Copyright | (c) Iago Abal, 2012-2015 (c) David Castro, 2012-2015 |
---|---|
License | BSD3 |
Maintainer | Iago Abal <mail@iagoabal.eu>, David Castro <david.castro.dcp@gmail.com> |
Safe Haskell | None |
Language | Haskell98 |
Low-level bindings to Z3 API.
There is (mostly) a one-to-one correspondence with Z3 C API, thus see http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html for further details.
- data Config
- data Context
- data Symbol
- data AST
- data Sort
- data FuncDecl
- data App
- data Pattern
- data Constructor
- data Model
- data FuncInterp
- data FuncEntry
- data Params
- data Solver
- data ASTKind
- data Result
- mkConfig :: IO Config
- delConfig :: Config -> IO ()
- setParamValue :: Config -> String -> String -> IO ()
- withConfig :: (Config -> IO a) -> IO a
- mkContext :: Config -> IO Context
- withContext :: Context -> (Ptr Z3_context -> IO r) -> IO r
- mkParams :: Context -> IO Params
- paramsSetBool :: Context -> Params -> Symbol -> Bool -> IO ()
- paramsSetUInt :: Context -> Params -> Symbol -> Word -> IO ()
- paramsSetDouble :: Context -> Params -> Symbol -> Double -> IO ()
- paramsSetSymbol :: Context -> Params -> Symbol -> Symbol -> IO ()
- paramsToString :: Context -> Params -> IO String
- mkIntSymbol :: Integral int => Context -> int -> IO Symbol
- mkStringSymbol :: Context -> String -> IO Symbol
- mkUninterpretedSort :: Context -> Symbol -> IO Sort
- mkBoolSort :: Context -> IO Sort
- mkIntSort :: Context -> IO Sort
- mkRealSort :: Context -> IO Sort
- mkBvSort :: Integral int => Context -> int -> IO Sort
- mkArraySort :: Context -> Sort -> Sort -> IO Sort
- mkTupleSort :: Context -> Symbol -> [(Symbol, Sort)] -> IO (Sort, FuncDecl, [FuncDecl])
- mkConstructor :: Context -> Symbol -> Symbol -> [(Symbol, Maybe Sort, Int)] -> IO Constructor
- mkDatatype :: Context -> Symbol -> [Constructor] -> IO Sort
- mkSetSort :: Context -> Sort -> IO Sort
- mkFuncDecl :: Context -> Symbol -> [Sort] -> Sort -> IO FuncDecl
- mkApp :: Context -> FuncDecl -> [AST] -> IO AST
- mkConst :: Context -> Symbol -> Sort -> IO AST
- mkFreshFuncDecl :: Context -> String -> [Sort] -> Sort -> IO FuncDecl
- mkFreshConst :: Context -> String -> Sort -> IO AST
- mkVar :: Context -> Symbol -> Sort -> IO AST
- mkBoolVar :: Context -> Symbol -> IO AST
- mkRealVar :: Context -> Symbol -> IO AST
- mkIntVar :: Context -> Symbol -> IO AST
- mkBvVar :: Context -> Symbol -> Int -> IO AST
- mkFreshVar :: Context -> String -> Sort -> IO AST
- mkFreshBoolVar :: Context -> String -> IO AST
- mkFreshRealVar :: Context -> String -> IO AST
- mkFreshIntVar :: Context -> String -> IO AST
- mkFreshBvVar :: Context -> String -> Int -> IO AST
- mkTrue :: Context -> IO AST
- mkFalse :: Context -> IO AST
- mkEq :: Context -> AST -> AST -> IO AST
- mkNot :: Context -> AST -> IO AST
- mkIte :: Context -> AST -> AST -> AST -> IO AST
- mkIff :: Context -> AST -> AST -> IO AST
- mkImplies :: Context -> AST -> AST -> IO AST
- mkXor :: Context -> AST -> AST -> IO AST
- mkAnd :: Context -> [AST] -> IO AST
- mkOr :: Context -> [AST] -> IO AST
- mkDistinct :: Context -> [AST] -> IO AST
- mkBool :: Context -> Bool -> IO AST
- mkAdd :: Context -> [AST] -> IO AST
- mkMul :: Context -> [AST] -> IO AST
- mkSub :: Context -> [AST] -> IO AST
- mkUnaryMinus :: Context -> AST -> IO AST
- mkDiv :: Context -> AST -> AST -> IO AST
- mkMod :: Context -> AST -> AST -> IO AST
- mkRem :: Context -> AST -> AST -> IO AST
- mkLt :: Context -> AST -> AST -> IO AST
- mkLe :: Context -> AST -> AST -> IO AST
- mkGt :: Context -> AST -> AST -> IO AST
- mkGe :: Context -> AST -> AST -> IO AST
- mkInt2Real :: Context -> AST -> IO AST
- mkReal2Int :: Context -> AST -> IO AST
- mkIsInt :: Context -> AST -> IO AST
- mkBvnot :: Context -> AST -> IO AST
- mkBvredand :: Context -> AST -> IO AST
- mkBvredor :: Context -> AST -> IO AST
- mkBvand :: Context -> AST -> AST -> IO AST
- mkBvor :: Context -> AST -> AST -> IO AST
- mkBvxor :: Context -> AST -> AST -> IO AST
- mkBvnand :: Context -> AST -> AST -> IO AST
- mkBvnor :: Context -> AST -> AST -> IO AST
- mkBvxnor :: Context -> AST -> AST -> IO AST
- mkBvneg :: Context -> AST -> IO AST
- mkBvadd :: Context -> AST -> AST -> IO AST
- mkBvsub :: Context -> AST -> AST -> IO AST
- mkBvmul :: Context -> AST -> AST -> IO AST
- mkBvudiv :: Context -> AST -> AST -> IO AST
- mkBvsdiv :: Context -> AST -> AST -> IO AST
- mkBvurem :: Context -> AST -> AST -> IO AST
- mkBvsrem :: Context -> AST -> AST -> IO AST
- mkBvsmod :: Context -> AST -> AST -> IO AST
- mkBvult :: Context -> AST -> AST -> IO AST
- mkBvslt :: Context -> AST -> AST -> IO AST
- mkBvule :: Context -> AST -> AST -> IO AST
- mkBvsle :: Context -> AST -> AST -> IO AST
- mkBvuge :: Context -> AST -> AST -> IO AST
- mkBvsge :: Context -> AST -> AST -> IO AST
- mkBvugt :: Context -> AST -> AST -> IO AST
- mkBvsgt :: Context -> AST -> AST -> IO AST
- mkConcat :: Context -> AST -> AST -> IO AST
- mkExtract :: Context -> Int -> Int -> AST -> IO AST
- mkSignExt :: Context -> Int -> AST -> IO AST
- mkZeroExt :: Context -> Int -> AST -> IO AST
- mkRepeat :: Context -> Int -> AST -> IO AST
- mkBvshl :: Context -> AST -> AST -> IO AST
- mkBvlshr :: Context -> AST -> AST -> IO AST
- mkBvashr :: Context -> AST -> AST -> IO AST
- mkRotateLeft :: Context -> Int -> AST -> IO AST
- mkRotateRight :: Context -> Int -> AST -> IO AST
- mkExtRotateLeft :: Context -> AST -> AST -> IO AST
- mkExtRotateRight :: Context -> AST -> AST -> IO AST
- mkInt2bv :: Context -> Int -> AST -> IO AST
- mkBv2int :: Context -> AST -> Bool -> IO AST
- mkBvnegNoOverflow :: Context -> AST -> IO AST
- mkBvaddNoOverflow :: Context -> AST -> AST -> Bool -> IO AST
- mkBvaddNoUnderflow :: Context -> AST -> AST -> IO AST
- mkBvsubNoOverflow :: Context -> AST -> AST -> IO AST
- mkBvsubNoUnderflow :: Context -> AST -> AST -> IO AST
- mkBvmulNoOverflow :: Context -> AST -> AST -> Bool -> IO AST
- mkBvmulNoUnderflow :: Context -> AST -> AST -> IO AST
- mkBvsdivNoOverflow :: Context -> AST -> AST -> IO AST
- mkSelect :: Context -> AST -> AST -> IO AST
- mkStore :: Context -> AST -> AST -> AST -> IO AST
- mkConstArray :: Context -> Sort -> AST -> IO AST
- mkMap :: Context -> FuncDecl -> [AST] -> IO AST
- mkArrayDefault :: Context -> AST -> IO AST
- mkEmptySet :: Context -> Sort -> IO AST
- mkFullSet :: Context -> Sort -> IO AST
- mkSetAdd :: Context -> AST -> AST -> IO AST
- mkSetDel :: Context -> AST -> AST -> IO AST
- mkSetUnion :: Context -> [AST] -> IO AST
- mkSetIntersect :: Context -> [AST] -> IO AST
- mkSetDifference :: Context -> AST -> AST -> IO AST
- mkSetComplement :: Context -> AST -> IO AST
- mkSetMember :: Context -> AST -> AST -> IO AST
- mkSetSubset :: Context -> AST -> AST -> IO AST
- mkNumeral :: Context -> String -> Sort -> IO AST
- mkReal :: Context -> Int -> Int -> IO AST
- mkInt :: Context -> Int -> Sort -> IO AST
- mkUnsignedInt :: Context -> Word -> Sort -> IO AST
- mkInt64 :: Context -> Int64 -> Sort -> IO AST
- mkUnsignedInt64 :: Context -> Word64 -> Sort -> IO AST
- mkIntegral :: Integral a => Context -> a -> Sort -> IO AST
- mkRational :: Context -> Rational -> IO AST
- mkFixed :: HasResolution a => Context -> Fixed a -> IO AST
- mkRealNum :: Real r => Context -> r -> IO AST
- mkInteger :: Context -> Integer -> IO AST
- mkIntNum :: Integral a => Context -> a -> IO AST
- mkBitvector :: Context -> Int -> Integer -> IO AST
- mkBvNum :: Integral i => Context -> Int -> i -> IO AST
- mkPattern :: Context -> [AST] -> IO Pattern
- mkBound :: Context -> Int -> Sort -> IO AST
- mkForall :: Context -> [Pattern] -> [Symbol] -> [Sort] -> AST -> IO AST
- mkExists :: Context -> [Pattern] -> [Symbol] -> [Sort] -> AST -> IO AST
- mkForallConst :: Context -> [Pattern] -> [App] -> AST -> IO AST
- mkExistsConst :: Context -> [Pattern] -> [App] -> AST -> IO AST
- getSymbolString :: Context -> Symbol -> IO String
- getBvSortSize :: Context -> Sort -> IO Int
- getDatatypeSortConstructors :: Context -> Sort -> IO [FuncDecl]
- getDatatypeSortRecognizers :: Context -> Sort -> IO [FuncDecl]
- getDeclName :: Context -> FuncDecl -> IO Symbol
- getSort :: Context -> AST -> IO Sort
- getBoolValue :: Context -> AST -> IO (Maybe Bool)
- getAstKind :: Context -> AST -> IO ASTKind
- toApp :: Context -> AST -> IO App
- getNumeralString :: Context -> AST -> IO String
- getBool :: Context -> AST -> IO Bool
- getInt :: Context -> AST -> IO Integer
- getReal :: Context -> AST -> IO Rational
- getBv :: Context -> AST -> Bool -> IO Integer
- modelEval :: Context -> Model -> AST -> Bool -> IO (Maybe AST)
- evalArray :: Context -> Model -> AST -> IO (Maybe FuncModel)
- getFuncInterp :: Context -> Model -> FuncDecl -> IO (Maybe FuncInterp)
- isAsArray :: Context -> AST -> IO Bool
- getAsArrayFuncDecl :: Context -> AST -> IO FuncDecl
- funcInterpGetNumEntries :: Context -> FuncInterp -> IO Int
- funcInterpGetEntry :: Context -> FuncInterp -> Int -> IO FuncEntry
- funcInterpGetElse :: Context -> FuncInterp -> IO AST
- funcInterpGetArity :: Context -> FuncInterp -> IO Int
- funcEntryGetValue :: Context -> FuncEntry -> IO AST
- funcEntryGetNumArgs :: Context -> FuncEntry -> IO Int
- funcEntryGetArg :: Context -> FuncEntry -> Int -> IO AST
- modelToString :: Context -> Model -> IO String
- showModel :: Context -> Model -> IO String
- type EvalAst a = Model -> AST -> IO (Maybe a)
- eval :: Context -> EvalAst AST
- evalBool :: Context -> EvalAst Bool
- evalInt :: Context -> EvalAst Integer
- evalReal :: Context -> EvalAst Rational
- evalBv :: Context -> Bool -> EvalAst Integer
- mapEval :: Traversable t => EvalAst a -> Model -> t AST -> IO (Maybe (t a))
- evalT :: Traversable t => Context -> Model -> t AST -> IO (Maybe (t AST))
- data FuncModel = FuncModel {
- interpMap :: [([AST], AST)]
- interpElse :: AST
- evalFunc :: Context -> Model -> FuncDecl -> IO (Maybe FuncModel)
- data ASTPrintMode
- setASTPrintMode :: Context -> ASTPrintMode -> IO ()
- astToString :: Context -> AST -> IO String
- patternToString :: Context -> Pattern -> IO String
- sortToString :: Context -> Sort -> IO String
- funcDeclToString :: Context -> FuncDecl -> IO String
- benchmarkToSMTLibString :: Context -> String -> String -> String -> String -> [AST] -> AST -> IO String
- data Z3Error = Z3Error {
- errCode :: Z3ErrorCode
- errMsg :: String
- data Z3ErrorCode
- data Version = Version {}
- getVersion :: IO Version
- data Logic
- mkSolver :: Context -> IO Solver
- mkSimpleSolver :: Context -> IO Solver
- mkSolverForLogic :: Context -> Logic -> IO Solver
- solverGetHelp :: Context -> Solver -> IO String
- solverSetParams :: Context -> Solver -> Params -> IO ()
- solverPush :: Context -> Solver -> IO ()
- solverPop :: Context -> Solver -> Int -> IO ()
- solverReset :: Context -> Solver -> IO ()
- solverGetNumScopes :: Context -> Solver -> IO Int
- solverAssertCnstr :: Context -> Solver -> AST -> IO ()
- solverAssertAndTrack :: Context -> Solver -> AST -> AST -> IO ()
- solverCheck :: Context -> Solver -> IO Result
- solverCheckAssumptions :: Context -> Solver -> [AST] -> IO Result
- solverGetModel :: Context -> Solver -> IO Model
- solverGetUnsatCore :: Context -> Solver -> IO [AST]
- solverGetReasonUnknown :: Context -> Solver -> IO String
- solverToString :: Context -> Solver -> IO String
- solverCheckAndGetModel :: Context -> Solver -> IO (Result, Maybe Model)
Types
data Symbol
A Z3 symbol.
Used to name types, constants and functions.
data AST
A Z3 AST node.
This is the data-structure used in Z3 to represent terms, formulas and types.
data FuncDecl
A kind of AST representing function symbols.
data Pattern
A kind of AST representing pattern and multi-patterns to guide quantifier instantiation.
data Constructor
A type contructor for a (recursive) datatype.
data Params
A Z3 parameter set.
Starting at Z3 4.0, parameter sets are used to configure many components such as: simplifiers, tactics, solvers, etc.
data Solver
A Z3 solver engine.
A(n) (incremental) solver, possibly specialized by a particular tactic or logic.
data ASTKind
Different kinds of Z3 AST nodes.
Satisfiability result
data Result
Result of a satisfiability check.
This corresponds to the z3_lbool type in the C API.
Create configuration
Create a configuration.
See withConfig
.
Delete a configuration.
See withConfig
.
setParamValue :: Config -> String -> String -> IO ()
Set a configuration parameter.
Helpers
withConfig :: (Config -> IO a) -> IO a
Run a computation using a temporally created configuration.
Note that the configuration object can be thrown away once
it has been used to create the Z3 Context
.
Create context
mkContext :: Config -> IO Context
Create a context using the given configuration.
Z3_del_context is called by Haskell's garbage collector before
freeing the Context
object.
withContext :: Context -> (Ptr Z3_context -> IO r) -> IO r
Parameters
mkParams :: Context -> IO Params
Create a Z3 (empty) parameter set.
Starting at Z3 4.0, parameter sets are used to configure many components such as: simplifiers, tactics, solvers, etc.
paramsSetBool :: Context -> Params -> Symbol -> Bool -> IO ()
Add a Boolean parameter k with value v to the parameter set p.
paramsSetUInt :: Context -> Params -> Symbol -> Word -> IO ()
Add a unsigned parameter k with value v to the parameter set p.
paramsSetDouble :: Context -> Params -> Symbol -> Double -> IO ()
Add a double parameter k with value v to the parameter set p.
paramsSetSymbol :: Context -> Params -> Symbol -> Symbol -> IO ()
Add a symbol parameter k with value v to the parameter set p.
paramsToString :: Context -> Params -> IO String
Convert a parameter set into a string.
This function is mainly used for printing the contents of a parameter set.
Symbols
mkIntSymbol :: Integral int => Context -> int -> IO Symbol
Create a Z3 symbol using an integer.
mkIntSymbol c i
requires 0 <= i < 2^30
Sorts
mkUninterpretedSort :: Context -> Symbol -> IO Sort
Create a free (uninterpreted) type using the given name (symbol).
Two free types are considered the same iff the have the same name.
mkBoolSort :: Context -> IO Sort
Create the boolean type.
This type is used to create propositional variables and predicates.
mkIntSort :: Context -> IO Sort
Create the integer type.
This is the type of arbitrary precision integers.
A machine integer can be represented using bit-vectors, see mkBvSort
.
mkRealSort :: Context -> IO Sort
Create the real type.
This type is not a floating point number. Z3 does not have support for floating point numbers yet.
mkBvSort :: Integral int => Context -> int -> IO Sort
Create a bit-vector type of the given size.
This type can also be seen as a machine integer.
mkBvSort c sz
requires sz >= 0
mkArraySort :: Context -> Sort -> Sort -> IO Sort
Create an array type
We usually represent the array type as: [domain -> range]. Arrays are usually used to model the heap/memory in software verification.
:: Context | Context |
-> Symbol | Name of the sort |
-> [(Symbol, Sort)] | Name and sort of each field |
-> IO (Sort, FuncDecl, [FuncDecl]) | Resulting sort, and function declarations for the constructor and projections. |
Create a tuple type
A tuple with n fields has a constructor and n projections. This function will also declare the constructor and projection functions.
:: Context | Context |
-> Symbol | Name of the constructor |
-> Symbol | Name of recognizer function |
-> [(Symbol, Maybe Sort, Int)] | Name, sort option, and sortRefs |
-> IO Constructor |
Create a contructor
mkDatatype :: Context -> Symbol -> [Constructor] -> IO Sort
Create datatype, such as lists, trees, records, enumerations or unions of records.
The datatype may be recursive. Returns the datatype sort.
Constants and Applications
:: Context | Logical context. |
-> Symbol | Name of the function (or constant). |
-> [Sort] | Function domain (empty for constants). |
-> Sort | Return sort of the function. |
-> IO FuncDecl |
Declare a constant or function.
mkConst :: Context -> Symbol -> Sort -> IO AST
Declare and create a constant.
This is a shorthand for:
do xd <- mkFunDecl c x [] s; mkApp c xd []
mkFreshFuncDecl :: Context -> String -> [Sort] -> Sort -> IO FuncDecl
Declare a fresh constant or function.
Declare and create a fresh constant.
Helpers
mkVar :: Context -> Symbol -> Sort -> IO AST
Declare and create a variable (aka constant).
An alias for mkConst
.
Declarate and create a variable of sort bit-vector.
See mkVar
.
mkFreshVar :: Context -> String -> Sort -> IO AST
Declare and create a fresh variable (aka constant).
An alias for mkFreshConst
.
mkFreshBoolVar :: Context -> String -> IO AST
Declarate and create a fresh variable of sort bool.
See mkFreshVar
.
mkFreshRealVar :: Context -> String -> IO AST
Declarate and create a fresh variable of sort real.
See mkFreshVar
.
mkFreshIntVar :: Context -> String -> IO AST
Declarate and create a fresh variable of sort int.
See mkFreshVar
.
Declarate and create a fresh variable of sort bit-vector.
See mkFreshVar
.
Propositional Logic and Equality
mkIte :: Context -> AST -> AST -> AST -> IO AST
Create an AST node representing an if-then-else: ite(t1, t2, t3).
mkAnd :: Context -> [AST] -> IO AST
Create an AST node representing args[0] and ... and args[num_args-1].
mkOr :: Context -> [AST] -> IO AST
Create an AST node representing args[0] or ... or args[num_args-1].
mkDistinct :: Context -> [AST] -> IO AST
The distinct construct is used for declaring the arguments pairwise distinct.
That is, and [ args!!i /= args!!j | i <- [0..length(args)-1], j <- [i+1..length(args)-1] ]
Helpers
Arithmetic: Integers and Reals
mkAdd :: Context -> [AST] -> IO AST
Create an AST node representing args[0] + ... + args[num_args-1].
mkMul :: Context -> [AST] -> IO AST
Create an AST node representing args[0] * ... * args[num_args-1].
mkSub :: Context -> [AST] -> IO AST
Create an AST node representing args[0] - ... - args[num_args - 1].
mkUnaryMinus :: Context -> AST -> IO AST
Create an AST node representing -arg.
mkInt2Real :: Context -> AST -> IO AST
Coerce an integer to a real.
mkReal2Int :: Context -> AST -> IO AST
Coerce a real to an integer.
Bit-vectors
mkBvredand :: Context -> AST -> IO AST
Take conjunction of bits in vector, return vector of length 1.
mkBvsrem :: Context -> AST -> AST -> IO AST
Two's complement signed remainder (sign follows dividend).
mkBvsmod :: Context -> AST -> AST -> IO AST
Two's complement signed remainder (sign follows divisor).
mkExtract :: Context -> Int -> Int -> AST -> IO AST
Extract the bits high down to low from a bitvector of size m to yield a new bitvector of size n, where n = high - low + 1.
mkSignExt :: Context -> Int -> AST -> IO AST
Sign-extend of the given bit-vector to the (signed) equivalent bitvector of size m+i, where m is the size of the given bit-vector.
mkZeroExt :: Context -> Int -> AST -> IO AST
Extend the given bit-vector with zeros to the (unsigned) equivalent bitvector of size m+i, where m is the size of the given bit-vector.
mkBv2int :: Context -> AST -> Bool -> IO AST
Create an integer from the bit-vector argument t1.
If is_signed is false, then the bit-vector t1 is treated as unsigned. So the result is non-negative and in the range [0..2^N-1], where N are the number of bits in t1. If is_signed is true, t1 is treated as a signed bit-vector.
mkBvnegNoOverflow :: Context -> AST -> IO AST
Check that bit-wise negation does not overflow when t1 is interpreted as a signed bit-vector.
mkBvaddNoOverflow :: Context -> AST -> AST -> Bool -> IO AST
Create a predicate that checks that the bit-wise addition of t1 and t2 does not overflow.
mkBvaddNoUnderflow :: Context -> AST -> AST -> IO AST
Create a predicate that checks that the bit-wise signed addition of t1 and t2 does not underflow.
mkBvsubNoOverflow :: Context -> AST -> AST -> IO AST
Create a predicate that checks that the bit-wise signed subtraction of t1 and t2 does not overflow.
mkBvsubNoUnderflow :: Context -> AST -> AST -> IO AST
Create a predicate that checks that the bit-wise subtraction of t1 and t2 does not underflow.
mkBvmulNoOverflow :: Context -> AST -> AST -> Bool -> IO AST
Create a predicate that checks that the bit-wise multiplication of t1 and t2 does not overflow.
mkBvmulNoUnderflow :: Context -> AST -> AST -> IO AST
Create a predicate that checks that the bit-wise signed multiplication of t1 and t2 does not underflow.
mkBvsdivNoOverflow :: Context -> AST -> AST -> IO AST
Create a predicate that checks that the bit-wise signed division of t1 and t2 does not overflow.
Arrays
Array read. The argument a is the array and i is the index of the array that gets read.
Array update.
The result of this function is an array that is equal to the input array (with respect to select) on all indices except for i, where it maps to v.
The semantics of this function is given by the theory of arrays described in the SMT-LIB standard. See http://smtlib.org for more details.
Create the constant array.
The resulting term is an array, such that a select on an arbitrary index produces the value v.
Map a function f on the the argument arrays.
The n nodes args must be of array sorts [domain -> range_i]. The function declaration f must have type range_1 .. range_n -> range. The sort of the result is [domain -> range].
Access the array default value.
Produces the default range value, for arrays that can be represented as finite maps with a default range value.
Sets
mkSetUnion :: Context -> [AST] -> IO AST
Take the union of a list of sets.
mkSetIntersect :: Context -> [AST] -> IO AST
Take the intersection of a list of sets.
Take the set difference between two sets.
Check if the first set is a subset of the second set.
Numerals
mkInt :: Context -> Int -> Sort -> IO AST
Create a numeral of an int, bit-vector, or finite-domain sort.
This function can be use to create numerals that fit in a
machine integer.
It is slightly faster than mkNumeral
since it is not necessary
to parse a string.
mkUnsignedInt :: Context -> Word -> Sort -> IO AST
Create a numeral of an int, bit-vector, or finite-domain sort.
This function can be use to create numerals that fit in a
machine unsigned integer.
It is slightly faster than mkNumeral
since it is not necessary
to parse a string.
mkInt64 :: Context -> Int64 -> Sort -> IO AST
Create a numeral of an int, bit-vector, or finite-domain sort.
This function can be use to create numerals that fit in a
machine 64-bit integer.
It is slightly faster than mkNumeral
since it is not necessary
to parse a string.
mkUnsignedInt64 :: Context -> Word64 -> Sort -> IO AST
Create a numeral of an int, bit-vector, or finite-domain sort.
This function can be use to create numerals that fit in a
machine unsigned 64-bit integer.
It is slightly faster than mkNumeral
since it is not necessary
to parse a string.
Helpers
mkIntegral :: Integral a => Context -> a -> Sort -> IO AST
Create a numeral of an int, bit-vector, or finite-domain sort.
mkFixed :: HasResolution a => Context -> Fixed a -> IO AST
Create a numeral of sort real from a Fixed
.
Create a numeral of sort Bit-vector from an Integer
.
Create a numeral of sort Bit-vector from an Integral
.
Quantifiers
Create a pattern for quantifier instantiation.
Z3 uses pattern matching to instantiate quantifiers. If a pattern is not provided for a quantifier, then Z3 will automatically compute a set of patterns for it. However, for optimal performance, the user should provide the patterns.
Patterns comprise a list of terms. The list should be non-empty. If the list comprises of more than one term, it is a called a multi-pattern.
In general, one can pass in a list of (multi-)patterns in the quantifier constructor.
Create a bound variable.
Bound variables are indexed by de-Bruijn indices.
:: Context | |
-> [Pattern] | Instantiation patterns (see |
-> [Symbol] | Bound (quantified) variables xs. |
-> [Sort] | Sorts of the bound variables. |
-> AST | Body of the quantifier. |
-> IO AST |
Create a forall formula.
The bound variables are de-Bruijn indices created using mkBound
.
Z3 applies the convention that the last element in xs refers to the variable with index 0, the second to last element of xs refers to the variable with index 1, etc.
mkExists :: Context -> [Pattern] -> [Symbol] -> [Sort] -> AST -> IO AST
Create an exists formula.
Similar to mkForall
.
:: Context | |
-> [Pattern] | Instantiation patterns (see |
-> [App] | Constants to be abstracted into bound variables. |
-> AST | Quantifier body. |
-> IO AST |
Create a universal quantifier using a list of constants that will form the set of bound variables.
:: Context | |
-> [Pattern] | Instantiation patterns (see |
-> [App] | Constants to be abstracted into bound variables. |
-> AST | Quantifier body. |
-> IO AST |
Create a existential quantifier using a list of constants that will form the set of bound variables.
Accessors
getSymbolString :: Context -> Symbol -> IO String
Return the symbol name.
getBvSortSize :: Context -> Sort -> IO Int
Return the size of the given bit-vector sort.
Get list of constructors for datatype.
Get list of recognizers for datatype.
getDeclName :: Context -> FuncDecl -> IO Symbol
Return the constant declaration name as a symbol.
getBoolValue :: Context -> AST -> IO (Maybe Bool)
Return Z3_L_TRUE if a is true, Z3_L_FALSE if it is false, and Z3_L_UNDEF otherwise.
getAstKind :: Context -> AST -> IO ASTKind
Return the kind of the given AST.
getNumeralString :: Context -> AST -> IO String
Return numeral value, as a string of a numeric constant term.
Helpers
Models
Evaluate an AST node in the given model.
The evaluation may fail for the following reasons:
- t contains a quantifier.
- the model m is partial.
- t is type incorrect.
evalArray :: Context -> Model -> AST -> IO (Maybe FuncModel)
Evaluate an array as a function, if possible.
getFuncInterp :: Context -> Model -> FuncDecl -> IO (Maybe FuncInterp)
Return the interpretation of the function f in the model m. Return NULL, if the model does not assign an interpretation for f. That should be interpreted as: the f does not matter.
isAsArray :: Context -> AST -> IO Bool
The (_ as-array f) AST node is a construct for assigning interpretations for arrays in Z3. It is the array such that forall indices i we have that (select (_ as-array f) i) is equal to (f i). This procedure returns Z3_TRUE if the a is an as-array AST node.
getAsArrayFuncDecl :: Context -> AST -> IO FuncDecl
Return the function declaration f associated with a (_ as_array f) node.
funcInterpGetNumEntries :: Context -> FuncInterp -> IO Int
Return the number of entries in the given function interpretation.
funcInterpGetEntry :: Context -> FuncInterp -> Int -> IO FuncEntry
Return a _point_ of the given function intepretation. It represents the value of f in a particular point.
funcInterpGetElse :: Context -> FuncInterp -> IO AST
Return the 'else' value of the given function interpretation.
funcInterpGetArity :: Context -> FuncInterp -> IO Int
Return the arity (number of arguments) of the given function interpretation.
funcEntryGetValue :: Context -> FuncEntry -> IO AST
Return the value of this point.
funcEntryGetNumArgs :: Context -> FuncEntry -> IO Int
Return the number of arguments in a Z3_func_entry object.
funcEntryGetArg :: Context -> FuncEntry -> Int -> IO AST
Return an argument of a Z3_func_entry object.
modelToString :: Context -> Model -> IO String
Convert the given model into a string.
showModel :: Context -> Model -> IO String
Deprecated: Use modelToString instead.
Alias for modelToString
.
Helpers
mapEval :: Traversable t => EvalAst a -> Model -> t AST -> IO (Maybe (t a))
Run a evaluation function on a Traversable
data structure of AST
s
(e.g. [AST]
, Vector AST
, Maybe AST
, etc).
This a generic version of evalT
which can be used in combination with
other helpers. For instance, mapEval (evalInt c)
can be used to obtain
the Integer
interpretation of a list of AST
of sort int.
evalT :: Traversable t => Context -> Model -> t AST -> IO (Maybe (t AST))
Evaluate a collection of AST nodes in the given model.
data FuncModel
The interpretation of a function.
evalFunc :: Context -> Model -> FuncDecl -> IO (Maybe FuncModel)
Evaluate a function declaration to a list of argument/value pairs.
String Conversion
data ASTPrintMode
Pretty-printing mode for converting ASTs to strings. The mode can be one of the following:
- Z3_PRINT_SMTLIB_FULL: Print AST nodes in SMTLIB verbose format.
- Z3_PRINT_LOW_LEVEL: Print AST nodes using a low-level format.
- Z3_PRINT_SMTLIB_COMPLIANT: Print AST nodes in SMTLIB 1.x compliant format.
- Z3_PRINT_SMTLIB2_COMPLIANT: Print AST nodes in SMTLIB 2.x compliant format.
setASTPrintMode :: Context -> ASTPrintMode -> IO ()
Set the pretty-printing mode for converting ASTs to strings.
astToString :: Context -> AST -> IO String
Convert an AST to a string.
patternToString :: Context -> Pattern -> IO String
Convert a pattern to a string.
sortToString :: Context -> Sort -> IO String
Convert a sort to a string.
funcDeclToString :: Context -> FuncDecl -> IO String
Convert a FuncDecl to a string.
:: Context | |
-> String | name |
-> String | logic |
-> String | status |
-> String | attributes |
-> [AST] | assumptions |
-> AST | formula |
-> IO String |
Convert the given benchmark into SMT-LIB formatted string.
The output format can be configured via setASTPrintMode
.
Error Handling
data Z3ErrorCode
Z3 error codes.
Miscellaneous
data Version
getVersion :: IO Version
Return Z3 version number information.
Solvers
data Logic
Solvers available in Z3.
These are described at http://smtlib.cs.uiowa.edu/logics.html
AUFLIA | Closed formulas over the theory of linear integer arithmetic and arrays extended with free sort and function symbols but restricted to arrays with integer indices and values. |
AUFLIRA | Closed linear formulas with free sort and function symbols over one- and two-dimentional arrays of integer index and real value. |
AUFNIRA | Closed formulas with free function and predicate symbols over a theory of arrays of arrays of integer index and real value. |
LRA | Closed linear formulas in linear real arithmetic. |
QF_ABV | Closed quantifier-free formulas over the theory of bitvectors and bitvector arrays. |
QF_AUFBV | Closed quantifier-free formulas over the theory of bitvectors and bitvector arrays extended with free sort and function symbols. |
QF_AUFLIA | Closed quantifier-free linear formulas over the theory of integer arrays extended with free sort and function symbols. |
QF_AX | Closed quantifier-free formulas over the theory of arrays with extensionality. |
QF_BV | Closed quantifier-free formulas over the theory of fixed-size bitvectors. |
QF_IDL | Difference Logic over the integers. In essence, Boolean combinations of inequations of the form x - y < b where x and y are integer variables and b is an integer constant. |
QF_LIA | Unquantified linear integer arithmetic. In essence, Boolean combinations of inequations between linear polynomials over integer variables. |
QF_LRA | Unquantified linear real arithmetic. In essence, Boolean combinations of inequations between linear polynomials over real variables. |
QF_NIA | Quantifier-free integer arithmetic. |
QF_NRA | Quantifier-free real arithmetic. |
QF_RDL | Difference Logic over the reals. In essence, Boolean combinations of inequations of the form x - y < b where x and y are real variables and b is a rational constant. |
QF_UF | Unquantified formulas built over a signature of uninterpreted (i.e., free) sort and function symbols. |
QF_UFBV | Unquantified formulas over bitvectors with uninterpreted sort function and symbols. |
QF_UFIDL | Difference Logic over the integers (in essence) but with uninterpreted sort and function symbols. |
QF_UFLIA | Unquantified linear integer arithmetic with uninterpreted sort and function symbols. |
QF_UFLRA | Unquantified linear real arithmetic with uninterpreted sort and function symbols. |
QF_UFNRA | Unquantified non-linear real arithmetic with uninterpreted sort and function symbols. |
UFLRA | Linear real arithmetic with uninterpreted sort and function symbols. |
UFNIA | Non-linear integer arithmetic with uninterpreted sort and function symbols. |
mkSimpleSolver :: Context -> IO Solver
mkSolverForLogic :: Context -> Logic -> IO Solver
solverGetHelp :: Context -> Solver -> IO String
Return a string describing all solver available parameters.
solverSetParams :: Context -> Solver -> Params -> IO ()
Set the given solver using the given parameters.
solverPush :: Context -> Solver -> IO ()
solverReset :: Context -> Solver -> IO ()
solverGetNumScopes :: Context -> Solver -> IO Int
Number of backtracking points.
solverAssertCnstr :: Context -> Solver -> AST -> IO ()
solverCheck :: Context -> Solver -> IO Result
Check whether the assertions in a given solver are consistent or not.
solverCheckAssumptions :: Context -> Solver -> [AST] -> IO Result
Check whether the assertions in the given solver and optional assumptions are consistent or not.
solverGetModel :: Context -> Solver -> IO Model
Retrieve the model for the last solverCheck
.
The error handler is invoked if a model is not available because
the commands above were not invoked for the given solver,
or if the result was Unsat
.
solverGetUnsatCore :: Context -> Solver -> IO [AST]
Retrieve the unsat core for the last solverCheckAssumptions
; the unsat core is a subset of the assumptions
solverGetReasonUnknown :: Context -> Solver -> IO String
Return a brief justification for an Unknown
result for the commands solverCheck
and solverCheckAssumptions
.
solverToString :: Context -> Solver -> IO String
Convert the given solver into a string.