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

Copyright(c) Levent Erkok
LicenseBSD3
Maintainererkokl@gmail.com
Stabilityexperimental
Safe HaskellNone
LanguageHaskell2010

Documentation.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
Eq Q Source # 
Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

Methods

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

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

Data Q Source # 
Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

Methods

gfoldl :: (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 #

dataTypeOf :: Q -> DataType #

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 #

Ord Q Source # 
Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

Methods

compare :: Q -> Q -> Ordering #

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

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

(>) :: Q -> Q -> Bool #

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

max :: Q -> Q -> Q #

min :: Q -> Q -> Q #

Read Q Source # 
Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

Show Q Source # 
Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

Methods

showsPrec :: Int -> Q -> ShowS #

show :: Q -> String #

showList :: [Q] -> ShowS #

HasKind Q Source # 
Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

SymVal Q Source # 
Instance details

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

f :: SBV Q -> SBV Q Source #

Declare an uninterpreted function that works over Q's

t1 :: IO SatResult Source #

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

  f :: Q -> Q
  f _ = Q!val!1

t2 :: IO SatResult Source #

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