-----------------------------------------------------------------------------
-- |
-- Module      :  Control.Monad.Indexed
-- Copyright   :  (C) 2008 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>
-- Stability   :  experimental
-- Portability :  portable
--
----------------------------------------------------------------------------
module Control.Monad.Indexed
  ( IxFunctor(..)
  , IxPointed(..)
  , IxApplicative(..)
  , IxMonad(..)
  , IxMonadZero(..)
  , IxMonadPlus(..)
  , ijoin, (>>>=), (=<<<)
  , iapIxMonad
  ) where

import Data.Functor.Indexed

class IxApplicative m => IxMonad m where
  ibind :: (a -> m j k b) -> m i j a -> m i k b

ijoin :: IxMonad m => m i j (m j k a) -> m i k a
ijoin :: forall {k} (m :: k -> k -> * -> *) (i :: k) (j :: k) (k :: k) a.
IxMonad m =>
m i j (m j k a) -> m i k a
ijoin = forall {k} (m :: k -> k -> * -> *) a (j :: k) (k :: k) b (i :: k).
IxMonad m =>
(a -> m j k b) -> m i j a -> m i k b
ibind forall a. a -> a
id

infixr 1 =<<<
infixl 1 >>>=

(>>>=) :: IxMonad m => m i j a -> (a -> m j k b) -> m i k b
m i j a
m >>>= :: forall {k} (m :: k -> k -> * -> *) (i :: k) (j :: k) a (k :: k) b.
IxMonad m =>
m i j a -> (a -> m j k b) -> m i k b
>>>= a -> m j k b
k = forall {k} (m :: k -> k -> * -> *) a (j :: k) (k :: k) b (i :: k).
IxMonad m =>
(a -> m j k b) -> m i j a -> m i k b
ibind a -> m j k b
k m i j a
m

(=<<<) :: IxMonad m => (a -> m j k b) -> m i j a -> m i k b
=<<< :: forall {k} (m :: k -> k -> * -> *) a (j :: k) (k :: k) b (i :: k).
IxMonad m =>
(a -> m j k b) -> m i j a -> m i k b
(=<<<) = forall {k} (m :: k -> k -> * -> *) a (j :: k) (k :: k) b (i :: k).
IxMonad m =>
(a -> m j k b) -> m i j a -> m i k b
ibind

iapIxMonad :: IxMonad m => m i j (a -> b) -> m j k a -> m i k b
iapIxMonad :: forall {k} (m :: k -> k -> * -> *) (i :: k) (j :: k) a b (k :: k).
IxMonad m =>
m i j (a -> b) -> m j k a -> m i k b
iapIxMonad m i j (a -> b)
f m j k a
x = m i j (a -> b)
f forall {k} (m :: k -> k -> * -> *) (i :: k) (j :: k) a (k :: k) b.
IxMonad m =>
m i j a -> (a -> m j k b) -> m i k b
>>>= \ a -> b
f' -> m j k a
x forall {k} (m :: k -> k -> * -> *) (i :: k) (j :: k) a (k :: k) b.
IxMonad m =>
m i j a -> (a -> m j k b) -> m i k b
>>>= \a
x' -> forall {k} (m :: k -> k -> * -> *) a (i :: k).
IxPointed m =>
a -> m i i a
ireturn (a -> b
f' a
x')

class IxMonad m => IxMonadZero m where
  imzero :: m i j a

class IxMonadZero m => IxMonadPlus m where
  implus :: m i j a -> m i j a -> m i j a