Types.hs

{-# LANGUAGE Rank2Types, GeneralizedNewtypeDeriving, TemplateHaskell, FlexibleContexts, FlexibleInstances, MultiParamTypeClasses, DeriveFunctor, DeriveFoldable, DeriveTraversable #-}
-- {-# OPTIONS_HADDOCK hide, prune #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Numeric.AD.Internal.Types
-- Copyright   :  (c) Edward Kmett 2010
-- License     :  BSD3
-- Maintainer  :  ekmett@gmail.com
-- Stability   :  experimental
-- Portability :  GHC only
--
-----------------------------------------------------------------------------
module Numeric.AD.Internal.Types
    ( AD(..)
    , UU, UF, FU, FF
    ) where

import Language.Haskell.TH
import Numeric.AD.Internal.Classes

-- | 'AD' serves as a common wrapper for different 'Mode' instances, exposing a traditional
-- numerical tower. Universal quantification is used to limit the actions in user code to
-- machinery that will return the same answers under all AD modes, allowing us to use modes
-- interchangeably as both the type level \"brand\" and dictionary, providing a common API.
newtype AD f a = AD { runAD :: f a } deriving (Iso (f a), Lifted, Mode, Primal)

-- > instance (Lifted f, Num a) => Num (AD f a)
-- etc.
let f = varT (mkName "f") in 
    deriveNumeric 
        (classP ''Lifted [f]:) 
        (conT ''AD `appT` f)

-- | A scalar-to-scalar automatically-differentiable function.
type UU a = forall s. Mode s => AD s a -> AD s a
-- | A scalar-to-non-scalar automatically-differentiable function.
type UF f a = forall s. Mode s => AD s a -> f (AD s a)
-- | A non-scalar-to-scalar automatically-differentiable function.
type FU f a = forall s. Mode s => f (AD s a) -> AD s a
-- | A non-scalar-to-non-scalar automatically-differentiable function.
type FF f g a = forall s. Mode s => f (AD s a) -> g (AD s a)