composition-extra

Some handy tools for working with algebraic structures.

Functors

We can fmap more deeply with Applicative-style syntax:

(+1) <$$> [Just 1, Nothing, Just 2]
> [Just 2, Nothing, Just 3]

Likewise, via contravariant functors:

:t (-2) <-$$$> (Predicate $ (==) Predicate $ (==) Predicate $ (==) 5)
> :: ( Eq b
     , Eq (Predicate b)
     , Eq (Predicate (Predicate b))
     , Num b
     , Num (a -> Predicate b)
     , Contravariant ((->) (Predicate (Predicate b) -> Bool))
     ) => Predicate (Predicate a)

(it's not that useful)

Functions

You can slyly prepend unanry functions to arbitrary arguments (contravariant function compositon):

before :: [q] -> d
func2 :: c -> d -> e
func3 :: b -> c -> d -> e
func4 :: a -> b -> c -> d -> e

before -.* func2 :: c -> [q] -> e
before -.** func3 :: b -> c -> [q] -> e
before -.*** func4 :: a -> b -> c -> [q] -> e

Monads

We can also do weird liftM-ish, applicative-y stuff, too:

import Data.Compositon -- from the `compositon` package

(return .: (+)) ==<< mx =<< my
mx >>==== (return .:: func4) -- apply to 4th arg