Types.hs

{-# LANGUAGE PolyKinds, TypeOperators, GADTs, RankNTypes, TypeFamilies,
             CPP, DataKinds #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Singletons.Types
-- Copyright   :  (C) 2013 Richard Eisenberg
-- License     :  BSD-style (see LICENSE)
-- Maintainer  :  Richard Eisenberg (eir@cis.upenn.edu)
-- Stability   :  experimental
-- Portability :  non-portable
--
-- Defines and exports types that are useful when working with singletons.
-- Some of these are re-exports from @Data.Type.Equality@.
--
----------------------------------------------------------------------------


module Data.Singletons.Types (
  Refuted, Decision(..),
#if __GLASGOW_HASKELL__ < 707
  KProxy(..), Proxy(..),
  (:~:)(..), gcastWith, TestEquality(..)
#endif
  ) where

import Data.Singletons.Void

#if __GLASGOW_HASKELL__ < 707

-- now in Data.Proxy
data KProxy (a :: *) = KProxy
data Proxy a = Proxy

-- now in Data.Type.Equality
data a :~: b where
  Refl :: a :~: a

gcastWith :: (a :~: b) -> ((a ~ b) => r) -> r
gcastWith Refl x = x

class TestEquality (f :: k -> *) where
  testEquality :: f a -> f b -> Maybe (a :~: b)

#endif

-- | Because we can never create a value of type 'Void', a function that type-checks
-- at @a -> Void@ shows that objects of type @a@ can never exist. Thus, we say that
-- @a@ is 'Refuted'
type Refuted a = (a -> Void)

-- | A 'Decision' about a type @a@ is either a proof of existence or a proof that @a@
-- cannot exist.
data Decision a = Proved a               -- ^ Witness for @a@
                | Disproved (Refuted a)  -- ^ Proof that no @a@ exists