var_sort().
def z3py.RealVal | ( | val, | |
ctx = None |
|||
) |
Return a Z3 real value. `val` may be a Python int, long, float or string representing a number in decimal or rational notation. If `ctx=None`, then the global context is used. >>> RealVal(1) 1 >>> RealVal(1).sort() Real >>> RealVal("3/5") 3/5 >>> RealVal("1.5") 3/2
Definition at line 2683 of file z3py.py.
Referenced by RatNumRef.as_decimal(), RatNumRef.as_fraction(), Cbrt(), RatNumRef.denominator_as_long(), is_algebraic_value(), is_int_value(), is_rational_value(), is_real(), RatNumRef.numerator(), RatNumRef.numerator_as_long(), and RatVal().
def z3py.RealVar | ( | idx, | |
ctx = None |
|||
) |
Create a real free variable. Free variables are used to create quantified formulas. They are also used to create polynomials. >>> RealVar(0) Var(0)
Definition at line 1182 of file z3py.py.
Referenced by RealVarVector().
def z3py.RealVarVector | ( | n, | |
ctx = None |
|||
) |
def z3py.RealVector | ( | prefix, | |
sz, | |||
ctx = None |
|||
) |
def z3py.Repeat | ( | t, | |
max = 4294967295 , |
|||
ctx = None |
|||
) |
Return a tactic that keeps applying `t` until the goal is not modified anymore or the maximum number of iterations `max` is reached. >>> x, y = Ints('x y') >>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y) >>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip'))) >>> r = t(c) >>> for subgoal in r: print(subgoal) [x == 0, y == 0, x > y] [x == 0, y == 1, x > y] [x == 1, y == 0, x > y] [x == 1, y == 1, x > y] >>> t = Then(t, Tactic('propagate-values')) >>> t(c) [[x == 1, y == 0]]
Definition at line 6660 of file z3py.py.
def z3py.RepeatBitVec | ( | n, | |
a | |||
) |
Return an expression representing `n` copies of `a`. >>> x = BitVec('x', 8) >>> n = RepeatBitVec(4, x) >>> n RepeatBitVec(4, x) >>> n.size() 32 >>> v0 = BitVecVal(10, 4) >>> print("%.x" % v0.as_long()) a >>> v = simplify(RepeatBitVec(4, v0)) >>> v.size() 16 >>> print("%.x" % v.as_long()) aaaa
Definition at line 3804 of file z3py.py.
def z3py.reset_params | ( | ) |
def z3py.RNA | ( | ctx = None | ) |
Definition at line 7769 of file z3py.py.
Referenced by get_default_rounding_mode().
def z3py.RNE | ( | ctx = None | ) |
Definition at line 7761 of file z3py.py.
Referenced by fpAbs(), fpAdd(), fpDiv(), fpMax(), fpMin(), fpMul(), fpNeg(), fpSub(), get_default_rounding_mode(), is_fprm(), and is_fprm_sort().
def z3py.RotateLeft | ( | a, | |
b | |||
) |
Return an expression representing `a` rotated to the left `b` times. >>> a, b = BitVecs('a b', 16) >>> RotateLeft(a, b) RotateLeft(a, b) >>> simplify(RotateLeft(a, 0)) a >>> simplify(RotateLeft(a, 16)) a
Definition at line 3718 of file z3py.py.
def z3py.RotateRight | ( | a, | |
b | |||
) |
Return an expression representing `a` rotated to the right `b` times. >>> a, b = BitVecs('a b', 16) >>> RotateRight(a, b) RotateRight(a, b) >>> simplify(RotateRight(a, 0)) a >>> simplify(RotateRight(a, 16)) a
Definition at line 3733 of file z3py.py.
def z3py.RoundNearestTiesToAway | ( | ctx = None | ) |
Definition at line 7765 of file z3py.py.
def z3py.RoundNearestTiesToEven | ( | ctx = None | ) |
Definition at line 7757 of file z3py.py.
def z3py.RoundTowardNegative | ( | ctx = None | ) |
Definition at line 7781 of file z3py.py.
def z3py.RoundTowardPositive | ( | ctx = None | ) |
Definition at line 7773 of file z3py.py.
def z3py.RoundTowardZero | ( | ctx = None | ) |
Definition at line 7789 of file z3py.py.
def z3py.RTN | ( | ctx = None | ) |
Definition at line 7785 of file z3py.py.
Referenced by get_default_rounding_mode().
def z3py.RTP | ( | ctx = None | ) |
Definition at line 7777 of file z3py.py.
Referenced by get_default_rounding_mode().
def z3py.RTZ | ( | ctx = None | ) |
Definition at line 7793 of file z3py.py.
Referenced by fpToSBV(), fpToUBV(), and get_default_rounding_mode().
def z3py.Select | ( | a, | |
i | |||
) |
def z3py.sequence_interpolant | ( | v, | |
p = None , |
|||
ctx = None |
|||
) |
Compute interpolant for a sequence of formulas. If len(v) == N, and if the conjunction of the formulas in v is unsatisfiable, the interpolant is a sequence of formulas w such that len(w) = N-1 and v[0] implies w[0] and for i in 0..N-1: 1) w[i] & v[i+1] implies w[i+1] (or false if i+1 = N) 2) All uninterpreted symbols in w[i] occur in both v[0]..v[i] and v[i+1]..v[n] Requires len(v) >= 1. If a & b is satisfiable, raises an object of class ModelRef that represents a model of a & b. If parameters p are supplied, these are used in creating the solver that determines satisfiability. >>> x = Int('x') >>> y = Int('y') >>> print sequence_interpolant([x < 0, y == x , y > 2]) [Not(x >= 0), Not(y >= 0)]
Definition at line 7414 of file z3py.py.
def z3py.set_option | ( | args, | |
kws | |||
) |
def z3py.set_param | ( | args, | |
kws | |||
) |
Set Z3 global (or module) parameters. >>> set_param(precision=10)
Definition at line 214 of file z3py.py.
Referenced by set_option().
def z3py.SignExt | ( | n, | |
a | |||
) |
Return a bit-vector expression with `n` extra sign-bits. >>> x = BitVec('x', 16) >>> n = SignExt(8, x) >>> n.size() 24 >>> n SignExt(8, x) >>> n.sort() BitVec(24) >>> v0 = BitVecVal(2, 2) >>> v0 2 >>> v0.size() 2 >>> v = simplify(SignExt(6, v0)) >>> v 254 >>> v.size() 8 >>> print("%.x" % v.as_long()) fe
Definition at line 3748 of file z3py.py.
def z3py.SimpleSolver | ( | ctx = None | ) |
Return a simple general purpose solver with limited amount of preprocessing. >>> s = SimpleSolver() >>> x = Int('x') >>> s.add(x > 0) >>> s.check() sat
Definition at line 6096 of file z3py.py.
Referenced by Solver.reason_unknown(), and Solver.statistics().
def z3py.simplify | ( | a, | |
arguments, | |||
keywords | |||
) |
Utils.
Simplify the expression `a` using the given options. This function has many options. Use `help_simplify` to obtain the complete list. >>> x = Int('x') >>> y = Int('y') >>> simplify(x + 1 + y + x + 1) 2 + 2*x + y >>> simplify((x + 1)*(y + 1), som=True) 1 + x + y + x*y >>> simplify(Distinct(x, y, 1), blast_distinct=True) And(Not(x == y), Not(x == 1), Not(y == 1)) >>> simplify(And(x == 0, y == 1), elim_and=True) Not(Or(Not(x == 0), Not(y == 1)))
Definition at line 6979 of file z3py.py.
Referenced by BitVecRef.__invert__(), BitVecRef.__lshift__(), ArithRef.__mod__(), ArithRef.__neg__(), BitVecRef.__neg__(), ArithRef.__pow__(), ArithRef.__rpow__(), BitVecRef.__rshift__(), AlgebraicNumRef.approx(), AlgebraicNumRef.as_decimal(), BitVecs(), Concat(), CreateDatatypes(), FPs(), Implies(), is_algebraic_value(), K(), LShR(), Not(), Q(), RatVal(), DatatypeSortRef.recognizer(), RepeatBitVec(), RotateLeft(), RotateRight(), SignExt(), Xor(), and ZeroExt().
def z3py.simplify_param_descrs | ( | ) |
Return the set of parameter descriptions for Z3 `simplify` procedure.
Definition at line 7007 of file z3py.py.
def z3py.solve | ( | args, | |
keywords | |||
) |
Solve the constraints `*args`. This is a simple function for creating demonstrations. It creates a solver, configure it using the options in `keywords`, adds the constraints in `args`, and invokes check. >>> a = Int('a') >>> solve(a > 0, a < 2) [a = 1]
Definition at line 7107 of file z3py.py.
Referenced by BV2Int(), and IsInt().
def z3py.solve_using | ( | s, | |
args, | |||
keywords | |||
) |
Solve the constraints `*args` using solver `s`. This is a simple function for creating demonstrations. It is similar to `solve`, but it uses the given solver `s`. It configures solver `s` using the options in `keywords`, adds the constraints in `args`, and invokes check.
Definition at line 7135 of file z3py.py.
def z3py.SolverFor | ( | logic, | |
ctx = None |
|||
) |
Create a solver customized for the given logic. The parameter `logic` is a string. It should be contains the name of a SMT-LIB logic. See http://www.smtlib.org/ for the name of all available logics. >>> s = SolverFor("QF_LIA") >>> x = Int('x') >>> s.add(x > 0) >>> s.add(x < 2) >>> s.check() sat >>> s.model() [x = 1]
Definition at line 6076 of file z3py.py.
def z3py.Sqrt | ( | a, | |
ctx = None |
|||
) |
Return a Z3 expression which represents the square root of a. >>> x = Real('x') >>> Sqrt(x) x**(1/2)
Definition at line 2878 of file z3py.py.
Referenced by AlgebraicNumRef.approx(), AlgebraicNumRef.as_decimal(), and is_algebraic_value().
def z3py.SRem | ( | a, | |
b | |||
) |
Create the Z3 expression signed remainder. Use the operator % for signed modulus, and URem() for unsigned remainder. >>> x = BitVec('x', 32) >>> y = BitVec('y', 32) >>> SRem(x, y) SRem(x, y) >>> SRem(x, y).sort() BitVec(32) >>> (x % y).sexpr() '(bvsmod x y)' >>> SRem(x, y).sexpr() '(bvsrem x y)'
Definition at line 3667 of file z3py.py.
Referenced by BitVecRef.__mod__(), BitVecRef.__rmod__(), and URem().
def z3py.Store | ( | a, | |
i, | |||
v | |||
) |
Return a Z3 store array expression. >>> a = Array('a', IntSort(), IntSort()) >>> i, v = Ints('i v') >>> s = Store(a, i, v) >>> s.sort() Array(Int, Int) >>> prove(s[i] == v) proved >>> j = Int('j') >>> prove(Implies(i != j, s[j] == a[j])) proved
Definition at line 4033 of file z3py.py.
Referenced by is_array(), and is_store().
def z3py.substitute | ( | t, | |
m | |||
) |
Apply substitution m on t, m is a list of pairs of the form (from, to). Every occurrence in t of from is replaced with to. >>> x = Int('x') >>> y = Int('y') >>> substitute(x + 1, (x, y + 1)) y + 1 + 1 >>> f = Function('f', IntSort(), IntSort()) >>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1))) 1 + 1
Definition at line 7011 of file z3py.py.
def z3py.substitute_vars | ( | t, | |
m | |||
) |
Substitute the free variables in t with the expression in m. >>> v0 = Var(0, IntSort()) >>> v1 = Var(1, IntSort()) >>> x = Int('x') >>> f = Function('f', IntSort(), IntSort(), IntSort()) >>> # replace v0 with x+1 and v1 with x >>> substitute_vars(f(v0, v1), x + 1, x) f(x + 1, x)
Definition at line 7037 of file z3py.py.
def z3py.Sum | ( | args | ) |
Create the sum of the Z3 expressions. >>> a, b, c = Ints('a b c') >>> Sum(a, b, c) a + b + c >>> Sum([a, b, c]) a + b + c >>> A = IntVector('a', 5) >>> Sum(A) a__0 + a__1 + a__2 + a__3 + a__4
Definition at line 7057 of file z3py.py.
Referenced by BitVecs(), FPs(), Ints(), IntVector(), Reals(), and RealVector().
def z3py.tactic_description | ( | name, | |
ctx = None |
|||
) |
Return a short description for the tactic named `name`. >>> d = tactic_description('simplify')
Definition at line 6697 of file z3py.py.
Referenced by describe_tactics().
def z3py.tactics | ( | ctx = None | ) |
Return a list of all available tactics in Z3. >>> l = tactics() >>> l.count('simplify') == 1 True
Definition at line 6687 of file z3py.py.
Referenced by describe_tactics().
def z3py.Then | ( | ts, | |
ks | |||
) |
Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks). >>> x, y = Ints('x y') >>> t = Then(Tactic('simplify'), Tactic('solve-eqs')) >>> t(And(x == 0, y > x + 1)) [[Not(y <= 1)]] >>> t(And(x == 0, y > x + 1)).as_expr() Not(y <= 1)
Definition at line 6579 of file z3py.py.
Referenced by Statistics.__getattr__(), Statistics.__getitem__(), Statistics.__len__(), Goal.depth(), Statistics.get_key_value(), and Statistics.keys().
def z3py.to_symbol | ( | s, | |
ctx = None |
|||
) |
Convert an integer or string into a Z3 symbol.
Definition at line 94 of file z3py.py.
Referenced by Fixedpoint.add_rule(), Array(), BitVec(), Bool(), Const(), CreateDatatypes(), DeclareSort(), EnumSort(), FP(), Function(), Int(), prove(), Real(), Fixedpoint.set_predicate_representation(), SolverFor(), and Fixedpoint.update_rule().
def z3py.ToInt | ( | a | ) |
Return the Z3 expression ToInt(a). >>> x = Real('x') >>> x.sort() Real >>> n = ToInt(x) >>> n ToInt(x) >>> n.sort() Int
Definition at line 2845 of file z3py.py.
Referenced by is_to_int().
def z3py.ToReal | ( | a | ) |
Return the Z3 expression ToReal(a). >>> x = Int('x') >>> x.sort() Int >>> n = ToReal(x) >>> n ToReal(x) >>> n.sort() Real
Definition at line 2828 of file z3py.py.
Referenced by ArithRef.__ge__(), ArithRef.__gt__(), ArithRef.__le__(), ArithRef.__lt__(), and is_to_real().
def z3py.tree_interpolant | ( | pat, | |
p = None , |
|||
ctx = None |
|||
) |
Compute interpolant for a tree of formulas. The input is an interpolation pattern over a set of formulas C. The pattern pat is a formula combining the formulas in C using logical conjunction and the "interp" operator (see Interp). This interp operator is logically the identity operator. It marks the sub-formulas of the pattern for which interpolants should be computed. The interpolant is a map sigma from marked subformulas to formulas, such that, for each marked subformula phi of pat (where phi sigma is phi with sigma(psi) substituted for each subformula psi of phi such that psi in dom(sigma)): 1) phi sigma implies sigma(phi), and 2) sigma(phi) is in the common uninterpreted vocabulary between the formulas of C occurring in phi and those not occurring in phi and moreover pat sigma implies false. In the simplest case an interpolant for the pattern "(and (interp A) B)" maps A to an interpolant for A /\ B. The return value is a vector of formulas representing sigma. This vector contains sigma(phi) for each marked subformula of pat, in pre-order traversal. This means that subformulas of phi occur before phi in the vector. Also, subformulas that occur multiply in pat will occur multiply in the result vector. If pat is satisfiable, raises an object of class ModelRef that represents a model of pat. If parameters p are supplied, these are used in creating the solver that determines satisfiability. >>> x = Int('x') >>> y = Int('y') >>> print tree_interpolant(And(Interpolant(x < 0), Interpolant(y > 2), x == y)) [Not(x >= 0), Not(y <= 2)] >>> g = And(Interpolant(x<0),x<2) >>> try: ... print tree_interpolant(g).sexpr() ... except ModelRef as m: ... print m.sexpr() (define-fun x () Int (- 1))
Definition at line 7332 of file z3py.py.
Referenced by binary_interpolant(), and sequence_interpolant().
def z3py.TryFor | ( | t, | |
ms, | |||
ctx = None |
|||
) |
Return a tactic that applies `t` to a given goal for `ms` milliseconds. If `t` does not terminate in `ms` milliseconds, then it fails.
Definition at line 6679 of file z3py.py.
def z3py.UDiv | ( | a, | |
b | |||
) |
Create the Z3 expression (unsigned) division `self / other`. Use the operator / for signed division. >>> x = BitVec('x', 32) >>> y = BitVec('y', 32) >>> UDiv(x, y) UDiv(x, y) >>> UDiv(x, y).sort() BitVec(32) >>> (x / y).sexpr() '(bvsdiv x y)' >>> UDiv(x, y).sexpr() '(bvudiv x y)'
Definition at line 3627 of file z3py.py.
Referenced by BitVecRef.__div__(), and BitVecRef.__rdiv__().
def z3py.UGE | ( | a, | |
b | |||
) |
Create the Z3 expression (unsigned) `other >= self`. Use the operator >= for signed greater than or equal to. >>> x, y = BitVecs('x y', 32) >>> UGE(x, y) UGE(x, y) >>> (x >= y).sexpr() '(bvsge x y)' >>> UGE(x, y).sexpr() '(bvuge x y)'
Definition at line 3593 of file z3py.py.
Referenced by BitVecRef.__ge__().
def z3py.UGT | ( | a, | |
b | |||
) |
Create the Z3 expression (unsigned) `other > self`. Use the operator > for signed greater than. >>> x, y = BitVecs('x y', 32) >>> UGT(x, y) UGT(x, y) >>> (x > y).sexpr() '(bvsgt x y)' >>> UGT(x, y).sexpr() '(bvugt x y)'
Definition at line 3610 of file z3py.py.
Referenced by BitVecRef.__gt__().
def z3py.ULE | ( | a, | |
b | |||
) |
Create the Z3 expression (unsigned) `other <= self`. Use the operator <= for signed less than or equal to. >>> x, y = BitVecs('x y', 32) >>> ULE(x, y) ULE(x, y) >>> (x <= y).sexpr() '(bvsle x y)' >>> ULE(x, y).sexpr() '(bvule x y)'
Definition at line 3559 of file z3py.py.
Referenced by BitVecRef.__le__().
def z3py.ULT | ( | a, | |
b | |||
) |
Create the Z3 expression (unsigned) `other < self`. Use the operator < for signed less than. >>> x, y = BitVecs('x y', 32) >>> ULT(x, y) ULT(x, y) >>> (x < y).sexpr() '(bvslt x y)' >>> ULT(x, y).sexpr() '(bvult x y)'
Definition at line 3576 of file z3py.py.
Referenced by BitVecRef.__lt__().
def z3py.Update | ( | a, | |
i, | |||
v | |||
) |
Return a Z3 store array expression. >>> a = Array('a', IntSort(), IntSort()) >>> i, v = Ints('i v') >>> s = Update(a, i, v) >>> s.sort() Array(Int, Int) >>> prove(s[i] == v) proved >>> j = Int('j') >>> prove(Implies(i != j, s[j] == a[j])) proved
Definition at line 4012 of file z3py.py.
Referenced by Store().
def z3py.URem | ( | a, | |
b | |||
) |
Create the Z3 expression (unsigned) remainder `self % other`. Use the operator % for signed modulus, and SRem() for signed remainder. >>> x = BitVec('x', 32) >>> y = BitVec('y', 32) >>> URem(x, y) URem(x, y) >>> URem(x, y).sort() BitVec(32) >>> (x % y).sexpr() '(bvsmod x y)' >>> URem(x, y).sexpr() '(bvurem x y)'
Definition at line 3647 of file z3py.py.
Referenced by BitVecRef.__mod__(), BitVecRef.__rmod__(), and SRem().
def z3py.Var | ( | idx, | |
s | |||
) |
Create a Z3 free variable. Free variables are used to create quantified formulas. >>> Var(0, IntSort()) Var(0) >>> eq(Var(0, IntSort()), Var(0, BoolSort())) False
Definition at line 1170 of file z3py.py.
Referenced by QuantifierRef.body(), QuantifierRef.children(), is_pattern(), MultiPattern(), QuantifierRef.pattern(), and RealVar().
def z3py.When | ( | p, | |
t, | |||
ctx = None |
|||
) |
Return a tactic that applies tactic `t` only if probe `p` evaluates to true. Otherwise, it returns the input goal unmodified. >>> t = When(Probe('size') > 2, Tactic('simplify')) >>> x, y = Ints('x y') >>> g = Goal() >>> g.add(x > 0) >>> g.add(y > 0) >>> t(g) [[x > 0, y > 0]] >>> g.add(x == y + 1) >>> t(g) [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
Definition at line 6945 of file z3py.py.
def z3py.With | ( | t, | |
args, | |||
keys | |||
) |
Return a tactic that applies tactic `t` using the given configuration options. >>> x, y = Ints('x y') >>> t = With(Tactic('simplify'), som=True) >>> t((x + 1)*(y + 2) == 0) [[2*x + y + x*y == -2]]
Definition at line 6647 of file z3py.py.
Referenced by Goal.prec().
def z3py.Xor | ( | a, | |
b, | |||
ctx = None |
|||
) |
Create a Z3 Xor expression. >>> p, q = Bools('p q') >>> Xor(p, q) Xor(p, q) >>> simplify(Xor(p, q)) Not(p) == q
Definition at line 1439 of file z3py.py.
def z3py.ZeroExt | ( | n, | |
a | |||
) |
Return a bit-vector expression with `n` extra zero-bits. >>> x = BitVec('x', 16) >>> n = ZeroExt(8, x) >>> n.size() 24 >>> n ZeroExt(8, x) >>> n.sort() BitVec(24) >>> v0 = BitVecVal(2, 2) >>> v0 2 >>> v0.size() 2 >>> v = simplify(ZeroExt(6, v0)) >>> v 2 >>> v.size() 8
Definition at line 3777 of file z3py.py.
_dflt_rounding_mode = Z3_OP_FPA_RM_TOWARD_ZERO |
tuple _error_handler_fptr = ctypes.CFUNCTYPE(None, ctypes.c_void_p, ctypes.c_uint) |
tuple _Z3Python_error_handler = _error_handler_fptr(_Z3python_error_handler_core) |
tuple sat = CheckSatResult(Z3_L_TRUE) |
tuple unknown = CheckSatResult(Z3_L_UNDEF) |
tuple unsat = CheckSatResult(Z3_L_FALSE) |