sbv-7.3: SMT Based Verification: Symbolic Haskell theorem prover using SMT solving.

Data.SBV.Examples.Uninterpreted.Sort

Description

Demonstrates uninterpreted sorts, together with axioms.

Synopsis

# Documentation

newtype Q Source #

A new data-type that we expect to use in an uninterpreted fashion in the backend SMT solver. Note the custom deriving clause, which takes care of most of the boilerplate. The () field is needed so SBV will not translate it to an enumerated data-type

Constructors

 Q ()

Instances

 Source # Methods(==) :: Q -> Q -> Bool #(/=) :: Q -> Q -> Bool # Source # Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Q -> c Q #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Q #toConstr :: Q -> Constr #dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Q) #dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Q) #gmapT :: (forall b. Data b => b -> b) -> Q -> Q #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Q -> r #gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Q -> r #gmapQ :: (forall d. Data d => d -> u) -> Q -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Q -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Q -> m Q #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Q -> m Q #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Q -> m Q # Source # Methodscompare :: Q -> Q -> Ordering #(<) :: Q -> Q -> Bool #(<=) :: Q -> Q -> Bool #(>) :: Q -> Q -> Bool #(>=) :: Q -> Q -> Bool #max :: Q -> Q -> Q #min :: Q -> Q -> Q # Source # MethodsreadList :: ReadS [Q] # Source # MethodsshowsPrec :: Int -> Q -> ShowS #show :: Q -> String #showList :: [Q] -> ShowS # Source # Methods Source # Methodssymbolics :: [String] -> Symbolic [SBV Q] Source #fromCW :: CW -> Q Source #isConcretely :: SBV Q -> (Q -> Bool) -> Bool Source #

f :: SBV Q -> SBV Q Source #

Declare an uninterpreted function that works over Q's

A satisfiable example, stating that there is an element of the domain Q such that f returns a different element. Note that this is valid only when the domain Q has at least two elements. We have:

>>> t1
Satisfiable. Model:
x = Q!val!0 :: Q


This is a variant on the first example, except we also add an axiom for the sort, stating that the domain Q has only one element. In this case the problem naturally becomes unsat. We have:

>>> t2
Unsatisfiable