{-# LANGUAGE ScopedTypeVariables #-}
{-# OPTIONS_GHC -Wall #-}
module Test.QuickCheck.Classes.Eq
( eqLaws
) where
import Data.Proxy (Proxy)
import Test.QuickCheck hiding ((.&.))
import Test.QuickCheck.Property (Property)
import Test.QuickCheck.Classes.Internal (Laws(..))
-- | Tests the following properties:
--
-- [/Transitive/]
-- @a == b ∧ b == c ⇒ a == c@
-- [/Symmetric/]
-- @a == b ⇒ b == a@
-- [/Reflexive/]
-- @a == a@
--
-- Some of these properties involve implication. In the case that
-- the left hand side of the implication arrow does not hold, we
-- do not retry. Consequently, these properties only end up being
-- useful when the data type has a small number of inhabitants.
eqLaws :: (Eq a, Arbitrary a, Show a) => Proxy a -> Laws
eqLaws p = Laws "Eq"
[ ("Transitive", eqTransitive p)
, ("Symmetric", eqSymmetric p)
, ("Reflexive", eqReflexive p)
]
eqTransitive :: forall a. (Show a, Eq a, Arbitrary a) => Proxy a -> Property
eqTransitive _ = property $ \(a :: a) b c -> case a == b of
True -> case b == c of
True -> a == c
False -> a /= c
False -> case b == c of
True -> a /= c
False -> True
eqSymmetric :: forall a. (Show a, Eq a, Arbitrary a) => Proxy a -> Property
eqSymmetric _ = property $ \(a :: a) b -> case a == b of
True -> b == a
False -> b /= a
eqReflexive :: forall a. (Show a, Eq a, Arbitrary a) => Proxy a -> Property
eqReflexive _ = property $ \(a :: a) -> a == a