Backprop.hs

{-# LANGUAGE FlexibleContexts #-}

-- |
-- Module      : Prelude.Backprop
-- Copyright   : (c) Justin Le 2023
-- License     : BSD3
--
-- Maintainer  : justin@jle.im
-- Stability   : experimental
-- Portability : non-portable
--
-- Some lifted versions of common functions found in 'Prelude' (or /base/
-- in general).
--
-- This module is intended to be a catch-all one, so feel free to suggest
-- other functions or submit a PR if you think one would make sense.
--
-- See "Prelude.Backprop.Num" for a version with 'Num' constraints instead
-- of 'Backprop' constraints, and "Prelude.Backprop.Explicit" for a version
-- allowing you to provide 'zero', 'add', and 'one' explicitly.
--
-- @since 0.1.3.0
module Prelude.Backprop (
  -- * Foldable and Traversable
  sum,
  product,
  length,
  minimum,
  maximum,
  traverse,
  toList,
  mapAccumL,
  mapAccumR,
  foldr,
  foldl',

  -- * Functor and Applicative
  fmap,
  fmapConst,
  (<$>),
  (<$),
  ($>),
  pure,
  liftA2,
  liftA3,

  -- * Numeric
  fromIntegral,
  realToFrac,
  round,
  fromIntegral',

  -- * Misc
  E.coerce,
) where

import Numeric.Backprop
import qualified Numeric.Backprop.Explicit as E
import qualified Prelude.Backprop.Explicit as E
import Prelude (
  Applicative,
  Foldable,
  Fractional (..),
  Functor,
  Num (..),
  Ord (..),
  Traversable,
 )
import qualified Prelude as P

-- | Lifted 'P.sum'.  More efficient than going through 'toList'.
sum ::
  (Foldable t, Functor t, Backprop (t a), Num a, Reifies s W) =>
  BVar s (t a) ->
  BVar s a
sum = E.sum E.addFunc
{-# INLINE sum #-}

-- | Lifted 'P.pure'.
pure ::
  (Foldable t, Applicative t, Backprop a, Reifies s W) =>
  BVar s a ->
  BVar s (t a)
pure = E.pure E.addFunc E.zeroFunc
{-# INLINE pure #-}

-- | Lifted 'P.product'.  More efficient than going through 'toList'.
product ::
  (Foldable t, Functor t, Backprop (t a), Fractional a, Reifies s W) =>
  BVar s (t a) ->
  BVar s a
product = E.product E.addFunc
{-# INLINE product #-}

-- | Lifted 'P.length'.  More efficient than going through 'toList'.
length ::
  (Foldable t, Backprop (t a), Num b, Reifies s W) =>
  BVar s (t a) ->
  BVar s b
length = E.length E.addFunc E.zeroFunc
{-# INLINE length #-}

-- | Lifted 'P.minimum'.  Undefined for situations where 'P.minimum' would
-- be undefined.  More efficient than going through 'toList'.
minimum ::
  (Foldable t, Functor t, Backprop a, Ord a, Backprop (t a), Reifies s W) =>
  BVar s (t a) ->
  BVar s a
minimum = E.minimum E.addFunc E.zeroFunc
{-# INLINE minimum #-}

-- | Lifted 'P.maximum'.  Undefined for situations where 'P.maximum' would
-- be undefined.  More efficient than going through 'toList'.
maximum ::
  (Foldable t, Functor t, Backprop a, Ord a, Backprop (t a), Reifies s W) =>
  BVar s (t a) ->
  BVar s a
maximum = E.maximum E.addFunc E.zeroFunc
{-# INLINE maximum #-}

-- | Lifed 'P.foldr'.  Essentially just 'toList' composed with a normal
-- list 'P.foldr', and is only here for convenience.
--
-- @since 0.2.3.0
foldr ::
  (Traversable t, Backprop a, Reifies s W) =>
  (BVar s a -> BVar s b -> BVar s b) ->
  BVar s b ->
  BVar s (t a) ->
  BVar s b
foldr = E.foldr E.addFunc E.zeroFunc
{-# INLINE foldr #-}

-- | Lifed 'P.foldl''.  Essentially just 'toList' composed with a normal
-- list 'P.foldl'', and is only here for convenience.
--
-- @since 0.2.3.0
foldl' ::
  (Traversable t, Backprop a, Reifies s W) =>
  (BVar s b -> BVar s a -> BVar s b) ->
  BVar s b ->
  BVar s (t a) ->
  BVar s b
foldl' = E.foldl' E.addFunc E.zeroFunc
{-# INLINE foldl' #-}

-- | Lifted 'P.fmap'.  Lifts backpropagatable functions to be
-- backpropagatable functions on 'Traversable' 'Functor's.
fmap ::
  (Traversable f, Backprop a, Backprop b, Reifies s W) =>
  (BVar s a -> BVar s b) ->
  BVar s (f a) ->
  BVar s (f b)
fmap = E.fmap E.addFunc E.addFunc E.zeroFunc E.zeroFunc
{-# INLINE fmap #-}

-- | Efficient version of 'fmap' when used to "replace" all values in
-- a 'Functor' value.
--
-- @
-- 'fmapConst' x = 'fmap' ('P.const' x)
-- @
--
-- but much more efficient.
--
-- @since 0.2.4.0
fmapConst ::
  (Functor f, Foldable f, Backprop b, Backprop (f a), Reifies s W) =>
  BVar s b ->
  BVar s (f a) ->
  BVar s (f b)
fmapConst = E.fmapConst E.addFunc E.addFunc E.zeroFunc E.zeroFunc
{-# INLINE fmapConst #-}

-- | Alias for 'fmap'.
(<$>) ::
  (Traversable f, Backprop a, Backprop b, Reifies s W) =>
  (BVar s a -> BVar s b) ->
  BVar s (f a) ->
  BVar s (f b)
(<$>) = fmap

infixl 4 <$>
{-# INLINE (<$>) #-}

-- | Alias for 'fmapConst'.
--
-- @since 0.2.4.0
(<$) ::
  (Traversable f, Backprop b, Backprop (f a), Reifies s W) =>
  BVar s b ->
  BVar s (f a) ->
  BVar s (f b)
(<$) = fmapConst

infixl 4 <$
{-# INLINE (<$) #-}

-- | Alias for @'flip' 'fmapConst'@.
--
-- @since 0.2.4.0
($>) ::
  (Traversable f, Backprop b, Backprop (f a), Reifies s W) =>
  BVar s (f a) ->
  BVar s b ->
  BVar s (f b)
xs $> x = x <$ xs

infixl 4 $>
{-# INLINE ($>) #-}

-- | Lifted 'P.traverse'.  Lifts backpropagatable functions to be
-- backpropagatable functions on 'Traversable' 'Functor's.
traverse ::
  (Traversable t, Applicative f, Foldable f, Backprop a, Backprop b, Backprop (t b), Reifies s W) =>
  (BVar s a -> f (BVar s b)) ->
  BVar s (t a) ->
  BVar s (f (t b))
traverse =
  E.traverse
    E.addFunc
    E.addFunc
    E.addFunc
    E.zeroFunc
    E.zeroFunc
{-# INLINE traverse #-}

-- | Lifted 'P.liftA2'.  Lifts backpropagatable functions to be
-- backpropagatable functions on 'Traversable' 'Applicative's.
liftA2 ::
  ( Traversable f
  , Applicative f
  , Backprop a
  , Backprop b
  , Backprop c
  , Reifies s W
  ) =>
  (BVar s a -> BVar s b -> BVar s c) ->
  BVar s (f a) ->
  BVar s (f b) ->
  BVar s (f c)
liftA2 =
  E.liftA2
    E.addFunc
    E.addFunc
    E.addFunc
    E.zeroFunc
    E.zeroFunc
    E.zeroFunc
{-# INLINE liftA2 #-}

-- | Lifted 'P.liftA3'.  Lifts backpropagatable functions to be
-- backpropagatable functions on 'Traversable' 'Applicative's.
liftA3 ::
  ( Traversable f
  , Applicative f
  , Backprop a
  , Backprop b
  , Backprop c
  , Backprop d
  , Reifies s W
  ) =>
  (BVar s a -> BVar s b -> BVar s c -> BVar s d) ->
  BVar s (f a) ->
  BVar s (f b) ->
  BVar s (f c) ->
  BVar s (f d)
liftA3 =
  E.liftA3
    E.addFunc
    E.addFunc
    E.addFunc
    E.addFunc
    E.zeroFunc
    E.zeroFunc
    E.zeroFunc
    E.zeroFunc
{-# INLINE liftA3 #-}

-- | Lifted conversion between two 'P.Integral' instances.
--
-- @since 0.2.1.0
fromIntegral ::
  (Backprop a, P.Integral a, P.Integral b, Reifies s W) =>
  BVar s a ->
  BVar s b
fromIntegral = E.fromIntegral E.addFunc
{-# INLINE fromIntegral #-}

-- | Lifted conversion between two 'Fractional' and 'P.Real' instances.
--
-- @since 0.2.1.0
realToFrac ::
  (Backprop a, Fractional a, P.Real a, Fractional b, P.Real b, Reifies s W) =>
  BVar s a ->
  BVar s b
realToFrac = E.realToFrac E.addFunc
{-# INLINE realToFrac #-}

-- | Lifted version of 'P.round'.
--
-- Gradient should technically diverge whenever the fractional part is 0.5,
-- but does not do this for convenience reasons.
--
-- @since 0.2.3.0
round ::
  (P.RealFrac a, P.Integral b, Reifies s W) =>
  BVar s a ->
  BVar s b
round = E.round E.afNum
{-# INLINE round #-}

-- | Lifted version of 'P.fromIntegral', defined to let you return
-- 'P.RealFrac' instances as targets, instead of only other 'P.Integral's.
-- Essentially the opposite of 'round'.
--
-- The gradient should technically diverge whenever the fractional part of
-- the downstream gradient is 0.5, but does not do this for convenience
-- reasons.
--
-- @since 0.2.3.0
fromIntegral' ::
  (P.Integral a, P.RealFrac b, Reifies s W) =>
  BVar s a ->
  BVar s b
fromIntegral' = E.fromIntegral' E.afNum
{-# INLINE fromIntegral' #-}

-- | Lifted version of 'P.toList'.  Takes a 'BVar' of a 'Traversable' of
-- items and returns a list of 'BVar's for each item.
--
-- You can use this to implement "lifted" versions of 'Foldable' methods
-- like 'P.foldr', 'P.foldl'', etc.; however, 'sum', 'product', 'length',
-- 'minimum', and 'maximum' have more efficient implementations than simply
-- @'P.minimum' . 'toList'.@
--
-- @since 0.2.2.0
toList ::
  (Traversable t, Backprop a, Reifies s W) =>
  BVar s (t a) ->
  [BVar s a]
toList = E.toList E.addFunc E.zeroFunc
{-# INLINE toList #-}

-- | Lifted version of 'P.mapAccumL'.
--
-- Prior to v0.2.3, required a 'Backprop' constraint on @t b@.
--
-- @since 0.2.2.0
mapAccumL ::
  (Traversable t, Backprop b, Backprop c, Reifies s W) =>
  (BVar s a -> BVar s b -> (BVar s a, BVar s c)) ->
  BVar s a ->
  BVar s (t b) ->
  (BVar s a, BVar s (t c))
mapAccumL = E.mapAccumL E.addFunc E.addFunc E.zeroFunc E.zeroFunc
{-# INLINE mapAccumL #-}

-- | Lifted version of 'P.mapAccumR'.
--
-- Prior to v0.2.3, required a 'Backprop' constraint on @t b@.
--
-- @since 0.2.2.0
mapAccumR ::
  (Traversable t, Backprop b, Backprop c, Reifies s W) =>
  (BVar s a -> BVar s b -> (BVar s a, BVar s c)) ->
  BVar s a ->
  BVar s (t b) ->
  (BVar s a, BVar s (t c))
mapAccumR = E.mapAccumR E.addFunc E.addFunc E.zeroFunc E.zeroFunc
{-# INLINE mapAccumR #-}