Data.SBV.Examples.Uninterpreted.UISortAllSat

Demonstrates uninterpreted sorts and how all-sat behaves for them. Thanks to Eric Seidel for the idea.

Documentation

data L

A "list-like" data type, but one we plan to uninterpret at the SMT level. The actual shape is really immaterial for us, but could be used as a proxy to generate test cases or explore data-space in some other part of a program. Note that we neither rely on the shape of this data, nor need the actual constructors.

Constructors

Nil

Cons Int L

Instances

Eq L

Methods

(==) :: L -> L -> Bool

(/=) :: L -> L -> Bool

Data L

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> L -> c L

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c L

toConstr :: L -> Constr

dataTypeOf :: L -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c L)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c L)

gmapT :: (forall b. Data b => b -> b) -> L -> L

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> L -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> L -> r

gmapQ :: (forall d. Data d => d -> u) -> L -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> L -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> L -> m L

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> L -> m L

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> L -> m L

Ord L

Methods

compare :: L -> L -> Ordering

(<) :: L -> L -> Bool

(<=) :: L -> L -> Bool

(>) :: L -> L -> Bool

(>=) :: L -> L -> Bool

max :: L -> L -> L

min :: L -> L -> L

Read L

Methods

readsPrec :: Int -> ReadS L

readList :: ReadS [L]

readPrec :: ReadPrec L

readListPrec :: ReadPrec [L]

Show L

Methods

showsPrec :: Int -> L -> ShowS

show :: L -> String

showList :: [L] -> ShowS

HasKind L

Similarly, HasKinds default implementation is sufficient.

Methods

kindOf :: L -> Kind

hasSign :: L -> Bool

intSizeOf :: L -> Int

isBoolean :: L -> Bool

isBounded :: L -> Bool

isReal :: L -> Bool

isFloat :: L -> Bool

isDouble :: L -> Bool

isInteger :: L -> Bool

isUninterpreted :: L -> Bool

showType :: L -> String

SymWord L

Declare instances to make L a usable uninterpreted sort. First we need the SymWord instance, with the default definition sufficing.

Methods

forall :: String -> Symbolic (SBV L)

forall_ :: Symbolic (SBV L)

mkForallVars :: Int -> Symbolic [SBV L]

exists :: String -> Symbolic (SBV L)

exists_ :: Symbolic (SBV L)

mkExistVars :: Int -> Symbolic [SBV L]

free :: String -> Symbolic (SBV L)

free_ :: Symbolic (SBV L)

mkFreeVars :: Int -> Symbolic [SBV L]

symbolic :: String -> Symbolic (SBV L)

symbolics :: [String] -> Symbolic [SBV L]

literal :: L -> SBV L

unliteral :: SBV L -> Maybe L

fromCW :: CW -> L

isConcrete :: SBV L -> Bool

isSymbolic :: SBV L -> Bool

isConcretely :: SBV L -> (L -> Bool) -> Bool

mkSymWord :: Maybe Quantifier -> Maybe String -> Symbolic (SBV L)

classify :: SBV L -> SInteger

An uninterpreted "classify" function. Really, we only care about the fact that such a function exists, not what it does.

genLs :: IO AllSatResult

Formulate a query that essentially asserts a cardinality constraint on the uninterpreted sort L. The goal is to say there are precisely 3 such things, as it might be the case. We manage this by declaring four elements, and asserting that for a free variable of this sort, the shape of the data matches one of these three instances. That is, we assert that all the instances of the data L can be classified into 3 equivalence classes. Then, allSat returns all the possible instances, which of course are all uninterpreted.

As expected, we have:

>>> genLs
Solution #1:
  l  = L!val!0 :: L
  l0 = L!val!0 :: L
  l1 = L!val!1 :: L
  l2 = L!val!2 :: L
Solution #2:
  l  = L!val!2 :: L
  l0 = L!val!0 :: L
  l1 = L!val!1 :: L
  l2 = L!val!2 :: L
Solution #3:
  l  = L!val!1 :: L
  l0 = L!val!0 :: L
  l1 = L!val!1 :: L
  l2 = L!val!2 :: L
Found 3 different solutions.