{-# LANGUAGE DeriveTraversable #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE LambdaCase #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE UndecidableInstances #-} -- | Operations on /sums/, combining effects into a /signature/. -- -- @since 0.1.0.0 module Control.Effect.Sum ( -- * Membership Member(..) , Members -- * Sums , (:+:)(..) , reassociateSumL ) where import Data.Kind (Constraint, Type) -- | Higher-order sums are used to combine multiple effects into a signature, typically by chaining on the right. data (f :+: g) (m :: Type -> Type) k = L (f m k) | R (g m k) deriving (Eq, Foldable, Functor, Ord, Show, Traversable) infixr 4 :+: -- | The class of types present in a signature. -- -- This is based on Wouter Swierstra’s design described in [Data types à la carte](http://www.cs.ru.nl/~W.Swierstra/Publications/DataTypesALaCarte.pdf). As described therein, overlapping instances are required in order to distinguish e.g. left-occurrence from right-recursion. -- -- It should not generally be necessary for you to define new 'Member' instances, but these are not specifically prohibited if you wish to get creative. -- -- @since 0.1.0.0 class Member (sub :: (Type -> Type) -> (Type -> Type)) sup where -- | Inject a member of a signature into the signature. inj :: sub m a -> sup m a -- | Reflexivity: @t@ is a member of itself. instance Member t t where inj = id {-# INLINE inj #-} -- | Left-recursion: if @t@ is a member of @l1 ':+:' l2 ':+:' r@, then we can inject it into @(l1 ':+:' l2) ':+:' r@ by injection into a right-recursive signature, followed by left-association. instance {-# OVERLAPPABLE #-} Member t (l1 :+: l2 :+: r) => Member t ((l1 :+: l2) :+: r) where inj = reassociateSumL . inj {-# INLINE inj #-} -- | Left-occurrence: if @t@ is at the head of a signature, we can inject it in O(1). instance {-# OVERLAPPABLE #-} Member l (l :+: r) where inj = L {-# INLINE inj #-} -- | Right-recursion: if @t@ is a member of @r@, we can inject it into @r@ in O(n), followed by lifting that into @l ':+:' r@ in O(1). instance {-# OVERLAPPABLE #-} Member l r => Member l (l' :+: r) where inj = R . inj {-# INLINE inj #-} -- | Reassociate a right-nested sum leftwards. -- -- @since 1.0.2.0 reassociateSumL :: (l1 :+: l2 :+: r) m a -> ((l1 :+: l2) :+: r) m a reassociateSumL = \case L l -> L (L l) R (L l) -> L (R l) R (R r) -> R r {-# INLINE reassociateSumL #-} -- | Decompose sums on the left into multiple 'Member' constraints. -- -- Note that while this, and by extension 'Control.Algebra.Has', can be used to group together multiple membership checks into a single (composite) constraint, large signatures on the left can slow compiles down due to [a problem with recursive type families](https://gitlab.haskell.org/ghc/ghc/issues/8095). -- -- @since 1.0.0.0 type family Members sub sup :: Constraint where Members (l :+: r) u = (Members l u, Members r u) Members t u = Member t u