{-# LANGUAGE DataKinds #-}
{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE InstanceSigs #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE QuantifiedConstraints #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_GHC -Wno-orphans #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Singletons.Prelude.Semigroup
-- Copyright   :  (C) 2018 Ryan Scott
-- License     :  BSD-style (see LICENSE)
-- Maintainer  :  Ryan Scott
-- Stability   :  experimental
-- Portability :  non-portable
--
-- Defines the promoted version of 'Semigroup', 'PSemigroup', and the
-- singleton version, 'SSemigroup'.
--
----------------------------------------------------------------------------

module Data.Singletons.Prelude.Semigroup (
  PSemigroup(..), SSemigroup(..),

  Sing(SMin, sGetMin, SMax, sGetMax,
       SFirst, sGetFirst, SLast, sGetLast,
       SWrapMonoid, sUnwrapMonoid, SDual, sGetDual,
       SAll, sGetAll, SAny, sGetAny,
       SSum, sGetSum, SProduct, sGetProduct,
       SOption, sGetOption, SArg),
  GetMin, GetMax, GetFirst, GetLast, GetDual,
  GetAll, GetAny, GetSum, GetProduct, GetOption,

  SMin, SMax, SFirst, SLast, SWrappedMonoid, SDual,
  SAll, SAny, SSum, SProduct, SOption, SArg,

  option_, sOption_, Option_,

  -- ** Defunctionalization symbols
  type (<>@#@$), type (<>@#@$$), type (<>@#@$$$),
  SconcatSym0, SconcatSym1,
  MinSym0, MinSym1, GetMinSym0, GetMinSym1,
  MaxSym0, MaxSym1, GetMaxSym0, GetMaxSym1,
  FirstSym0, FirstSym1, GetFirstSym0, GetFirstSym1,
  LastSym0, LastSym1, GetLastSym0, GetLastSym1,
  WrapMonoidSym0, WrapMonoidSym1, UnwrapMonoidSym0, UnwrapMonoidSym1,
  DualSym0, DualSym1, GetDualSym0, GetDualSym1,
  AllSym0, AllSym1, GetAllSym0, GetAllSym1,
  AnySym0, AnySym1, GetAnySym0, GetAnySym1,
  SumSym0, SumSym1, GetSumSym0, GetSumSym1,
  ProductSym0, ProductSym1, GetProductSym0, GetProductSym1,
  OptionSym0, OptionSym1, GetOptionSym0, GetOptionSym1,
  ArgSym0, ArgSym1, ArgSym2
  ) where

import Control.Applicative
import Control.Monad
import qualified Data.Semigroup as Semi (Min(..), Max(..))
import Data.Semigroup (First(..), Last(..), WrappedMonoid(..), Option(..), Arg(..))
import Data.Singletons.Prelude.Base hiding
       (Foldr, FoldrSym0, FoldrSym1, FoldrSym2, FoldrSym3, sFoldr)
import Data.Singletons.Prelude.Enum
import Data.Singletons.Prelude.Eq
import Data.Singletons.Prelude.Foldable hiding
       ( All,     AllSym0,     AllSym1
       , Any,     AnySym0,     AnySym1
       , Product, ProductSym0, ProductSym1
       , Sum,     SumSym0,     SumSym1 )
import Data.Singletons.Prelude.Functor
import Data.Singletons.Prelude.Instances
import Data.Singletons.Prelude.Maybe
import Data.Singletons.Prelude.Monad.Internal
import Data.Singletons.Prelude.Monoid hiding
       (Sing(SFirst, SLast), SFirst, sGetFirst, SLast, sGetLast,
        FirstSym0, FirstSym1, LastSym0, LastSym1,
        GetFirst,  GetFirstSym0, GetFirstSym1,
        GetLast,   GetLastSym0,  GetLastSym1)
import Data.Singletons.Prelude.Num
import Data.Singletons.Prelude.Ord hiding
       (MinSym0, MinSym1, MaxSym0, MaxSym1)
import Data.Singletons.Prelude.Semigroup.Internal
import Data.Singletons.Prelude.Show
import Data.Singletons.Prelude.Traversable
import Data.Singletons.Single
import Data.Singletons.Util

$(genSingletons [''Arg])
$(showSingInstances $ ''Option : semigroupBasicTypes)
$(singShowInstances $ ''Option : semigroupBasicTypes)

$(singletonsOnly [d|
  instance Applicative Semi.Min where
    pure = Semi.Min
    a <* _ = a
    _ *> a = a
    Semi.Min f <*> Semi.Min x = Semi.Min (f x)
    liftA2 f (Semi.Min a) (Semi.Min b) = Semi.Min (f a b)

  instance Enum a => Enum (Semi.Min a) where
    succ (Semi.Min a) = Semi.Min (succ a)
    pred (Semi.Min a) = Semi.Min (pred a)
    toEnum = Semi.Min . toEnum
    fromEnum (Semi.Min a) = fromEnum a
    enumFromTo (Semi.Min a) (Semi.Min b) = Semi.Min `map` enumFromTo a b
    enumFromThenTo (Semi.Min a) (Semi.Min b) (Semi.Min c) = Semi.Min `map` enumFromThenTo a b c

  deriving instance Functor Semi.Min

  instance Monad Semi.Min where
    (>>) = (*>)
    Semi.Min a >>= f = f a

  instance Ord a => Semigroup (Semi.Min a) where
    Semi.Min a <> Semi.Min b = Semi.Min (a `min_` b)

  instance (Ord a, Bounded a) => Monoid (Semi.Min a) where
    mempty = maxBound

  instance Num a => Num (Semi.Min a) where
    (Semi.Min a) + (Semi.Min b) = Semi.Min (a + b)
    (Semi.Min a) * (Semi.Min b) = Semi.Min (a * b)
    (Semi.Min a) - (Semi.Min b) = Semi.Min (a - b)
    negate (Semi.Min a) = Semi.Min (negate a)
    abs    (Semi.Min a) = Semi.Min (abs a)
    signum (Semi.Min a) = Semi.Min (signum a)
    fromInteger         = Semi.Min . fromInteger

  deriving instance Foldable Semi.Min
  deriving instance Traversable Semi.Min

  instance Applicative Semi.Max where
    pure = Semi.Max
    a <* _ = a
    _ *> a = a
    Semi.Max f <*> Semi.Max x = Semi.Max (f x)
    liftA2 f (Semi.Max a) (Semi.Max b) = Semi.Max (f a b)

  instance Enum a => Enum (Semi.Max a) where
    succ (Semi.Max a) = Semi.Max (succ a)
    pred (Semi.Max a) = Semi.Max (pred a)
    toEnum = Semi.Max . toEnum
    fromEnum (Semi.Max a) = fromEnum a
    enumFromTo (Semi.Max a) (Semi.Max b) = Semi.Max `map` enumFromTo a b
    enumFromThenTo (Semi.Max a) (Semi.Max b) (Semi.Max c) = Semi.Max `map` enumFromThenTo a b c

  deriving instance Functor Semi.Max

  instance Monad Semi.Max where
    (>>) = (*>)
    Semi.Max a >>= f = f a

  instance Ord a => Semigroup (Semi.Max a) where
    Semi.Max a <> Semi.Max b = Semi.Max (a `max_` b)

  instance (Ord a, Bounded a) => Monoid (Semi.Max a) where
    mempty = minBound

  instance Num a => Num (Semi.Max a) where
    (Semi.Max a) + (Semi.Max b) = Semi.Max (a + b)
    (Semi.Max a) * (Semi.Max b) = Semi.Max (a * b)
    (Semi.Max a) - (Semi.Max b) = Semi.Max (a - b)
    negate (Semi.Max a) = Semi.Max (negate a)
    abs    (Semi.Max a) = Semi.Max (abs a)
    signum (Semi.Max a) = Semi.Max (signum a)
    fromInteger         = Semi.Max . fromInteger

  deriving instance Foldable Semi.Max
  deriving instance Traversable Semi.Max

  instance Eq a => Eq (Arg a b) where
    Arg a _ == Arg b _ = a == b

  deriving instance Functor (Arg a)

  instance Ord a => Ord (Arg a b) where
    Arg a _ `compare` Arg b _ = compare a b
    min x@(Arg a _) y@(Arg b _)
      | a <= b    = x
      | otherwise = y
    max x@(Arg a _) y@(Arg b _)
      | a >= b    = x
      | otherwise = y

  deriving instance (Show a, Show b) => Show (Arg a b)
  deriving instance Foldable (Arg a)
  deriving instance Traversable (Arg a)

  instance Applicative First where
    pure x = First x
    a <* _ = a
    _ *> a = a
    First f <*> First x = First (f x)
    liftA2 f (First a) (First b) = First (f a b)

  instance Enum a => Enum (First a) where
    succ (First a) = First (succ a)
    pred (First a) = First (pred a)
    toEnum = First . toEnum
    fromEnum (First a) = fromEnum a
    enumFromTo (First a) (First b) = First `map` enumFromTo a b
    enumFromThenTo (First a) (First b) (First c) = First `map` enumFromThenTo a b c

  deriving instance Functor First

  instance Monad First where
    (>>) = (*>)
    First a >>= f = f a

  instance Semigroup (First a) where
    a <> _ = a

  deriving instance Foldable First
  deriving instance Traversable First

  instance Applicative Last where
    pure x = Last x
    a <* _ = a
    _ *> a = a
    Last f <*> Last x = Last (f x)
    liftA2 f (Last a) (Last b) = Last (f a b)

  instance Enum a => Enum (Last a) where
    succ (Last a) = Last (succ a)
    pred (Last a) = Last (pred a)
    toEnum = Last . toEnum
    fromEnum (Last a) = fromEnum a
    enumFromTo (Last a) (Last b) = Last `map` enumFromTo a b
    enumFromThenTo (Last a) (Last b) (Last c) = Last `map` enumFromThenTo a b c

  deriving instance Functor Last

  instance Monad Last where
    (>>) = (*>)
    Last a >>= f = f a

  instance Semigroup (Last a) where
    _ <> b = b

  deriving instance Foldable Last
  deriving instance Traversable Last

  instance Monoid m => Semigroup (WrappedMonoid m) where
    WrapMonoid a <> WrapMonoid b = WrapMonoid (a `mappend` b)

  instance Monoid m => Monoid (WrappedMonoid m) where
    mempty = WrapMonoid mempty

  instance Enum a => Enum (WrappedMonoid a) where
    succ (WrapMonoid a) = WrapMonoid (succ a)
    pred (WrapMonoid a) = WrapMonoid (pred a)
    toEnum = WrapMonoid . toEnum
    fromEnum (WrapMonoid a) = fromEnum a
    enumFromTo (WrapMonoid a) (WrapMonoid b) = WrapMonoid `map` enumFromTo a b
    enumFromThenTo (WrapMonoid a) (WrapMonoid b) (WrapMonoid c) =
        WrapMonoid `map` enumFromThenTo a b c

  instance Alternative Option where
    empty = Option Nothing
    Option Nothing    <|> b = b
    a@(Option Just{}) <|> _ = a

  instance Applicative Option where
    pure a = Option (Just a)
    Option a <*> Option b = Option (a <*> b)
    liftA2 f (Option x) (Option y) = Option (liftA2 f x y)

    Option Nothing  *>  _ = Option Nothing
    Option Just{}   *>  b = b

  deriving instance Functor Option

  instance Monad Option where
    Option (Just a) >>= k = k a
    Option Nothing  >>= _ = Option Nothing
    (>>) = (*>)

  instance MonadPlus Option

  -- deriving newtype instance Semigroup a => Semigroup (Option a)
  instance Semigroup a => Semigroup (Option a) where
    Option a <> Option b = Option (a <> b)

  instance Semigroup a => Monoid (Option a) where
    mempty = Option Nothing

  instance Foldable Option where
    foldMap f (Option (Just m)) = f m
    foldMap _ (Option Nothing)  = mempty

  instance Traversable Option where
    traverse f (Option (Just a)) = Option . Just <$> f a
    traverse _ (Option Nothing)  = pure (Option Nothing)
  |])

$(singletons [d|
  -- Renamed to avoid name clash
  -- -| Fold an 'Option' case-wise, just like 'maybe'.
  option_ :: b -> (a -> b) -> Option a -> b
  option_ n j (Option m) = maybe_ n j m
  |])