-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Data types as fixpoints
--   
--   This package allows data types to be seen and manipulated as fixpoints
--   of their underlying functors. It is mostly based on <a>Functional
--   Programming with Bananas, Lenses, Envelopes and Barbed Wire</a> by
--   Erik Meijer, Maarten Fokkinga and Ross Paterson
--   (<a>http://citeseer.ist.psu.edu/meijer91functional.html</a>). It makes
--   essential use of associated types and related extensions.
@package fixpoint
@version 0.1.1

module Data.Fixpoint.Algorithms
size :: (Fixpoint t, Foldable (Pre t)) => t -> Int

module Data.Fixpoint

-- | The class of data types representable by fixpoints.
class Functor (Pre t) => Fixpoint t where { data family Pre t :: * -> *; }
project :: Fixpoint t => t -> Pre t t
inject :: Fixpoint t => Pre t t -> t

-- | Catamorphism (same as <a>fold</a>)
cata :: Fixpoint t => (Pre t s -> s) -> t -> s

-- | Catamorphism (same as <a>cata</a>)
fold :: Fixpoint t => (Pre t s -> s) -> t -> s

-- | Anamorphism (same as <a>unfold</a>)
ana :: Fixpoint t => (s -> Pre t s) -> s -> t

-- | Anamorphism (same as <a>ana</a>)
unfold :: Fixpoint t => (s -> Pre t s) -> s -> t

-- | Hylomorphism
hylo :: Fixpoint t => (Pre t s -> s) -> (p -> Pre t p) -> p -> s

-- | Paramorphism
para :: Fixpoint t => (Pre t (t, s) -> s) -> t -> s