{-# LANGUAGE FlexibleInstances     #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE UndecidableInstances  #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
-- |
-- Copyright  : (c) Ivan Perez and Manuel Baerenz, 2016
-- License    : BSD3
-- Maintainer : ivan.perez@keera.co.uk
--
-- 'VectorSpace' instances for 'MSF's that produce vector spaces. This allows
-- you to use vector operators with 'MSF's that output vectors, for example,
-- you can write:
--
-- @
-- msf1 :: MSF Input (Double, Double) -- defined however you want
-- msf2 :: MSF Input (Double, Double) -- defined however you want
-- msf3 :: MSF Input (Double, Double)
-- msf3 = msf1 ^+^ msf2
-- @
--
-- instead of
--
-- @
-- msf3 = (msf1 &&& msf2) >>> arr (uncurry (^+^))
-- @
--
--
-- Instances are provided for the type class 'VectorSpace'.

-- Note: This module uses undecidable instances, because GHC does not know
-- enough to assert that it will be able to determine the type of 's' from the
-- type of 'v', because 'v' only appears under 'MSF' in the instance head and
-- it cannot determine what 'MSF' will do to 'v' and whether the type can be
-- resolved.
module Data.MonadicStreamFunction.Instances.VectorSpace where

-- External imports
import Control.Arrow    ((>>^))
import Data.VectorSpace (VectorSpace (..))

-- Internal imports
import Control.Arrow.Util              (constantly, elementwise2)
import Data.MonadicStreamFunction.Core (MSF)

-- | Vector-space instance for 'MSF's.
instance (Monad m, VectorSpace v s, Eq s, Floating s)
      => VectorSpace (MSF m a v) s
  where
    zeroVector :: MSF m a v
zeroVector   = forall (a :: * -> * -> *) b c. Arrow a => b -> a c b
constantly forall v a. VectorSpace v a => v
zeroVector
    s
r *^ :: s -> MSF m a v -> MSF m a v
*^ MSF m a v
msf     = MSF m a v
msf forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> (c -> d) -> a b d
>>^ (s
r forall v a. VectorSpace v a => a -> v -> v
*^)
    MSF m a v
msf ^/ :: MSF m a v -> s -> MSF m a v
^/ s
r     = MSF m a v
msf forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> (c -> d) -> a b d
>>^ (forall v a. VectorSpace v a => v -> a -> v
^/ s
r)
    ^+^ :: MSF m a v -> MSF m a v -> MSF m a v
(^+^)        = forall (a :: * -> * -> *) c d e b.
Arrow a =>
(c -> d -> e) -> a b c -> a b d -> a b e
elementwise2 forall v a. VectorSpace v a => v -> v -> v
(^+^)
    ^-^ :: MSF m a v -> MSF m a v -> MSF m a v
(^-^)        = forall (a :: * -> * -> *) c d e b.
Arrow a =>
(c -> d -> e) -> a b c -> a b d -> a b e
elementwise2 forall v a. VectorSpace v a => v -> v -> v
(^-^)
    negateVector :: MSF m a v -> MSF m a v
negateVector = (forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> (c -> d) -> a b d
>>^ forall v a. VectorSpace v a => v -> v
negateVector)