sbv-8.4: SMT Based Verification: Symbolic Haskell theorem prover using SMT solving.

Copyright(c) Brian Huffman
LicenseBSD3
Maintainererkokl@gmail.com
Stabilityexperimental
Safe HaskellNone
LanguageHaskell2010

Data.SBV.Dynamic

Contents

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

Programming with symbolic values

Symbolic types

Abstract symbolic value type

data SVal Source #

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
Eq SVal Source #

This instance is only defined so that we can define an instance for Bits. == and /= simply throw an error.

Instance details

Defined in Data.SBV.Core.Symbolic

Methods

(==) :: SVal -> SVal -> Bool #

(/=) :: SVal -> SVal -> Bool #

Show SVal Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> SVal -> ShowS #

show :: SVal -> String #

showList :: [SVal] -> ShowS #

NFData SVal Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: SVal -> () #

HasKind SVal Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

ArithOverflow SVal Source # 
Instance details

Defined in Data.SBV.Tools.Overflow

Testable (Symbolic SVal) Source # 
Instance details

Defined in Data.SBV.Core.Model

Methods

property :: Symbolic SVal -> Property #

propertyForAllShrinkShow :: Gen a -> (a -> [a]) -> (a -> [String]) -> (a -> Symbolic SVal) -> Property #

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

Instances
HasKind Bool Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Char Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Double Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Float Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Int8 Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Int16 Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Int32 Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Int64 Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Integer Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Word8 Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Word16 Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Word32 Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Word64 Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind () Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind AlgReal Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind Kind Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind ExtCV Source #

Kind instance for Extended CV

Instance details

Defined in Data.SBV.Core.Concrete

HasKind GeneralizedCV Source #

Kind instance for generalized CV

Instance details

Defined in Data.SBV.Core.Concrete

HasKind CV Source #

Kind instance for CV

Instance details

Defined in Data.SBV.Core.Concrete

HasKind RoundingMode Source #

RoundingMode kind

Instance details

Defined in Data.SBV.Core.Symbolic

HasKind SVal Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

HasKind SV Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

HasKind State Source # 
Instance details

Defined in Documentation.SBV.Examples.Lists.BoundedMutex

HasKind E Source # 
Instance details

Defined in Documentation.SBV.Examples.Misc.Enumerate

HasKind Day Source # 
Instance details

Defined in Documentation.SBV.Examples.Optimization.Enumerate

HasKind Color Source # 
Instance details

Defined in Documentation.SBV.Examples.Puzzles.Fish

HasKind Nationality Source # 
Instance details

Defined in Documentation.SBV.Examples.Puzzles.Fish

HasKind Beverage Source # 
Instance details

Defined in Documentation.SBV.Examples.Puzzles.Fish

HasKind Pet Source # 
Instance details

Defined in Documentation.SBV.Examples.Puzzles.Fish

HasKind Sport Source # 
Instance details

Defined in Documentation.SBV.Examples.Puzzles.Fish

HasKind Color Source # 
Instance details

Defined in Documentation.SBV.Examples.Puzzles.Garden

HasKind Color Source # 
Instance details

Defined in Documentation.SBV.Examples.Puzzles.HexPuzzle

HasKind U2Member Source # 
Instance details

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

HasKind Location Source # 
Instance details

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

HasKind Day Source # 
Instance details

Defined in Documentation.SBV.Examples.Queries.Enums

HasKind BinOp Source # 
Instance details

Defined in Documentation.SBV.Examples.Queries.FourFours

HasKind UnOp Source # 
Instance details

Defined in Documentation.SBV.Examples.Queries.FourFours

HasKind B Source # 
Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.Deduce

HasKind Q Source # 
Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

HasKind L Source #

Similarly, HasKinds default implementation is sufficient.

Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.UISortAllSat

(Typeable a, HasKind a) => HasKind [a] Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

kindOf :: [a] -> Kind Source #

hasSign :: [a] -> Bool Source #

intSizeOf :: [a] -> Int Source #

isBoolean :: [a] -> Bool Source #

isBounded :: [a] -> Bool Source #

isReal :: [a] -> Bool Source #

isFloat :: [a] -> Bool Source #

isDouble :: [a] -> Bool Source #

isUnbounded :: [a] -> Bool Source #

isUninterpreted :: [a] -> Bool Source #

isChar :: [a] -> Bool Source #

isString :: [a] -> Bool Source #

isList :: [a] -> Bool Source #

isSet :: [a] -> Bool Source #

isTuple :: [a] -> Bool Source #

isMaybe :: [a] -> Bool Source #

isEither :: [a] -> Bool Source #

showType :: [a] -> String Source #

HasKind a => HasKind (Maybe a) Source # 
Instance details

Defined in Data.SBV.Core.Kind

HasKind a => HasKind (RCSet a) Source # 
Instance details

Defined in Data.SBV.Core.Concrete

HasKind a => HasKind (SBV a) Source # 
Instance details

Defined in Data.SBV.Core.Data

(KnownNat n, IsNonZero n) => HasKind (IntN n) Source #

IntN has a kind

Instance details

Defined in Data.SBV.Core.Sized

(KnownNat n, IsNonZero n) => HasKind (WordN n) Source #

WordN has a kind

Instance details

Defined in Data.SBV.Core.Sized

(HasKind a, HasKind b) => HasKind (Either a b) Source # 
Instance details

Defined in Data.SBV.Core.Kind

(HasKind a, HasKind b) => HasKind (a, b) Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b) -> Kind Source #

hasSign :: (a, b) -> Bool Source #

intSizeOf :: (a, b) -> Int Source #

isBoolean :: (a, b) -> Bool Source #

isBounded :: (a, b) -> Bool Source #

isReal :: (a, b) -> Bool Source #

isFloat :: (a, b) -> Bool Source #

isDouble :: (a, b) -> Bool Source #

isUnbounded :: (a, b) -> Bool Source #

isUninterpreted :: (a, b) -> Bool Source #

isChar :: (a, b) -> Bool Source #

isString :: (a, b) -> Bool Source #

isList :: (a, b) -> Bool Source #

isSet :: (a, b) -> Bool Source #

isTuple :: (a, b) -> Bool Source #

isMaybe :: (a, b) -> Bool Source #

isEither :: (a, b) -> Bool Source #

showType :: (a, b) -> String Source #

HasKind a => HasKind (Proxy a) Source #

This instance allows us to use the `kindOf (Proxy @a)` idiom instead of the `kindOf (undefined :: a)`, which is safer and looks more idiomatic.

Instance details

Defined in Data.SBV.Core.Kind

(HasKind a, HasKind b, HasKind c) => HasKind (a, b, c) Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c) -> Kind Source #

hasSign :: (a, b, c) -> Bool Source #

intSizeOf :: (a, b, c) -> Int Source #

isBoolean :: (a, b, c) -> Bool Source #

isBounded :: (a, b, c) -> Bool Source #

isReal :: (a, b, c) -> Bool Source #

isFloat :: (a, b, c) -> Bool Source #

isDouble :: (a, b, c) -> Bool Source #

isUnbounded :: (a, b, c) -> Bool Source #

isUninterpreted :: (a, b, c) -> Bool Source #

isChar :: (a, b, c) -> Bool Source #

isString :: (a, b, c) -> Bool Source #

isList :: (a, b, c) -> Bool Source #

isSet :: (a, b, c) -> Bool Source #

isTuple :: (a, b, c) -> Bool Source #

isMaybe :: (a, b, c) -> Bool Source #

isEither :: (a, b, c) -> Bool Source #

showType :: (a, b, c) -> String Source #

(HasKind a, HasKind b, HasKind c, HasKind d) => HasKind (a, b, c, d) Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d) -> Kind Source #

hasSign :: (a, b, c, d) -> Bool Source #

intSizeOf :: (a, b, c, d) -> Int Source #

isBoolean :: (a, b, c, d) -> Bool Source #

isBounded :: (a, b, c, d) -> Bool Source #

isReal :: (a, b, c, d) -> Bool Source #

isFloat :: (a, b, c, d) -> Bool Source #

isDouble :: (a, b, c, d) -> Bool Source #

isUnbounded :: (a, b, c, d) -> Bool Source #

isUninterpreted :: (a, b, c, d) -> Bool Source #

isChar :: (a, b, c, d) -> Bool Source #

isString :: (a, b, c, d) -> Bool Source #

isList :: (a, b, c, d) -> Bool Source #

isSet :: (a, b, c, d) -> Bool Source #

isTuple :: (a, b, c, d) -> Bool Source #

isMaybe :: (a, b, c, d) -> Bool Source #

isEither :: (a, b, c, d) -> Bool Source #

showType :: (a, b, c, d) -> String Source #

(HasKind a, HasKind b, HasKind c, HasKind d, HasKind e) => HasKind (a, b, c, d, e) Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d, e) -> Kind Source #

hasSign :: (a, b, c, d, e) -> Bool Source #

intSizeOf :: (a, b, c, d, e) -> Int Source #

isBoolean :: (a, b, c, d, e) -> Bool Source #

isBounded :: (a, b, c, d, e) -> Bool Source #

isReal :: (a, b, c, d, e) -> Bool Source #

isFloat :: (a, b, c, d, e) -> Bool Source #

isDouble :: (a, b, c, d, e) -> Bool Source #

isUnbounded :: (a, b, c, d, e) -> Bool Source #

isUninterpreted :: (a, b, c, d, e) -> Bool Source #

isChar :: (a, b, c, d, e) -> Bool Source #

isString :: (a, b, c, d, e) -> Bool Source #

isList :: (a, b, c, d, e) -> Bool Source #

isSet :: (a, b, c, d, e) -> Bool Source #

isTuple :: (a, b, c, d, e) -> Bool Source #

isMaybe :: (a, b, c, d, e) -> Bool Source #

isEither :: (a, b, c, d, e) -> Bool Source #

showType :: (a, b, c, d, e) -> String Source #

(HasKind a, HasKind b, HasKind c, HasKind d, HasKind e, HasKind f) => HasKind (a, b, c, d, e, f) Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d, e, f) -> Kind Source #

hasSign :: (a, b, c, d, e, f) -> Bool Source #

intSizeOf :: (a, b, c, d, e, f) -> Int Source #

isBoolean :: (a, b, c, d, e, f) -> Bool Source #

isBounded :: (a, b, c, d, e, f) -> Bool Source #

isReal :: (a, b, c, d, e, f) -> Bool Source #

isFloat :: (a, b, c, d, e, f) -> Bool Source #

isDouble :: (a, b, c, d, e, f) -> Bool Source #

isUnbounded :: (a, b, c, d, e, f) -> Bool Source #

isUninterpreted :: (a, b, c, d, e, f) -> Bool Source #

isChar :: (a, b, c, d, e, f) -> Bool Source #

isString :: (a, b, c, d, e, f) -> Bool Source #

isList :: (a, b, c, d, e, f) -> Bool Source #

isSet :: (a, b, c, d, e, f) -> Bool Source #

isTuple :: (a, b, c, d, e, f) -> Bool Source #

isMaybe :: (a, b, c, d, e, f) -> Bool Source #

isEither :: (a, b, c, d, e, f) -> Bool Source #

showType :: (a, b, c, d, e, f) -> String Source #

(HasKind a, HasKind b, HasKind c, HasKind d, HasKind e, HasKind f, HasKind g) => HasKind (a, b, c, d, e, f, g) Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d, e, f, g) -> Kind Source #

hasSign :: (a, b, c, d, e, f, g) -> Bool Source #

intSizeOf :: (a, b, c, d, e, f, g) -> Int Source #

isBoolean :: (a, b, c, d, e, f, g) -> Bool Source #

isBounded :: (a, b, c, d, e, f, g) -> Bool Source #

isReal :: (a, b, c, d, e, f, g) -> Bool Source #

isFloat :: (a, b, c, d, e, f, g) -> Bool Source #

isDouble :: (a, b, c, d, e, f, g) -> Bool Source #

isUnbounded :: (a, b, c, d, e, f, g) -> Bool Source #

isUninterpreted :: (a, b, c, d, e, f, g) -> Bool Source #

isChar :: (a, b, c, d, e, f, g) -> Bool Source #

isString :: (a, b, c, d, e, f, g) -> Bool Source #

isList :: (a, b, c, d, e, f, g) -> Bool Source #

isSet :: (a, b, c, d, e, f, g) -> Bool Source #

isTuple :: (a, b, c, d, e, f, g) -> Bool Source #

isMaybe :: (a, b, c, d, e, f, g) -> Bool Source #

isEither :: (a, b, c, d, e, f, g) -> Bool Source #

showType :: (a, b, c, d, e, f, g) -> String Source #

(HasKind a, HasKind b, HasKind c, HasKind d, HasKind e, HasKind f, HasKind g, HasKind h) => HasKind (a, b, c, d, e, f, g, h) Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d, e, f, g, h) -> Kind Source #

hasSign :: (a, b, c, d, e, f, g, h) -> Bool Source #

intSizeOf :: (a, b, c, d, e, f, g, h) -> Int Source #

isBoolean :: (a, b, c, d, e, f, g, h) -> Bool Source #

isBounded :: (a, b, c, d, e, f, g, h) -> Bool Source #

isReal :: (a, b, c, d, e, f, g, h) -> Bool Source #

isFloat :: (a, b, c, d, e, f, g, h) -> Bool Source #

isDouble :: (a, b, c, d, e, f, g, h) -> Bool Source #

isUnbounded :: (a, b, c, d, e, f, g, h) -> Bool Source #

isUninterpreted :: (a, b, c, d, e, f, g, h) -> Bool Source #

isChar :: (a, b, c, d, e, f, g, h) -> Bool Source #

isString :: (a, b, c, d, e, f, g, h) -> Bool Source #

isList :: (a, b, c, d, e, f, g, h) -> Bool Source #

isSet :: (a, b, c, d, e, f, g, h) -> Bool Source #

isTuple :: (a, b, c, d, e, f, g, h) -> Bool Source #

isMaybe :: (a, b, c, d, e, f, g, h) -> Bool Source #

isEither :: (a, b, c, d, e, f, g, h) -> Bool Source #

showType :: (a, b, c, d, e, f, g, h) -> String Source #

data Kind Source #

Kind of symbolic value

Instances
Eq Kind Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

(==) :: Kind -> Kind -> Bool #

(/=) :: Kind -> Kind -> Bool #

Ord Kind Source # 
Instance details

Defined in Data.SBV.Core.Kind

Methods

compare :: Kind -> Kind -> Ordering #

(<) :: Kind -> Kind -> Bool #

(<=) :: Kind -> Kind -> Bool #

(>) :: Kind -> Kind -> Bool #

(>=) :: Kind -> Kind -> Bool #

max :: Kind -> Kind -> Kind #

min :: Kind -> Kind -> Kind #

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 KUninterpreted, we make sure we don't use any of the reserved names; see constructUKind for details.

Instance details

Defined in Data.SBV.Core.Kind

Methods

showsPrec :: Int -> Kind -> ShowS #

show :: Kind -> String #

showList :: [Kind] -> ShowS #

NFData Kind Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: Kind -> () #

HasKind Kind Source # 
Instance details

Defined in Data.SBV.Core.Kind

data CV Source #

CV represents a concrete word of a fixed size: For signed words, the most significant digit is considered to be the sign.

Constructors

CV 

Fields

Instances
Eq CV Source # 
Instance details

Defined in Data.SBV.Core.Concrete

Methods

(==) :: CV -> CV -> Bool #

(/=) :: CV -> CV -> Bool #

Ord CV Source # 
Instance details

Defined in Data.SBV.Core.Concrete

Methods

compare :: CV -> CV -> Ordering #

(<) :: CV -> CV -> Bool #

(<=) :: CV -> CV -> Bool #

(>) :: CV -> CV -> Bool #

(>=) :: CV -> CV -> Bool #

max :: CV -> CV -> CV #

min :: CV -> CV -> CV #

Show CV Source #

Show instance for CV.

Instance details

Defined in Data.SBV.Core.Concrete

Methods

showsPrec :: Int -> CV -> ShowS #

show :: CV -> String #

showList :: [CV] -> ShowS #

NFData CV Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: CV -> () #

HasKind CV Source #

Kind instance for CV

Instance details

Defined in Data.SBV.Core.Concrete

PrettyNum CV Source # 
Instance details

Defined in Data.SBV.Utils.PrettyNum

SatModel CV Source #

CV as extracted from a model; trivial definition

Instance details

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (CV, [CV]) Source #

cvtModel :: (CV -> Maybe b) -> Maybe (CV, [CV]) -> Maybe (b, [CV]) Source #

SDivisible CV Source # 
Instance details

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: CV -> CV -> (CV, CV) Source #

sDivMod :: CV -> CV -> (CV, CV) Source #

sQuot :: CV -> CV -> CV Source #

sRem :: CV -> CV -> CV Source #

sDiv :: CV -> CV -> CV Source #

sMod :: CV -> CV -> CV Source #

data CVal Source #

A constant value

Constructors

CAlgReal !AlgReal

Algebraic real

CInteger !Integer

Bit-vector/unbounded integer

CFloat !Float

Float

CDouble !Double

Double

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:

Instance details

Defined in Data.SBV.Core.Concrete

Methods

(==) :: CVal -> CVal -> Bool #

(/=) :: CVal -> CVal -> Bool #

Ord CVal Source #

Ord instance for VWVal. Same comments as the Eq instance why this cannot be derived.

Instance details

Defined in Data.SBV.Core.Concrete

Methods

compare :: CVal -> CVal -> Ordering #

(<) :: CVal -> CVal -> Bool #

(<=) :: CVal -> CVal -> Bool #

(>) :: CVal -> CVal -> Bool #

(>=) :: CVal -> CVal -> Bool #

max :: CVal -> CVal -> CVal #

min :: CVal -> CVal -> CVal #

cvToBool :: CV -> Bool Source #

Convert a CV to a Haskell boolean (NB. Assumes input is well-kinded)

SMT Arrays of symbolic values

data SArr Source #

Arrays in terms of SMT-Lib arrays

readSArr :: SArr -> SVal -> SVal Source #

Read the array element at a

writeSArr :: SArr -> SVal -> SVal -> SArr Source #

Update the element at a to be b

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

eqSArr :: SArr -> SArr -> SVal Source #

Compare two arrays for equality

Functional arrays of symbolic values

data SFunArr Source #

Arrays managed internally

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.

writeSFunArr :: SFunArr -> SVal -> SVal -> SFunArr Source #

Update the element at address to be b

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

type Symbolic = SymbolicT IO Source #

Symbolic is specialization of SymbolicT to the IO monad. Unless you are using transformers explicitly, this is the type you should prefer.

data Quantifier Source #

Quantifiers: forall or exists. Note that we allow arbitrary nestings.

Constructors

ALL 
EX 
Instances
Eq Quantifier Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

Show Quantifier Source #

Show instance for Quantifier

Instance details

Defined in Data.SBV.Core.Symbolic

NFData Quantifier Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: Quantifier -> () #

svMkSymVar :: Maybe Quantifier -> 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.

sWordN :: MonadSymbolic m => Int -> String -> m SVal Source #

Generalization of sWordN

sWordN_ :: MonadSymbolic m => Int -> m SVal Source #

Generalization of sWordN_

sIntN :: MonadSymbolic m => Int -> String -> m SVal Source #

Generalization of sIntN

sIntN_ :: MonadSymbolic m => Int -> m SVal Source #

Generalization of sIntN_

Operations on symbolic values

Boolean literals

svTrue :: SVal Source #

Boolean True.

svFalse :: SVal Source #

Boolean False.

svBool :: Bool -> SVal Source #

Convert from a Boolean.

svAsBool :: SVal -> Maybe Bool Source #

Extract a bool, by properly interpreting the integer stored.

Integer literals

svInteger :: Kind -> Integer -> SVal Source #

Convert from an Integer.

svAsInteger :: SVal -> Maybe Integer Source #

Extract an integer from a concrete value.

Float literals

svFloat :: Float -> SVal Source #

Convert from a Float

svDouble :: Double -> SVal Source #

Convert from a Float

Algebraic reals (only from rationals)

svReal :: Rational -> SVal Source #

Convert from a Rational

svNumerator :: SVal -> Maybe Integer Source #

Grab the numerator of an SReal, if available

svDenominator :: SVal -> Maybe Integer Source #

Grab the denominator of an SReal, if available

Symbolic equality

svEqual :: SVal -> SVal -> SVal Source #

Equality.

svNotEqual :: SVal -> SVal -> SVal Source #

Inequality.

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

svLessThan :: SVal -> SVal -> SVal Source #

Less than.

svGreaterThan :: SVal -> SVal -> SVal Source #

Greater than.

svLessEq :: SVal -> SVal -> SVal Source #

Less than or equal to.

svGreaterEq :: SVal -> SVal -> SVal Source #

Greater than or equal to.

svStructuralLessThan :: SVal -> SVal -> SVal Source #

Given a composite structure, figure out how to compare for less than

Arithmetic operations

svPlus :: SVal -> SVal -> SVal Source #

Addition.

svTimes :: SVal -> SVal -> SVal Source #

Multiplication.

svMinus :: SVal -> SVal -> SVal Source #

Subtraction.

svUNeg :: SVal -> SVal Source #

Unary minus.

svAbs :: SVal -> SVal Source #

Absolute value.

svDivide :: SVal -> SVal -> SVal Source #

Division.

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.

svQuotRem :: SVal -> SVal -> (SVal, SVal) Source #

Combination of quot and rem

svExp :: SVal -> SVal -> SVal Source #

Exponentiation.

svAddConstant :: Integral a => SVal -> a -> SVal Source #

Add a constant value:

svIncrement :: SVal -> SVal Source #

Increment:

svDecrement :: SVal -> SVal Source #

Decrement:

Logical operations

svAnd :: SVal -> SVal -> SVal Source #

Bitwise and.

svOr :: SVal -> SVal -> SVal Source #

Bitwise or.

svXOr :: SVal -> SVal -> SVal Source #

Bitwise xor.

svNot :: SVal -> SVal Source #

Bitwise complement.

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

svExtract :: Int -> Int -> SVal -> SVal Source #

Extract bit-sequences.

svJoin :: SVal -> SVal -> SVal Source #

Join two words, by concataneting

Sign-casting

svSign :: SVal -> SVal Source #

Convert a symbolic bitvector from unsigned to signed.

svUnsign :: SVal -> SVal Source #

Convert a symbolic bitvector from signed to unsigned.

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.

svSetBit :: SVal -> Int -> SVal Source #

Set a given bit at index

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.

svBlastLE :: SVal -> [SVal] Source #

Bit-blast: Little-endian. Assumes the input is a bit-vector.

svBlastBE :: SVal -> [SVal] Source #

Bit-blast: Big-endian. Assumes the input is a bit-vector.

Conditionals: Mergeable values

svIte :: SVal -> SVal -> SVal -> SVal Source #

If-then-else. This one will force branches.

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.

Quick-check

svQuickCheck :: Symbolic SVal -> IO Bool Source #

Dynamic variant of quick-check

Model extraction

Inspecting proof results

newtype AllSatResult Source #

An allSat call results in a AllSatResult. The first boolean says whether we hit the max-model limit as we searched. The second boolean says whether there were prefix-existentials. The third boolean says whether we stopped because the solver returned Unknown.

Constructors

AllSatResult (Bool, Bool, Bool, [SMTResult]) 
Instances
Show AllSatResult Source # 
Instance details

Defined in Data.SBV.SMT.SMT

newtype SafeResult Source #

A safe call results in a SafeResult

Instances
Show SafeResult Source # 
Instance details

Defined in Data.SBV.SMT.SMT

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.

data SMTResult Source #

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

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

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

data SMTConfig Source #

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. If base 2 or 16 is used, then floating-point values will be printed in their internal memory-layout format as well, which can come in handy for bit-precise analysis.

Constructors

SMTConfig 

Fields

Instances
NFData SMTConfig Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: SMTConfig -> () #

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 

data Solver Source #

Solvers that SBV is aware of

Constructors

Z3 
Yices 
Boolector 
CVC4 
MathSAT 
ABC 
Instances
Bounded Solver Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

Enum Solver Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

Show Solver Source # 
Instance details

Defined in Data.SBV.Core.Symbolic

data SMTSolver Source #

An SMT solver

Constructors

SMTSolver 

Fields

boolector :: SMTConfig Source #

Default configuration for the Boolector SMT solver

cvc4 :: SMTConfig Source #

Default configuration for the CVC4 SMT Solver.

yices :: SMTConfig Source #

Default configuration for the Yices SMT Solver.

z3 :: SMTConfig Source #

Default configuration for the Z3 SMT solver

mathSAT :: SMTConfig Source #

Default configuration for the MathSAT SMT solver

abc :: SMTConfig Source #

Default configuration for the ABC synthesis and verification tool.

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.

sbvAvailableSolvers :: 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
Monad SBVCodeGen Source # 
Instance details

Defined in Data.SBV.Compilers.CodeGen

Methods

(>>=) :: SBVCodeGen a -> (a -> SBVCodeGen b) -> SBVCodeGen b #

(>>) :: SBVCodeGen a -> SBVCodeGen b -> SBVCodeGen b #

return :: a -> SBVCodeGen a #

fail :: String -> SBVCodeGen a #

Functor SBVCodeGen Source # 
Instance details

Defined in Data.SBV.Compilers.CodeGen

Methods

fmap :: (a -> b) -> SBVCodeGen a -> SBVCodeGen b #

(<$) :: a -> SBVCodeGen b -> SBVCodeGen a #

MonadFail SBVCodeGen Source # 
Instance details

Defined in Data.SBV.Compilers.CodeGen

Methods

fail :: String -> SBVCodeGen a #

Applicative SBVCodeGen Source # 
Instance details

Defined in Data.SBV.Compilers.CodeGen

Methods

pure :: a -> SBVCodeGen a #

(<*>) :: SBVCodeGen (a -> b) -> SBVCodeGen a -> SBVCodeGen b #

liftA2 :: (a -> b -> c) -> SBVCodeGen a -> SBVCodeGen b -> SBVCodeGen c #

(*>) :: SBVCodeGen a -> SBVCodeGen b -> SBVCodeGen b #

(<*) :: SBVCodeGen a -> SBVCodeGen b -> SBVCodeGen a #

MonadIO SBVCodeGen Source # 
Instance details

Defined in Data.SBV.Compilers.CodeGen

Methods

liftIO :: IO a -> SBVCodeGen a #

MonadSymbolic SBVCodeGen Source # 
Instance details

Defined in Data.SBV.Compilers.CodeGen

MonadState CgState SBVCodeGen Source # 
Instance details

Defined in Data.SBV.Compilers.CodeGen

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 contituent 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

Compilation to C

compileToC :: Maybe FilePath -> String -> SBVCodeGen () -> IO () 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 ".". Use Nothing for 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.

compileToCLib :: Maybe FilePath -> String -> [(String, SBVCodeGen ())] -> IO () 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 ".". Use Nothing for 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.