sbv-9.1: SMT Based Verification: Symbolic Haskell theorem prover using SMT solving.
Copyright(c) Levent Erkok
LicenseBSD3
Maintainererkokl@gmail.com
Stabilityexperimental
Safe HaskellSafe-Inferred
LanguageHaskell2010

Documentation.SBV.Examples.Misc.Enumerate

Description

Demonstrates how enumerations can be translated to their SMT-Lib counterparts, without losing any information content. Also see Documentation.SBV.Examples.Puzzles.U2Bridge for a more detailed example involving enumerations.

Synopsis

Documentation

data E Source #

A simple enumerated type, that we'd like to translate to SMT-Lib intact; i.e., this type will not be uninterpreted but rather preserved and will be just like any other symbolic type SBV provides.

Also note that we need to have the following LANGUAGE options defined: TemplateHaskell, StandaloneDeriving, DeriveDataTypeable, DeriveAnyClass for this to work.

Constructors

A 
B 
C 

Instances

Instances details
Data E Source # 
Instance details

Defined in Documentation.SBV.Examples.Misc.Enumerate

Methods

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

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

toConstr :: E -> Constr #

dataTypeOf :: E -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c E) #

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

gmapT :: (forall b. Data b => b -> b) -> E -> E #

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

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

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

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

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

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

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

Read E Source # 
Instance details

Defined in Documentation.SBV.Examples.Misc.Enumerate

Show E Source # 
Instance details

Defined in Documentation.SBV.Examples.Misc.Enumerate

Methods

showsPrec :: Int -> E -> ShowS #

show :: E -> String #

showList :: [E] -> ShowS #

Eq E Source # 
Instance details

Defined in Documentation.SBV.Examples.Misc.Enumerate

Methods

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

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

Ord E Source # 
Instance details

Defined in Documentation.SBV.Examples.Misc.Enumerate

Methods

compare :: E -> E -> Ordering #

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

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

(>) :: E -> E -> Bool #

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

max :: E -> E -> E #

min :: E -> E -> E #

SymVal E Source # 
Instance details

Defined in Documentation.SBV.Examples.Misc.Enumerate

HasKind E Source # 
Instance details

Defined in Documentation.SBV.Examples.Misc.Enumerate

SatModel E Source # 
Instance details

Defined in Documentation.SBV.Examples.Misc.Enumerate

Methods

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

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

type SE = SBV E Source #

Symbolic version of the type E.

sC :: SBV E Source #

Symbolic version of the constructor C.

sB :: SBV E Source #

Symbolic version of the constructor B.

sA :: SBV E Source #

Symbolic version of the constructor A.

elts :: IO AllSatResult Source #

Have the SMT solver enumerate the elements of the domain. We have:

>>> elts
Solution #1:
  s0 = C :: E
Solution #2:
  s0 = B :: E
Solution #3:
  s0 = A :: E
Found 3 different solutions.

four :: IO SatResult Source #

Shows that if we require 4 distinct elements of the type E, we shall fail; as the domain only has three elements. We have:

>>> four
Unsatisfiable

maxE :: IO SatResult Source #

Enumerations are automatically ordered, so we can ask for the maximum element. Note the use of quantification. We have:

>>> maxE
Satisfiable. Model:
  maxE = C :: E

minE :: IO SatResult Source #

Similarly, we get the minimum element. We have:

>>> minE
Satisfiable. Model:
  minE = A :: E