-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Countable, Searchable, Finite, Empty classes -- -- -- -- Some orphan instances: -- -- @package countable @version 0.2 module Data.Countable class Eq a => Countable a countPrevious :: Countable a => a -> Maybe a countMaybeNext :: Countable a => Maybe a -> Maybe a countDown :: Countable a => a -> [a] boundedCountPrevious :: (Eq a, Bounded a, Enum a) => a -> Maybe a boundedCountMaybeNext :: (Eq a, Bounded a, Enum a) => Maybe a -> Maybe a maybeRecount :: (Countable a, Countable b) => a -> Maybe b countDownUp :: (Countable down, Countable up) => (down, up) -> Maybe (down, up) countUpDown :: (Countable up, Countable down) => (up, down) -> Maybe (up, down) finalIteration :: (a -> Maybe a) -> a -> a class Countable a => AtLeastOneCountable a countFirst :: AtLeastOneCountable a => a class AtLeastOneCountable a => InfiniteCountable a countNext :: InfiniteCountable a => Maybe a -> a recount :: (Countable a, InfiniteCountable b) => a -> b instance AtLeastOneCountable a => InfiniteCountable [a] instance Countable a => AtLeastOneCountable [a] instance Countable a => Countable [a] instance (Countable a, InfiniteCountable b) => InfiniteCountable (Either a b) instance (AtLeastOneCountable a, InfiniteCountable b) => InfiniteCountable (a, b) instance InfiniteCountable a => InfiniteCountable (Maybe a) instance InfiniteCountable Integer instance (AtLeastOneCountable a, AtLeastOneCountable b) => AtLeastOneCountable (a, b) instance (Countable a, AtLeastOneCountable b) => AtLeastOneCountable (Either a b) instance Countable a => AtLeastOneCountable (Maybe a) instance AtLeastOneCountable Integer instance AtLeastOneCountable Int64 instance AtLeastOneCountable Int32 instance AtLeastOneCountable Int16 instance AtLeastOneCountable Int8 instance AtLeastOneCountable Word64 instance AtLeastOneCountable Word32 instance AtLeastOneCountable Word16 instance AtLeastOneCountable Word8 instance AtLeastOneCountable Bool instance AtLeastOneCountable () instance (Countable a, Countable b) => Countable (a, b) instance (Countable a, Countable b) => Countable (Either a b) instance Countable a => Countable (Maybe a) instance Countable Integer instance Countable Int64 instance Countable Int32 instance Countable Int16 instance Countable Int8 instance Countable Word64 instance Countable Word32 instance Countable Word16 instance Countable Word8 instance Countable Bool instance Countable () module Data.Expression data Expression a b f r ClosedExpression :: (f r) -> Expression a b f r OpenExpression :: a -> (Expression a b f (b -> r)) -> Expression a b f r expressionSym :: a -> f (b -> r) -> Expression a b f r runExpression :: Functor f => Expression a b f r -> f ((a -> b) -> r) instance Applicative f => Applicative (Expression a b f) instance Functor f => Functor (Expression a b f) -- | This module also includes these orphan instances: -- -- module Data.Searchable -- | It turns out there are Searchable instances that are not -- Finite. The (c -> s) instance is based on the -- algorithm at -- http://math.andrej.com/2007/09/28/seemingly-impossible-functional-programs/. class Searchable a search :: Searchable a => (a -> Maybe b) -> Maybe b forsome :: Searchable a => (a -> Bool) -> Bool forevery :: Searchable a => (a -> Bool) -> Bool class (Searchable a, Countable a) => Finite a where assemble afb = fmap listLookup (traverse (\ a -> fmap (\ b -> (a, b)) (afb a)) allValues) where listLookup [] _ = error "missing value" listLookup ((a, b) : _) a' | a == a' = b listLookup (_ : l) a' = listLookup l a' allValues :: Finite a => [a] assemble :: (Finite a, Applicative f) => (a -> f b) -> f (a -> b) finiteSearch :: Finite a => (a -> Maybe b) -> Maybe b finiteCountPrevious :: Finite a => a -> Maybe a finiteCountMaybeNext :: Finite a => Maybe a -> Maybe a instance (Show a, Finite a, Show b) => Show (a -> b) instance (Finite a, Finite b) => Finite (a -> b) instance (Finite a, AtLeastOneCountable a, InfiniteCountable b) => InfiniteCountable (a -> b) instance (Finite a, AtLeastOneCountable b) => AtLeastOneCountable (a -> b) instance (Finite a, Countable b) => Countable (a -> b) instance (Finite a, Finite b) => Finite (a, b) instance (Finite a, Finite b) => Finite (Either a b) instance Finite a => Finite (Maybe a) instance Finite Int64 instance Searchable Int64 instance Finite Int32 instance Searchable Int32 instance Finite Int16 instance Searchable Int16 instance Finite Int8 instance Searchable Int8 instance Finite Word64 instance Searchable Word64 instance Finite Word32 instance Searchable Word32 instance Finite Word16 instance Searchable Word16 instance Finite Word8 instance Searchable Word8 instance Finite Bool instance Searchable Bool instance Finite () instance Searchable () instance Finite a => Traversable ((->) a) instance Finite t => Foldable ((->) t) instance (Searchable a, Eq b) => Eq (a -> b) instance (Countable c, Searchable s) => Searchable (c -> s) instance (Searchable a, Searchable b) => Searchable (a, b) instance (Searchable a, Searchable b) => Searchable (Either a b) instance Searchable a => Searchable (Maybe a) module Data.Empty class Finite n => Empty n where never n = seq n undefined never :: Empty n => n -> a data Nothing instance Show Nothing instance Ord Nothing instance Eq Nothing instance Empty Nothing instance Finite Nothing instance Searchable Nothing instance Countable Nothing instance (AtLeastOneCountable a, Finite a, Empty b) => Empty (a -> b) instance (Empty a, Finite b) => Empty (a, b) instance (Empty a, Empty b) => Empty (Either a b)