moapfu.hs

{-# LANGUAGE
    UnicodeSyntax
  , InstanceSigs
  , KindSignatures
  , RankNTypes
#-}


module MAF
  where


import Prelude
  hiding (fmap, pure)



class Functors (t ∷ * → *)
  where

    fmap ∷ forall a b . (a → b) → t a → t b



class (Functors t) ⇒
      Applicatives (t ∷ * → *)
  where

    pure ∷ forall a . a → t a

    appl ∷ forall a b . t (a → b) → t a → t b



class (Applicatives t) ⇒
      Monads (t ∷ * → *)
  where

    retu ∷ forall a . a → t a

    bind ∷ forall a b . t a → (a → t b) → t b



instance Functors []
  where

    fmap ∷ forall a b . (a → b) → [] a → [] b
    fmap = map



instance Applicatives []
  where

    pure ∷ forall a . a → [] a
    pure = \ x → [x]

    appl ∷ forall a b . [] (a → b) → [] a → [] b
    appl = \ fs xs → concat (map (\ f → map (\ x → f x) xs) fs)



instance Monads []
  where

    retu ∷ forall a . a → [] a
    retu = pure

    bind ∷ forall a b . [] a → (a → [] b) → [] b
    bind = \ l f → concat $ map f l



-- ⋅ --



class (Monads t) ⇒
      Functorm (t ∷ * → *)
  where

    fmapm ∷ forall a b . (a → b) → t a → t b
    fmapm = \ f m → m `bind` (\ x → retu $ f x)



class (Monads t) ⇒
      Applicativem (t ∷ * → *)
  where

    purem ∷ forall a . a → t a
    purem = retu

    applm ∷ forall a b . t (a → b) → t a → t b
    applm = \ mf mx → mf `bind` (\ f → mx `bind` (\ x → purem $ f x))