-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Combinators for unorthodox function composition
--
-- Combinators for unorthodox function composition
@package composition
@version 1.0.2.1
-- | This module is for convenience and demonstrative purposes more than it
-- is for providing actual value. I do not recommend that you rely on
-- this module for performance-sensitive code. Because this module is not
-- based on Prelude's (.), some chances at optimization might be missed
-- by your compiler.
module Data.Composition
-- | The mathematical symbol for function composition.
(∘) :: (b -> c) -> (a -> b) -> a -> c
-- | Compose two functions. f .: g is similar to f . g
-- except that g will be fed two arguments instead of one
-- before handing its result to f.
--
-- This function is defined as
--
--
-- (f .: g) x y = f (g x y)
--
--
-- Example usage:
--
--
-- concatMap :: (a -> b) -> [a] -> [b]
-- concatMap = concat .: map
--
--
-- Notice how two arguments (the function and the list)
-- will be given to map before the result is passed to
-- concat. This is equivalent to:
--
--
-- concatMap f xs = concat (map f xs)
--
(.:) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
-- | One compact pattern for composition operators is to "count the dots
-- after the first one", which begins with the common .:, and
-- proceeds by first appending another . and then replacing it
-- with :
(.:.) :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e
(.::) :: (d -> e) -> (a -> a1 -> b -> c -> d) -> a -> a1 -> b -> c -> e
(.::.) :: (d -> e) -> (a -> a1 -> a2 -> b -> c -> d) -> a -> a1 -> a2 -> b -> c -> e
(.:::) :: (d -> e) -> (a -> a1 -> a2 -> a3 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> b -> c -> e
(.:::.) :: (d -> e) -> (a -> a1 -> a2 -> a3 -> a4 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> a4 -> b -> c -> e
(.::::) :: (d -> e) -> (a -> a1 -> a2 -> a3 -> a4 -> a5 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> a4 -> a5 -> b -> c -> e
(.::::.) :: (d -> e) -> (a -> a1 -> a2 -> a3 -> a4 -> a5 -> a6 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> a4 -> a5 -> a6 -> b -> c -> e
-- | Equivalent to .:
--
-- The pattern of appending asterisks is straightforward to extend to
-- similar functions: (compose2 = .*, compose3 = .**, etc). However,
-- .: has been commonly adopted amongst Haskellers, and the need
-- for compose3 and beyond is rare in practice.
(.*) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
(.**) :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e
(.***) :: (d -> e) -> (a -> a1 -> b -> c -> d) -> a -> a1 -> b -> c -> e
(.****) :: (d -> e) -> (a -> a1 -> a2 -> b -> c -> d) -> a -> a1 -> a2 -> b -> c -> e
(.*****) :: (d -> e) -> (a -> a1 -> a2 -> a3 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> b -> c -> e
(.******) :: (d -> e) -> (a -> a1 -> a2 -> a3 -> a4 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> a4 -> b -> c -> e
(.*******) :: (d -> e) -> (a -> a1 -> a2 -> a3 -> a4 -> a5 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> a4 -> a5 -> b -> c -> e
(.********) :: (d -> e) -> (a -> a1 -> a2 -> a3 -> a4 -> a5 -> a6 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> a4 -> a5 -> a6 -> b -> c -> e
-- | composeN f g means give g N inputs and then
-- pass its result to f.
compose1 :: (b -> c) -> (a -> b) -> a -> c
compose2 :: (c -> d) -> (a -> b -> c) -> a -> b -> d
compose3 :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e
compose4 :: (d -> e) -> (a -> a1 -> b -> c -> d) -> a -> a1 -> b -> c -> e
compose5 :: (d -> e) -> (a -> a1 -> a2 -> b -> c -> d) -> a -> a1 -> a2 -> b -> c -> e
compose6 :: (d -> e) -> (a -> a1 -> a2 -> a3 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> b -> c -> e
compose7 :: (d -> e) -> (a -> a1 -> a2 -> a3 -> a4 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> a4 -> b -> c -> e
compose8 :: (d -> e) -> (a -> a1 -> a2 -> a3 -> a4 -> a5 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> a4 -> a5 -> b -> c -> e
compose9 :: (d -> e) -> (a -> a1 -> a2 -> a3 -> a4 -> a5 -> a6 -> b -> c -> d) -> a -> a1 -> a2 -> a3 -> a4 -> a5 -> a6 -> b -> c -> e