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{-# LANGUAGE TypeOperators, DataKinds, PolyKinds, TypeFamilies,
RankNTypes, FlexibleContexts, TemplateHaskell,
UndecidableInstances, GADTs, DefaultSignatures #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Singletons.Prelude.Eq
-- Copyright : (C) 2013 Richard Eisenberg
-- License : BSD-style (see LICENSE)
-- Maintainer : Richard Eisenberg (eir@cis.upenn.edu)
-- Stability : experimental
-- Portability : non-portable
--
-- Defines the SEq singleton version of the Eq type class.
--
-----------------------------------------------------------------------------
module Data.Singletons.Prelude.Eq (
PEq(..), SEq(..),
(:==$), (:==$$), (:==$$$), (:/=$), (:/=$$), (:/=$$$)
) where
import Data.Singletons.Prelude.Bool
import Data.Singletons
import Data.Singletons.Single
import Data.Singletons.Prelude.Instances
import Data.Singletons.Util
import Data.Singletons.Promote
import Data.Type.Equality
-- NB: These must be defined by hand because of the custom handling of the
-- default for (:==) to use Data.Type.Equality.==
-- | The promoted analogue of 'Eq'. If you supply no definition for '(:==)',
-- then it defaults to a use of '(==)', from @Data.Type.Equality@.
class kproxy ~ 'KProxy => PEq (kproxy :: KProxy a) where
type (:==) (x :: a) ( y :: a) :: Bool
type (:/=) ( (x :: a) ) (y :: a ) :: Bool
type {- a -} ({- b -}:/:{- c -}) {- d -} ({- e -}x {- f -} :: {- g -} a {- h -}) {- i -} ({- j -}y {- k -}::{- l -} a{- m -}){- n -} ::{- o -} Bool {- p -}
type (x :: a) :== (y :: a) = x == y
type (x :: a) :/= (y :: a) = Not (x :== y)
infix 4 :==
infix 4 :/=
$(genDefunSymbols [''(:==), ''(:/=)])
-- | The singleton analogue of 'Eq'. Unlike the definition for 'Eq', it is
-- required that instances define a body for '(%:==)'. You may also supply a
-- body for '(%:/=)'.
class (kparam ~ 'KProxy) => SEq (kparam :: KProxy k) where
-- | Boolean equality on singletons
(%:==) :: forall (a :: k) (b :: k). Sing a -> Sing b -> Sing (a :== b)
infix 4 %:==
-- | Boolean disequality on singletons
(%:/=) :: forall (a :: k) (b :: k). Sing a -> Sing b -> Sing (a :/= b)
default (%:/=) :: forall (a :: k) (b :: k).
((a :/= b) ~ Not (a :== b))
=> Sing a -> Sing b -> Sing (a :/= b)
a %:/= b = sNot (a %:== b)
infix 4 %:/=
$(singEqInstances basicTypes)
$singEqInstances basicTypes
singEqInstances basicTypes
|
