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

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

import Data.GenValidity
import Test.QuickCheck

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

reflexivityOnGen ::
  Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
reflexivityOnGen :: (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
reflexivityOnGen a -> a -> Bool
func Gen a
gen a -> [a]
s = Gen a -> (a -> [a]) -> (a -> Bool) -> Property
forall a prop.
(Show a, Testable prop) =>
Gen a -> (a -> [a]) -> (a -> prop) -> Property
forAllShrink Gen a
gen a -> [a]
s ((a -> Bool) -> Property) -> (a -> Bool) -> Property
forall a b. (a -> b) -> a -> b
$ (a -> a -> Bool) -> a -> Bool
forall a. (a -> a -> Bool) -> a -> Bool
reflexiveOnElem a -> a -> Bool
func

-- |
--
-- 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, GenValid a) => (a -> a -> Bool) -> Property
reflexivity :: (a -> a -> Bool) -> Property
reflexivity a -> a -> Bool
func = (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
forall a.
Show a =>
(a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
reflexivityOnGen a -> a -> Bool
func Gen a
forall a. GenValid a => Gen a
genValid a -> [a]
forall a. GenValid a => a -> [a]
shrinkValid

-- |
--
-- 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 :: (a -> a -> Bool) -> Property
reflexivityOnArbitrary a -> a -> Bool
func = (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
forall a.
Show a =>
(a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
reflexivityOnGen a -> a -> Bool
func Gen a
forall a. Arbitrary a => Gen a
arbitrary a -> [a]
forall a. Arbitrary a => a -> [a]
shrink