| Copyright | (c) Brian Huffman |
|---|---|
| License | BSD3 |
| Maintainer | erkokl@gmail.com |
| Stability | experimental |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.SBV.Dynamic
Contents
- Programming with symbolic values
- Uninterpreted sorts, constants, and functions
- Properties, proofs, and satisfiability
- Proving properties using multiple solvers
- Proving properties using multiple threads
- Quick-check
- Model extraction
- SMT Interface: Configurations and solvers
- Symbolic computations
- Code generation from symbolic programs
Description
Dynamically typed low-level API to the SBV library, for users who want to generate symbolic values at run-time. Note that with this API it is possible to create terms that are not type correct; use at your own risk!
Synopsis
- data SVal
- class HasKind a where
- kindOf :: a -> Kind
- hasSign :: a -> Bool
- intSizeOf :: a -> Int
- isBoolean :: a -> Bool
- isBounded :: a -> Bool
- isReal :: a -> Bool
- isFloat :: a -> Bool
- isDouble :: a -> Bool
- isFP :: a -> Bool
- isUnbounded :: a -> Bool
- isUserSort :: a -> Bool
- isChar :: a -> Bool
- isString :: a -> Bool
- isList :: a -> Bool
- isSet :: a -> Bool
- isTuple :: a -> Bool
- isMaybe :: a -> Bool
- isEither :: a -> Bool
- showType :: a -> String
- data Kind
- data CV = CV {}
- data CVal
- cvToBool :: CV -> Bool
- data SArr
- readSArr :: SArr -> SVal -> SVal
- writeSArr :: SArr -> SVal -> SVal -> SArr
- mergeSArr :: SVal -> SArr -> SArr -> SArr
- newSArr :: State -> (Kind, Kind) -> (Int -> String) -> Maybe SVal -> IO SArr
- eqSArr :: SArr -> SArr -> SVal
- data SFunArr
- readSFunArr :: SFunArr -> SVal -> SVal
- writeSFunArr :: SFunArr -> SVal -> SVal -> SFunArr
- mergeSFunArr :: SVal -> SFunArr -> SFunArr -> SFunArr
- newSFunArr :: State -> (Kind, Kind) -> (Int -> String) -> Maybe SVal -> IO SFunArr
- type Symbolic = SymbolicT IO
- data Quantifier
- svMkSymVar :: VarContext -> Kind -> Maybe String -> State -> IO SVal
- sWordN :: MonadSymbolic m => Int -> String -> m SVal
- sWordN_ :: MonadSymbolic m => Int -> m SVal
- sIntN :: MonadSymbolic m => Int -> String -> m SVal
- sIntN_ :: MonadSymbolic m => Int -> m SVal
- svTrue :: SVal
- svFalse :: SVal
- svBool :: Bool -> SVal
- svAsBool :: SVal -> Maybe Bool
- svInteger :: Kind -> Integer -> SVal
- svAsInteger :: SVal -> Maybe Integer
- svFloat :: Float -> SVal
- svDouble :: Double -> SVal
- svFloatingPoint :: FP -> SVal
- svReal :: Rational -> SVal
- svNumerator :: SVal -> Maybe Integer
- svDenominator :: SVal -> Maybe Integer
- svEqual :: SVal -> SVal -> SVal
- svNotEqual :: SVal -> SVal -> SVal
- svEnumFromThenTo :: SVal -> Maybe SVal -> SVal -> Maybe [SVal]
- svLessThan :: SVal -> SVal -> SVal
- svGreaterThan :: SVal -> SVal -> SVal
- svLessEq :: SVal -> SVal -> SVal
- svGreaterEq :: SVal -> SVal -> SVal
- svStructuralLessThan :: SVal -> SVal -> SVal
- svPlus :: SVal -> SVal -> SVal
- svTimes :: SVal -> SVal -> SVal
- svMinus :: SVal -> SVal -> SVal
- svUNeg :: SVal -> SVal
- svAbs :: SVal -> SVal
- svDivide :: SVal -> SVal -> SVal
- svQuot :: SVal -> SVal -> SVal
- svRem :: SVal -> SVal -> SVal
- svQuotRem :: SVal -> SVal -> (SVal, SVal)
- svExp :: SVal -> SVal -> SVal
- svAddConstant :: Integral a => SVal -> a -> SVal
- svIncrement :: SVal -> SVal
- svDecrement :: SVal -> SVal
- svAnd :: SVal -> SVal -> SVal
- svOr :: SVal -> SVal -> SVal
- svXOr :: SVal -> SVal -> SVal
- svNot :: SVal -> SVal
- svShl :: SVal -> Int -> SVal
- svShr :: SVal -> Int -> SVal
- svRol :: SVal -> Int -> SVal
- svRor :: SVal -> Int -> SVal
- svExtract :: Int -> Int -> SVal -> SVal
- svJoin :: SVal -> SVal -> SVal
- svSign :: SVal -> SVal
- svUnsign :: SVal -> SVal
- svFromIntegral :: Kind -> SVal -> SVal
- svSelect :: [SVal] -> SVal -> SVal -> SVal
- svToWord1 :: SVal -> SVal
- svFromWord1 :: SVal -> SVal
- svTestBit :: SVal -> Int -> SVal
- svSetBit :: SVal -> Int -> SVal
- svShiftLeft :: SVal -> SVal -> SVal
- svShiftRight :: SVal -> SVal -> SVal
- svRotateLeft :: SVal -> SVal -> SVal
- svRotateRight :: SVal -> SVal -> SVal
- svBarrelRotateLeft :: SVal -> SVal -> SVal
- svBarrelRotateRight :: SVal -> SVal -> SVal
- svWordFromBE :: [SVal] -> SVal
- svWordFromLE :: [SVal] -> SVal
- svBlastLE :: SVal -> [SVal]
- svBlastBE :: SVal -> [SVal]
- svIte :: SVal -> SVal -> SVal -> SVal
- svLazyIte :: Kind -> SVal -> SVal -> SVal -> SVal
- svSymbolicMerge :: Kind -> Bool -> SVal -> SVal -> SVal -> SVal
- svUninterpreted :: Kind -> String -> Maybe [String] -> [SVal] -> SVal
- proveWith :: SMTConfig -> Symbolic SVal -> IO ThmResult
- satWith :: SMTConfig -> Symbolic SVal -> IO SatResult
- allSatWith :: SMTConfig -> Symbolic SVal -> IO AllSatResult
- safeWith :: SMTConfig -> Symbolic SVal -> IO [SafeResult]
- proveWithAll :: [SMTConfig] -> Symbolic SVal -> IO [(Solver, NominalDiffTime, ThmResult)]
- proveWithAny :: [SMTConfig] -> Symbolic SVal -> IO (Solver, NominalDiffTime, ThmResult)
- satWithAll :: [SMTConfig] -> Symbolic SVal -> IO [(Solver, NominalDiffTime, SatResult)]
- satWithAny :: [SMTConfig] -> Symbolic SVal -> IO (Solver, NominalDiffTime, SatResult)
- proveConcurrentWithAll :: SMTConfig -> Symbolic SVal -> [Query SVal] -> IO [(Solver, NominalDiffTime, ThmResult)]
- proveConcurrentWithAny :: SMTConfig -> Symbolic SVal -> [Query SVal] -> IO (Solver, NominalDiffTime, ThmResult)
- satConcurrentWithAny :: SMTConfig -> [Query b] -> Symbolic SVal -> IO (Solver, NominalDiffTime, SatResult)
- satConcurrentWithAll :: SMTConfig -> [Query b] -> Symbolic SVal -> IO [(Solver, NominalDiffTime, SatResult)]
- svQuickCheck :: Symbolic SVal -> IO Bool
- newtype ThmResult = ThmResult SMTResult
- newtype SatResult = SatResult SMTResult
- data AllSatResult = AllSatResult {}
- newtype SafeResult = SafeResult (Maybe String, String, SMTResult)
- data OptimizeResult
- data SMTResult
- genParse :: Integral a => Kind -> [CV] -> Maybe (a, [CV])
- getModelAssignment :: SMTResult -> Either String (Bool, [CV])
- getModelDictionary :: SMTResult -> Map String CV
- data SMTConfig = SMTConfig {
- verbose :: Bool
- timing :: Timing
- printBase :: Int
- printRealPrec :: Int
- crackNum :: Bool
- satCmd :: String
- allSatMaxModelCount :: Maybe Int
- allSatPrintAlong :: Bool
- satTrackUFs :: Bool
- isNonModelVar :: String -> Bool
- validateModel :: Bool
- optimizeValidateConstraints :: Bool
- transcript :: Maybe FilePath
- smtLibVersion :: SMTLibVersion
- dsatPrecision :: Maybe Double
- solver :: SMTSolver
- extraArgs :: [String]
- allowQuantifiedQueries :: Bool
- roundingMode :: RoundingMode
- solverSetOptions :: [SMTOption]
- ignoreExitCode :: Bool
- redirectVerbose :: Maybe FilePath
- data SMTLibVersion = SMTLib2
- data Solver
- data SMTSolver = SMTSolver {
- name :: Solver
- executable :: String
- preprocess :: String -> String
- options :: SMTConfig -> [String]
- engine :: SMTEngine
- capabilities :: SolverCapabilities
- boolector :: SMTConfig
- cvc4 :: SMTConfig
- yices :: SMTConfig
- z3 :: SMTConfig
- mathSAT :: SMTConfig
- abc :: SMTConfig
- defaultSolverConfig :: Solver -> SMTConfig
- defaultSMTCfg :: SMTConfig
- sbvCheckSolverInstallation :: SMTConfig -> IO Bool
- getAvailableSolvers :: IO [SMTConfig]
- outputSVal :: MonadSymbolic m => SVal -> m ()
- data SBVCodeGen a
- cgPerformRTCs :: Bool -> SBVCodeGen ()
- cgSetDriverValues :: [Integer] -> SBVCodeGen ()
- cgGenerateDriver :: Bool -> SBVCodeGen ()
- cgGenerateMakefile :: Bool -> SBVCodeGen ()
- svCgInput :: Kind -> String -> SBVCodeGen SVal
- svCgInputArr :: Kind -> Int -> String -> SBVCodeGen [SVal]
- svCgOutput :: String -> SVal -> SBVCodeGen ()
- svCgOutputArr :: String -> [SVal] -> SBVCodeGen ()
- svCgReturn :: SVal -> SBVCodeGen ()
- svCgReturnArr :: [SVal] -> SBVCodeGen ()
- cgAddPrototype :: [String] -> SBVCodeGen ()
- cgAddDecl :: [String] -> SBVCodeGen ()
- cgAddLDFlags :: [String] -> SBVCodeGen ()
- cgIgnoreSAssert :: Bool -> SBVCodeGen ()
- cgIntegerSize :: Int -> SBVCodeGen ()
- cgSRealType :: CgSRealType -> SBVCodeGen ()
- data CgSRealType
- compileToC :: Maybe FilePath -> String -> SBVCodeGen a -> IO a
- compileToCLib :: Maybe FilePath -> String -> [(String, SBVCodeGen a)] -> IO [a]
- generateSMTBenchmark :: Bool -> Symbolic SVal -> IO String
Programming with symbolic values
Symbolic types
Abstract symbolic value type
The Symbolic value. Either a constant (Left) or a symbolic
value (Right Cached). Note that caching is essential for making
sure sharing is preserved.
Instances
class HasKind a where Source #
A class for capturing values that have a sign and a size (finite or infinite)
minimal complete definition: kindOf, unless you can take advantage of the default
signature: This class can be automatically derived for data-types that have
a Data instance; this is useful for creating uninterpreted sorts. So, in
reality, end users should almost never need to define any methods.
Minimal complete definition
Nothing
Methods
intSizeOf :: a -> Int Source #
isBoolean :: a -> Bool Source #
isBounded :: a -> Bool Source #
isDouble :: a -> Bool Source #
isUnbounded :: a -> Bool Source #
isUserSort :: a -> Bool Source #
isString :: a -> Bool Source #
Instances
Kind of symbolic value
Constructors
| KBool | |
| KBounded !Bool !Int | |
| KUnbounded | |
| KReal | |
| KUserSort String (Maybe [String]) | |
| KFloat | |
| KDouble | |
| KFP !Int !Int | |
| KChar | |
| KString | |
| KList Kind | |
| KSet Kind | |
| KTuple [Kind] | |
| KMaybe Kind | |
| KEither Kind Kind |
Instances
| Eq Kind Source # | |
| Data Kind Source # | |
Defined in Data.SBV.Core.Kind Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Kind -> c Kind # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Kind # dataTypeOf :: Kind -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Kind) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Kind) # gmapT :: (forall b. Data b => b -> b) -> Kind -> Kind # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Kind -> r # gmapQ :: (forall d. Data d => d -> u) -> Kind -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Kind -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Kind -> m Kind # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Kind -> m Kind # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Kind -> m Kind # | |
| Ord Kind Source # | |
| Show Kind Source # | The interesting about the show instance is that it can tell apart two kinds nicely; since it conveniently
ignores the enumeration constructors. Also, when we construct a |
| NFData Kind Source # | |
Defined in Data.SBV.Core.Symbolic | |
| HasKind Kind Source # | |
Defined in Data.SBV.Core.Kind Methods kindOf :: Kind -> Kind Source # hasSign :: Kind -> Bool Source # intSizeOf :: Kind -> Int Source # isBoolean :: Kind -> Bool Source # isBounded :: Kind -> Bool Source # isReal :: Kind -> Bool Source # isFloat :: Kind -> Bool Source # isDouble :: Kind -> Bool Source # isUnbounded :: Kind -> Bool Source # isUserSort :: Kind -> Bool Source # isChar :: Kind -> Bool Source # isString :: Kind -> Bool Source # isList :: Kind -> Bool Source # isSet :: Kind -> Bool Source # isTuple :: Kind -> Bool Source # isMaybe :: Kind -> Bool Source # | |
CV represents a concrete word of a fixed size:
For signed words, the most significant digit is considered to be the sign.
Instances
| Eq CV Source # | |
| Ord CV Source # | |
| Show CV Source # | Show instance for |
| NFData CV Source # | |
Defined in Data.SBV.Core.Symbolic | |
| HasKind CV Source # |
|
Defined in Data.SBV.Core.Concrete Methods hasSign :: CV -> Bool Source # intSizeOf :: CV -> Int Source # isBoolean :: CV -> Bool Source # isBounded :: CV -> Bool Source # isFloat :: CV -> Bool Source # isDouble :: CV -> Bool Source # isUnbounded :: CV -> Bool Source # isUserSort :: CV -> Bool Source # isString :: CV -> Bool Source # isTuple :: CV -> Bool Source # isMaybe :: CV -> Bool Source # | |
| PrettyNum CV Source # | |
| SatModel CV Source # |
|
| SDivisible CV Source # | |
A constant value
Constructors
| CAlgReal !AlgReal | Algebraic real |
| CInteger !Integer | Bit-vector/unbounded integer |
| CFloat !Float | Float |
| CDouble !Double | Double |
| CFP !FP | Arbitrary float |
| CChar !Char | Character |
| CString !String | String |
| CList ![CVal] | List |
| CSet !(RCSet CVal) | Set. Can be regular or complemented. |
| CUserSort !(Maybe Int, String) | Value of an uninterpreted/user kind. The Maybe Int shows index position for enumerations |
| CTuple ![CVal] | Tuple |
| CMaybe !(Maybe CVal) | Maybe |
| CEither !(Either CVal CVal) | Disjoint union |
Instances
| Eq CVal Source # | Eq instance for CVVal. Note that we cannot simply derive Eq/Ord, since CVAlgReal doesn't have proper instances for these when values are infinitely precise reals. However, we do need a structural eq/ord for Map indexes; so define custom ones here: |
| Ord CVal Source # | Ord instance for VWVal. Same comments as the |
SMT Arrays of symbolic values
mergeSArr :: SVal -> SArr -> SArr -> SArr Source #
Merge two given arrays on the symbolic condition
Intuitively: mergeArrays cond a b = if cond then a else b.
Merging pushes the if-then-else choice down on to elements
newSArr :: State -> (Kind, Kind) -> (Int -> String) -> Maybe SVal -> IO SArr Source #
Create a named new array
Functional arrays of symbolic values
readSFunArr :: SFunArr -> SVal -> SVal Source #
Read the array element at a. For efficiency purposes, we create a memo-table
as we go along, as otherwise we suffer significant performance penalties. See:
http://github.com/LeventErkok/sbv/issues/402 and
http://github.com/LeventErkok/sbv/issues/396.
mergeSFunArr :: SVal -> SFunArr -> SFunArr -> SFunArr Source #
Merge two given arrays on the symbolic condition
Intuitively: mergeArrays cond a b = if cond then a else b.
Merging pushes the if-then-else choice down on to elements
newSFunArr :: State -> (Kind, Kind) -> (Int -> String) -> Maybe SVal -> IO SFunArr Source #
Create a named new array
Creating a symbolic variable
data Quantifier Source #
Quantifiers: forall or exists. Note that we allow arbitrary nestings.
Instances
| Eq Quantifier Source # | |
Defined in Data.SBV.Core.Symbolic | |
| Show Quantifier Source # | Show instance for |
Defined in Data.SBV.Core.Symbolic Methods showsPrec :: Int -> Quantifier -> ShowS # show :: Quantifier -> String # showList :: [Quantifier] -> ShowS # | |
| NFData Quantifier Source # | |
Defined in Data.SBV.Core.Symbolic Methods rnf :: Quantifier -> () # | |
svMkSymVar :: VarContext -> Kind -> Maybe String -> State -> IO SVal Source #
Create a symbolic value, based on the quantifier we have. If an
explicit quantifier is given, we just use that. If not, then we
pick the quantifier appropriately based on the run-mode.
randomCV is used for generating random values for this variable
when used for quickCheck or genTest purposes.
Operations on symbolic values
Boolean literals
Integer literals
Float literals
svFloatingPoint :: FP -> SVal Source #
Convert from a generalized floating point
Algebraic reals (only from rationals)
Symbolic equality
Constructing concrete lists
svEnumFromThenTo :: SVal -> Maybe SVal -> SVal -> Maybe [SVal] Source #
Constructing [x, y, .. z] and [x .. y]. Only works when all arguments are concrete and integral and the result is guaranteed finite
Note that the it isn't "obviously" clear why the following works; after all we're doing the construction over Integer's and mapping
it back to other types such as SIntN/SWordN. The reason is that the values we receive are guaranteed to be in their domains; and thus
the lifting to Integers preserves the bounds; and then going back is just fine. So, things like [1, 5 .. 200] :: [SInt8] work just
fine (end evaluate to empty list), since we see [1, 5 .. -56] in the Integer domain. Also note the explicit check for s /= f
below to make sure we don't stutter and produce an infinite list.
Symbolic ordering
svStructuralLessThan :: SVal -> SVal -> SVal Source #
Given a composite structure, figure out how to compare for less than
Arithmetic operations
svUNeg :: SVal -> SVal Source #
Unary minus. We handle arbitrary-FP's specially here, just for the negated literals.
svQuot :: SVal -> SVal -> SVal Source #
Quotient: Overloaded operation whose meaning depends on the kind at which
it is used: For unbounded integers, it corresponds to the SMT-Lib
"div" operator (Euclidean division, which always has a
non-negative remainder). For unsigned bitvectors, it is "bvudiv";
and for signed bitvectors it is "bvsdiv", which rounds toward zero.
Division by 0 is defined s.t. x/0 = 0, which holds even when x itself is 0.
svRem :: SVal -> SVal -> SVal Source #
Remainder: Overloaded operation whose meaning depends on the kind at which
it is used: For unbounded integers, it corresponds to the SMT-Lib
"mod" operator (always non-negative). For unsigned bitvectors, it
is "bvurem"; and for signed bitvectors it is "bvsrem", which rounds
toward zero (sign of remainder matches that of x). Division by 0 is
defined s.t. x/0 = 0, which holds even when x itself is 0.
svIncrement :: SVal -> SVal Source #
Increment:
svDecrement :: SVal -> SVal Source #
Decrement:
Logical operations
svShl :: SVal -> Int -> SVal Source #
Shift left by a constant amount. Translates to the "bvshl" operation in SMT-Lib.
NB. Haskell spec says the behavior is undefined if the shift amount is negative. We arbitrarily return the value unchanged if this is the case.
svShr :: SVal -> Int -> SVal Source #
Shift right by a constant amount. Translates to either "bvlshr"
(logical shift right) or "bvashr" (arithmetic shift right) in
SMT-Lib, depending on whether x is a signed bitvector.
NB. Haskell spec says the behavior is undefined if the shift amount is negative. We arbitrarily return the value unchanged if this is the case.
svRol :: SVal -> Int -> SVal Source #
Rotate-left, by a constant.
NB. Haskell spec says the behavior is undefined if the shift amount is negative. We arbitrarily return the value unchanged if this is the case.
svRor :: SVal -> Int -> SVal Source #
Rotate-right, by a constant.
NB. Haskell spec says the behavior is undefined if the shift amount is negative. We arbitrarily return the value unchanged if this is the case.
Splitting, joining, and extending
Sign-casting
Numeric conversions
svFromIntegral :: Kind -> SVal -> SVal Source #
Convert a symbolic bitvector from one integral kind to another.
Indexed lookups
svSelect :: [SVal] -> SVal -> SVal -> SVal Source #
Total indexing operation. svSelect xs default index is
intuitively the same as xs !! index, except it evaluates to
default if index overflows. Translates to SMT-Lib tables.
Word-level operations
svToWord1 :: SVal -> SVal Source #
Convert an SVal from kind Bool to an unsigned bitvector of size 1.
svFromWord1 :: SVal -> SVal Source #
Convert an SVal from a bitvector of size 1 (signed or unsigned) to kind Bool.
svTestBit :: SVal -> Int -> SVal Source #
Test the value of a bit. Note that we do an extract here as opposed to masking and checking against zero, as we found extraction to be much faster with large bit-vectors.
svShiftLeft :: SVal -> SVal -> SVal Source #
Generalization of svShl, where the shift-amount is symbolic.
svShiftRight :: SVal -> SVal -> SVal Source #
Generalization of svShr, where the shift-amount is symbolic.
NB. If the shiftee is signed, then this is an arithmetic shift; otherwise it's logical.
svRotateLeft :: SVal -> SVal -> SVal Source #
Generalization of svRol, where the rotation amount is symbolic.
If the first argument is not bounded, then the this is the same as shift.
svRotateRight :: SVal -> SVal -> SVal Source #
Generalization of svRor, where the rotation amount is symbolic.
If the first argument is not bounded, then the this is the same as shift.
svBarrelRotateLeft :: SVal -> SVal -> SVal Source #
A variant of svRotateLeft that uses a barrel-rotate design, which can lead to
better verification code. Only works when both arguments are finite and the second
argument is unsigned.
svBarrelRotateRight :: SVal -> SVal -> SVal Source #
A variant of svRotateLeft that uses a barrel-rotate design, which can lead to
better verification code. Only works when both arguments are finite and the second
argument is unsigned.
svWordFromBE :: [SVal] -> SVal Source #
Un-bit-blast from little-endian representation to a word of the right size. The input is assumed to be unsigned.
svWordFromLE :: [SVal] -> SVal Source #
Un-bit-blast from big-endian representation to a word of the right size. The input is assumed to be unsigned.
Conditionals: Mergeable values
svLazyIte :: Kind -> SVal -> SVal -> SVal -> SVal Source #
Lazy If-then-else. This one will delay forcing the branches unless it's really necessary.
svSymbolicMerge :: Kind -> Bool -> SVal -> SVal -> SVal -> SVal Source #
Merge two symbolic values, at kind k, possibly force'ing the branches to make
sure they do not evaluate to the same result.
Uninterpreted sorts, constants, and functions
svUninterpreted :: Kind -> String -> Maybe [String] -> [SVal] -> SVal Source #
Uninterpreted constants and functions. An uninterpreted constant is a value that is indexed by its name. The only property the prover assumes about these values are that they are equivalent to themselves; i.e., (for functions) they return the same results when applied to same arguments. We support uninterpreted-functions as a general means of black-box'ing operations that are irrelevant for the purposes of the proof; i.e., when the proofs can be performed without any knowledge about the function itself.
Properties, proofs, and satisfiability
Proving properties
proveWith :: SMTConfig -> Symbolic SVal -> IO ThmResult Source #
Proves the predicate using the given SMT-solver
Checking satisfiability
satWith :: SMTConfig -> Symbolic SVal -> IO SatResult Source #
Find a satisfying assignment using the given SMT-solver
allSatWith :: SMTConfig -> Symbolic SVal -> IO AllSatResult Source #
Find all satisfying assignments using the given SMT-solver
Checking safety
safeWith :: SMTConfig -> Symbolic SVal -> IO [SafeResult] Source #
Check safety using the given SMT-solver
Proving properties using multiple solvers
proveWithAll :: [SMTConfig] -> Symbolic SVal -> IO [(Solver, NominalDiffTime, ThmResult)] Source #
Prove a property with multiple solvers, running them in separate threads. The results will be returned in the order produced.
proveWithAny :: [SMTConfig] -> Symbolic SVal -> IO (Solver, NominalDiffTime, ThmResult) Source #
Prove a property with multiple solvers, running them in separate threads. Only the result of the first one to finish will be returned, remaining threads will be killed.
satWithAll :: [SMTConfig] -> Symbolic SVal -> IO [(Solver, NominalDiffTime, SatResult)] Source #
Find a satisfying assignment to a property with multiple solvers, running them in separate threads. The results will be returned in the order produced.
satWithAny :: [SMTConfig] -> Symbolic SVal -> IO (Solver, NominalDiffTime, SatResult) Source #
Find a satisfying assignment to a property with multiple solvers, running them in separate threads. Only the result of the first one to finish will be returned, remaining threads will be killed.
Proving properties using multiple threads
proveConcurrentWithAll :: SMTConfig -> Symbolic SVal -> [Query SVal] -> IO [(Solver, NominalDiffTime, ThmResult)] Source #
proveConcurrentWithAny :: SMTConfig -> Symbolic SVal -> [Query SVal] -> IO (Solver, NominalDiffTime, ThmResult) Source #
satConcurrentWithAny :: SMTConfig -> [Query b] -> Symbolic SVal -> IO (Solver, NominalDiffTime, SatResult) Source #
satConcurrentWithAll :: SMTConfig -> [Query b] -> Symbolic SVal -> IO [(Solver, NominalDiffTime, SatResult)] Source #
Quick-check
Model extraction
Inspecting proof results
Instances
| Show ThmResult Source # | |
| NFData ThmResult Source # | |
Defined in Data.SBV.SMT.SMT | |
| Modelable ThmResult Source # |
|
Defined in Data.SBV.SMT.SMT Methods modelExists :: ThmResult -> Bool Source # getModelAssignment :: SatModel b => ThmResult -> Either String (Bool, b) Source # getModelDictionary :: ThmResult -> Map String CV Source # getModelValue :: SymVal b => String -> ThmResult -> Maybe b Source # getModelUninterpretedValue :: String -> ThmResult -> Maybe String Source # extractModel :: SatModel b => ThmResult -> Maybe b Source # getModelObjectives :: ThmResult -> Map String GeneralizedCV Source # getModelObjectiveValue :: String -> ThmResult -> Maybe GeneralizedCV Source # getModelUIFuns :: ThmResult -> Map String (SBVType, ([([CV], CV)], CV)) Source # getModelUIFunValue :: String -> ThmResult -> Maybe (SBVType, ([([CV], CV)], CV)) Source # | |
A sat call results in a SatResult
The reason for having a separate SatResult is to have a more meaningful Show instance.
Instances
| Show SatResult Source # | |
| NFData SatResult Source # | |
Defined in Data.SBV.SMT.SMT | |
| Modelable SatResult Source # |
|
Defined in Data.SBV.SMT.SMT Methods modelExists :: SatResult -> Bool Source # getModelAssignment :: SatModel b => SatResult -> Either String (Bool, b) Source # getModelDictionary :: SatResult -> Map String CV Source # getModelValue :: SymVal b => String -> SatResult -> Maybe b Source # getModelUninterpretedValue :: String -> SatResult -> Maybe String Source # extractModel :: SatModel b => SatResult -> Maybe b Source # getModelObjectives :: SatResult -> Map String GeneralizedCV Source # getModelObjectiveValue :: String -> SatResult -> Maybe GeneralizedCV Source # getModelUIFuns :: SatResult -> Map String (SBVType, ([([CV], CV)], CV)) Source # getModelUIFunValue :: String -> SatResult -> Maybe (SBVType, ([([CV], CV)], CV)) Source # | |
data AllSatResult Source #
An allSat call results in a AllSatResult
Constructors
| AllSatResult | |
Fields
| |
Instances
| Show AllSatResult Source # | |
Defined in Data.SBV.SMT.SMT Methods showsPrec :: Int -> AllSatResult -> ShowS # show :: AllSatResult -> String # showList :: [AllSatResult] -> ShowS # | |
newtype SafeResult Source #
A safe call results in a SafeResult
Constructors
| SafeResult (Maybe String, String, SMTResult) |
Instances
| Show SafeResult Source # | |
Defined in Data.SBV.SMT.SMT Methods showsPrec :: Int -> SafeResult -> ShowS # show :: SafeResult -> String # showList :: [SafeResult] -> ShowS # | |
data OptimizeResult Source #
An optimize call results in a OptimizeResult. In the ParetoResult case, the boolean is True
if we reached pareto-query limit and so there might be more unqueried results remaining. If False,
it means that we have all the pareto fronts returned. See the Pareto OptimizeStyle for details.
Constructors
| LexicographicResult SMTResult | |
| ParetoResult (Bool, [SMTResult]) | |
| IndependentResult [(String, SMTResult)] |
Instances
| Show OptimizeResult Source # | |
Defined in Data.SBV.SMT.SMT Methods showsPrec :: Int -> OptimizeResult -> ShowS # show :: OptimizeResult -> String # showList :: [OptimizeResult] -> ShowS # | |
The result of an SMT solver call. Each constructor is tagged with
the SMTConfig that created it so that further tools can inspect it
and build layers of results, if needed. For ordinary uses of the library,
this type should not be needed, instead use the accessor functions on
it. (Custom Show instances and model extractors.)
Constructors
| Unsatisfiable SMTConfig (Maybe [String]) | Unsatisfiable. If unsat-cores are enabled, they will be returned in the second parameter. |
| Satisfiable SMTConfig SMTModel | Satisfiable with model |
| DeltaSat SMTConfig (Maybe String) SMTModel | Delta satisfiable with queried string if available and model |
| SatExtField SMTConfig SMTModel | Prover returned a model, but in an extension field containing Infinite/epsilon |
| Unknown SMTConfig SMTReasonUnknown | Prover returned unknown, with the given reason |
| ProofError SMTConfig [String] (Maybe SMTResult) | Prover errored out, with possibly a bogus result |
Instances
| NFData SMTResult Source # | |
Defined in Data.SBV.Core.Symbolic | |
| Modelable SMTResult Source # |
|
Defined in Data.SBV.SMT.SMT Methods modelExists :: SMTResult -> Bool Source # getModelAssignment :: SatModel b => SMTResult -> Either String (Bool, b) Source # getModelDictionary :: SMTResult -> Map String CV Source # getModelValue :: SymVal b => String -> SMTResult -> Maybe b Source # getModelUninterpretedValue :: String -> SMTResult -> Maybe String Source # extractModel :: SatModel b => SMTResult -> Maybe b Source # getModelObjectives :: SMTResult -> Map String GeneralizedCV Source # getModelObjectiveValue :: String -> SMTResult -> Maybe GeneralizedCV Source # getModelUIFuns :: SMTResult -> Map String (SBVType, ([([CV], CV)], CV)) Source # getModelUIFunValue :: String -> SMTResult -> Maybe (SBVType, ([([CV], CV)], CV)) Source # | |
Programmable model extraction
genParse :: Integral a => Kind -> [CV] -> Maybe (a, [CV]) Source #
Parse a signed/sized value from a sequence of CVs
getModelAssignment :: SMTResult -> Either String (Bool, [CV]) Source #
Extract a model, the result is a tuple where the first argument (if True) indicates whether the model was "probable". (i.e., if the solver returned unknown.)
getModelDictionary :: SMTResult -> Map String CV Source #
Extract a model dictionary. Extract a dictionary mapping the variables to
their respective values as returned by the SMT solver. Also see getModelDictionaries.
SMT Interface: Configurations and solvers
Solver configuration. See also z3, yices, cvc4, boolector, mathSAT, etc.
which are instantiations of this type for those solvers, with reasonable defaults. In particular, custom configuration can be
created by varying those values. (Such as z3{verbose=True}.)
Most fields are self explanatory. The notion of precision for printing algebraic reals stems from the fact that such values does
not necessarily have finite decimal representations, and hence we have to stop printing at some depth. It is important to
emphasize that such values always have infinite precision internally. The issue is merely with how we print such an infinite
precision value on the screen. The field printRealPrec controls the printing precision, by specifying the number of digits after
the decimal point. The default value is 16, but it can be set to any positive integer.
When printing, SBV will add the suffix ... at the and of a real-value, if the given bound is not sufficient to represent the real-value
exactly. Otherwise, the number will be written out in standard decimal notation. Note that SBV will always print the whole value if it
is precise (i.e., if it fits in a finite number of digits), regardless of the precision limit. The limit only applies if the representation
of the real value is not finite, i.e., if it is not rational.
The printBase field can be used to print numbers in base 2, 10, or 16.
The crackNum field can be used to display numbers in detail, all its bits and how they are laid out in memory. Works with all bounded number types
(i.e., SWord and SInt), but also with floats. It is particularly useful with floating-point numbers, as it shows you how they are laid out in
memory following the IEEE754 rules.
Constructors
| SMTConfig | |
Fields
| |
data SMTLibVersion Source #
Representation of SMTLib Program versions. As of June 2015, we're dropping support for SMTLib1, and supporting SMTLib2 only. We keep this data-type around in case SMTLib3 comes along and we want to support 2 and 3 simultaneously.
Constructors
| SMTLib2 |
Instances
| Bounded SMTLibVersion Source # | |
Defined in Data.SBV.Core.Symbolic | |
| Enum SMTLibVersion Source # | |
Defined in Data.SBV.Core.Symbolic Methods succ :: SMTLibVersion -> SMTLibVersion # pred :: SMTLibVersion -> SMTLibVersion # toEnum :: Int -> SMTLibVersion # fromEnum :: SMTLibVersion -> Int # enumFrom :: SMTLibVersion -> [SMTLibVersion] # enumFromThen :: SMTLibVersion -> SMTLibVersion -> [SMTLibVersion] # enumFromTo :: SMTLibVersion -> SMTLibVersion -> [SMTLibVersion] # enumFromThenTo :: SMTLibVersion -> SMTLibVersion -> SMTLibVersion -> [SMTLibVersion] # | |
| Eq SMTLibVersion Source # | |
Defined in Data.SBV.Core.Symbolic Methods (==) :: SMTLibVersion -> SMTLibVersion -> Bool # (/=) :: SMTLibVersion -> SMTLibVersion -> Bool # | |
| Show SMTLibVersion Source # | |
Defined in Data.SBV.Core.Symbolic Methods showsPrec :: Int -> SMTLibVersion -> ShowS # show :: SMTLibVersion -> String # showList :: [SMTLibVersion] -> ShowS # | |
| NFData SMTLibVersion Source # | |
Defined in Data.SBV.Core.Symbolic Methods rnf :: SMTLibVersion -> () # | |
Solvers that SBV is aware of
An SMT solver
Constructors
| SMTSolver | |
Fields
| |
defaultSolverConfig :: Solver -> SMTConfig Source #
The default configs corresponding to supported SMT solvers
defaultSMTCfg :: SMTConfig Source #
The default solver used by SBV. This is currently set to z3.
sbvCheckSolverInstallation :: SMTConfig -> IO Bool Source #
Check whether the given solver is installed and is ready to go. This call does a simple call to the solver to ensure all is well.
getAvailableSolvers :: IO [SMTConfig] Source #
Return the known available solver configs, installed on your machine.
Symbolic computations
outputSVal :: MonadSymbolic m => SVal -> m () Source #
Generalization of outputSVal
Code generation from symbolic programs
data SBVCodeGen a Source #
The code-generation monad. Allows for precise layout of input values reference parameters (for returning composite values in languages such as C), and return values.
Instances
Setting code-generation options
cgPerformRTCs :: Bool -> SBVCodeGen () Source #
Sets RTC (run-time-checks) for index-out-of-bounds, shift-with-large value etc. on/off. Default: False.
cgSetDriverValues :: [Integer] -> SBVCodeGen () Source #
Sets driver program run time values, useful for generating programs with fixed drivers for testing. Default: None, i.e., use random values.
cgGenerateDriver :: Bool -> SBVCodeGen () Source #
Should we generate a driver program? Default: True. When a library is generated, it will have
a driver if any of the constituent functions has a driver. (See compileToCLib.)
cgGenerateMakefile :: Bool -> SBVCodeGen () Source #
Should we generate a Makefile? Default: True.
Designating inputs
svCgInput :: Kind -> String -> SBVCodeGen SVal Source #
Creates an atomic input in the generated code.
svCgInputArr :: Kind -> Int -> String -> SBVCodeGen [SVal] Source #
Creates an array input in the generated code.
Designating outputs
svCgOutput :: String -> SVal -> SBVCodeGen () Source #
Creates an atomic output in the generated code.
svCgOutputArr :: String -> [SVal] -> SBVCodeGen () Source #
Creates an array output in the generated code.
Designating return values
svCgReturn :: SVal -> SBVCodeGen () Source #
Creates a returned (unnamed) value in the generated code.
svCgReturnArr :: [SVal] -> SBVCodeGen () Source #
Creates a returned (unnamed) array value in the generated code.
Code generation with uninterpreted functions
cgAddPrototype :: [String] -> SBVCodeGen () Source #
Adds the given lines to the header file generated, useful for generating programs with uninterpreted functions.
cgAddDecl :: [String] -> SBVCodeGen () Source #
Adds the given lines to the program file generated, useful for generating programs with uninterpreted functions.
cgAddLDFlags :: [String] -> SBVCodeGen () Source #
Adds the given words to the compiler options in the generated Makefile, useful for linking extra stuff in.
cgIgnoreSAssert :: Bool -> SBVCodeGen () Source #
Ignore assertions (those generated by sAssert calls) in the generated C code
Code generation with SInteger and SReal types
cgIntegerSize :: Int -> SBVCodeGen () Source #
Sets number of bits to be used for representing the SInteger type in the generated C code.
The argument must be one of 8, 16, 32, or 64. Note that this is essentially unsafe as
the semantics of unbounded Haskell integers becomes reduced to the corresponding bit size, as
typical in most C implementations.
cgSRealType :: CgSRealType -> SBVCodeGen () Source #
Sets the C type to be used for representing the SReal type in the generated C code.
The setting can be one of C's "float", "double", or "long double", types, depending
on the precision needed. Note that this is essentially unsafe as the semantics of
infinite precision SReal values becomes reduced to the corresponding floating point type in
C, and hence it is subject to rounding errors.
data CgSRealType Source #
Possible mappings for the SReal type when translated to C. Used in conjunction
with the function cgSRealType. Note that the particular characteristics of the
mapped types depend on the platform and the compiler used for compiling the generated
C program. See http://en.wikipedia.org/wiki/C_data_types for details.
Constructors
| CgFloat | float |
| CgDouble | double |
| CgLongDouble | long double |
Instances
| Eq CgSRealType Source # | |
Defined in Data.SBV.Compilers.CodeGen | |
| Show CgSRealType Source # | |
Defined in Data.SBV.Compilers.CodeGen Methods showsPrec :: Int -> CgSRealType -> ShowS # show :: CgSRealType -> String # showList :: [CgSRealType] -> ShowS # | |
Compilation to C
compileToC :: Maybe FilePath -> String -> SBVCodeGen a -> IO a Source #
Given a symbolic computation, render it as an equivalent collection of files that make up a C program:
- The first argument is the directory name under which the files will be saved. To save
files in the current directory pass
Just"."Nothingfor printing to stdout. - The second argument is the name of the C function to generate.
- The final argument is the function to be compiled.
Compilation will also generate a Makefile, a header file, and a driver (test) program, etc. As a
result, we return whatever the code-gen function returns. Most uses should simply have () as
the return type here, but the value can be useful if you want to chain the result of
one compilation act to the next.
compileToCLib :: Maybe FilePath -> String -> [(String, SBVCodeGen a)] -> IO [a] Source #
Create code to generate a library archive (.a) from given symbolic functions. Useful when generating code from multiple functions that work together as a library.
- The first argument is the directory name under which the files will be saved. To save
files in the current directory pass
Just"."Nothingfor printing to stdout. - The second argument is the name of the archive to generate.
- The third argument is the list of functions to include, in the form of function-name/code pairs, similar
to the second and third arguments of
compileToC, except in a list.
Compilation to SMTLib
generateSMTBenchmark :: Bool -> Symbolic SVal -> IO String Source #
Create SMT-Lib benchmarks. The first argument is the basename of the file, we will automatically
add ".smt2" per SMT-Lib2 convention. The Bool argument controls whether this is a SAT instance, i.e.,
translate the query directly, or a PROVE instance, i.e., translate the negated query.