Yaya.Fold.Common

Common algebras that are useful when folding.

Documentation

lowerMonoid :: Monoid m => (a -> m) -> XNor a m -> m

Converts the free monoid (a list) into some other Monoid.

lowerSemigroup :: Semigroup m => (a -> m) -> AndMaybe a m -> m

Converts the free semigroup (a non-empty list) into some other Semigroup.

lowerMonad :: Monad m => (forall x. f x -> m x) -> FreeF f a (m a) -> m a

Converts the free monad into some other Monad.

equal :: (Functor f, Foldable f, Eq1 f) => Day f f Bool -> Bool

Provides equality over arbitrary pattern functors.

height :: Foldable f => f Integer -> Integer

When folded, returns the height of the data structure.

size :: Foldable f => f Natural -> Natural

When folded, returns the number of nodes in the data structure.

NB: This is not the same as the length when applied to a list. I.e., length xs + 1 == cata size xs, because this is counting the nodes of the structure (how many Neithers and Boths), not how many elements (which would be equivalent to only counting Boths).

toRight :: Identity b -> Either a b

Converts a provably infinite structure into a Partial one (that will never terminate).

definedOrInput :: (a -> Maybe b) -> a -> Either a b

Captures the input value if the application was undefined.

fromEither :: Either a a -> a

Collapses a Partial structure to a value (probably requiring unsafe instances).

never :: a -> Identity a

Generates an infinite structure from an arbitrary seed.

le :: Day Maybe Maybe Bool -> Bool

takeAnother :: Day Maybe ((,) a) b -> XNor a b

takeAvailable :: Day Maybe (XNor a) b -> XNor a b

takeNext :: Day Maybe ((,) a) a -> a

maybeTakeNext :: Day Maybe (XNor a) (Maybe a) -> Maybe a

truncate' :: Functor f => Day Maybe f a -> FreeF f () a

diagonal :: a -> (a, a)

Converts a single value into a tuple with the same value on both sides. > x &&& y = (x *** y) . diagonal

sequence generators

unarySequence :: (a -> b) -> a -> (a, b)

binarySequence :: (a -> b -> c) -> (a, b) -> (a, (b, c))

ternarySequence :: (a -> b -> c -> d) -> (a, b, c) -> (a, (b, c, d))

lucasSequence' :: Integral i => i -> i -> (i, i) -> (i, (i, i))