Documentation.SBV.Examples.Puzzles.Rabbits

A puzzle, attributed to Lewis Caroll:

• All rabbits, that are not greedy, are black
• No old rabbits are free from greediness
• Therefore: Some black rabbits are not old

What's implicit here is that there is a rabbit that must be not-greedy; which we add to our constraints.

Documentation

data Rabbit

A universe of rabbits

Instances

Data Rabbit

Defined in Documentation.SBV.Examples.Puzzles.Rabbits

Methods

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

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

toConstr :: Rabbit -> Constr

dataTypeOf :: Rabbit -> DataType

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

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

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

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

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

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

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

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

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

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

Read Rabbit

Defined in Documentation.SBV.Examples.Puzzles.Rabbits

Methods

readsPrec :: Int -> ReadS Rabbit

readList :: ReadS [Rabbit]

readPrec :: ReadPrec Rabbit

readListPrec :: ReadPrec [Rabbit]

Show Rabbit

Defined in Documentation.SBV.Examples.Puzzles.Rabbits

Methods

showsPrec :: Int -> Rabbit -> ShowS

show :: Rabbit -> String

showList :: [Rabbit] -> ShowS

SymVal Rabbit

Defined in Documentation.SBV.Examples.Puzzles.Rabbits

Methods

mkSymVal :: MonadSymbolic m => VarContext -> Maybe String -> m (SBV Rabbit)

literal :: Rabbit -> SBV Rabbit

fromCV :: CV -> Rabbit

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

free :: MonadSymbolic m => String -> m (SBV Rabbit)

free_ :: MonadSymbolic m => m (SBV Rabbit)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Rabbit]

symbolic :: MonadSymbolic m => String -> m (SBV Rabbit)

symbolics :: MonadSymbolic m => [String] -> m [SBV Rabbit]

unliteral :: SBV Rabbit -> Maybe Rabbit

isConcrete :: SBV Rabbit -> Bool

isSymbolic :: SBV Rabbit -> Bool

HasKind Rabbit

Defined in Documentation.SBV.Examples.Puzzles.Rabbits

Methods

kindOf :: Rabbit -> Kind

hasSign :: Rabbit -> Bool

intSizeOf :: Rabbit -> Int

isBoolean :: Rabbit -> Bool

isBounded :: Rabbit -> Bool

isReal :: Rabbit -> Bool

isFloat :: Rabbit -> Bool

isDouble :: Rabbit -> Bool

isRational :: Rabbit -> Bool

isFP :: Rabbit -> Bool

isUnbounded :: Rabbit -> Bool

isUserSort :: Rabbit -> Bool

isChar :: Rabbit -> Bool

isString :: Rabbit -> Bool

isList :: Rabbit -> Bool

isSet :: Rabbit -> Bool

isTuple :: Rabbit -> Bool

isMaybe :: Rabbit -> Bool

isEither :: Rabbit -> Bool

isArray :: Rabbit -> Bool

showType :: Rabbit -> String

SatModel Rabbit

Defined in Documentation.SBV.Examples.Puzzles.Rabbits

Methods

parseCVs :: [CV] -> Maybe (Rabbit, [CV])

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

type SRabbit = SBV Rabbit

Symbolic version of the type Rabbit.

greedy :: SRabbit -> SBool

Identify those rabbits that are greedy. Note that we leave the predicate uninterpreted.

black :: SRabbit -> SBool

Identify those rabbits that are black. Note that we leave the predicate uninterpreted.

old :: SRabbit -> SBool

Identify those rabbits that are old. Note that we leave the predicate uninterpreted.

rabbits :: Predicate

Express the puzzle.

rabbitsAreOK :: IO ThmResult

Prove the claim. We have:

>>> rabbitsAreOK
Q.E.D.