module Control.Bind.Indexed
  ( class IxBind
  , ibind, (:>>=)
  , ibindFlipped, (=<<:)
  , composeiKleisli, (:>=>)
  , composeiKleisliFlipped, (<=<:)
  , class IxDiscard
  , idiscard
  , ijoin
  , module Control.Apply.Indexed
  ) where

import Prelude (flip, identity, Unit)
import Control.Apply.Indexed

class IxBind ∷ ∀ ix. (ix → ix → Type → Type) → Constraint
class IxApply m ⇐ IxBind m where
  ibind ∷ ∀ a b x y z. m x y a → (a → m y z b) → m x z b

infixl 1 ibind as :>>=

ibindFlipped ∷ ∀ m a b x y z. IxBind m ⇒ (a → m y z b) → m x y a → m x z b
ibindFlipped = flip ibind

infixr 1 ibindFlipped as =<<:

ijoin ∷ forall m z y x a. IxBind m => m x y (m y z a) -> m x z a
ijoin m = m :>>= identity

composeiKleisli ∷ ∀ m a b c x y z. IxBind m ⇒ (a → m x y b) → (b → m y z c) → a → m x z c
composeiKleisli f g a = f a :>>= g

infixr 1 composeiKleisli as :>=>

composeiKleisliFlipped ∷ ∀ m a b c x y z. IxBind m ⇒ (b → m y z c) → (a → m x y b) → a → m x z c
composeiKleisliFlipped f g a = f =<<: g a

infixr 1 composeiKleisliFlipped as <=<:

class IxDiscard a where
  idiscard ∷ ∀ k f b (x :: k) (y :: k) (z :: k). IxBind f ⇒ f x y a → (a → f y z b) → f x z b

instance ixDiscardUnit :: IxDiscard Unit where
  idiscard = ibind