Reflexivity.hs

{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}

module Test.Syd.Validity.Relations.Reflexivity
    ( reflexiveOnElem
    , reflexivityOnGen
    , reflexivityOnValid
    , reflexivity
    , reflexivityOnArbitrary
    ) where

import Data.GenValidity

import Test.QuickCheck

-- |
--
-- \[
--   Reflexive(\prec)
--   \quad\equiv\quad
--   \forall a: (a \prec a)
-- \]
reflexiveOnElem ::
       (a -> a -> Bool) -- ^ A relation
    -> a -- ^ An element
    -> Bool
reflexiveOnElem func a = func a a

reflexivityOnGen ::
       Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
reflexivityOnGen func gen s = forAllShrink gen s $ reflexiveOnElem func

-- |
--
-- prop> reflexivityOnValid ((<=) :: Rational -> Rational -> Bool)
-- prop> reflexivityOnValid ((==) :: Rational -> Rational -> Bool)
-- prop> reflexivityOnValid ((>=) :: Rational -> Rational -> Bool)
-- prop> reflexivityOnValid (Data.List.isPrefixOf :: [Rational] -> [Rational] -> Bool)
-- prop> reflexivityOnValid (Data.List.isSuffixOf :: [Rational] -> [Rational] -> Bool)
-- prop> reflexivityOnValid (Data.List.isInfixOf :: [Rational] -> [Rational] -> Bool)
reflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
reflexivityOnValid func = reflexivityOnGen func genValid shrinkValid

-- |
--
-- prop> reflexivity ((<=) :: Int -> Int -> Bool)
-- prop> reflexivity ((==) :: Int -> Int -> Bool)
-- prop> reflexivity ((>=) :: Int -> Int -> Bool)
-- prop> reflexivity (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
-- prop> reflexivity (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
-- prop> reflexivity (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
reflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property
reflexivity func = reflexivityOnGen func genUnchecked shrinkUnchecked

-- |
--
-- prop> reflexivityOnArbitrary ((<=) :: Int -> Int -> Bool)
-- prop> reflexivityOnArbitrary ((==) :: Int -> Int -> Bool)
-- prop> reflexivityOnArbitrary ((>=) :: Int -> Int -> Bool)
-- prop> reflexivityOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
-- prop> reflexivityOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
-- prop> reflexivityOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
reflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
reflexivityOnArbitrary func = reflexivityOnGen func arbitrary shrink