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

module Test.Validity.Relations.Antireflexivity
  ( antireflexiveOnElem,
    antireflexivityOnGen,
    antireflexivity,
    antireflexivityOnArbitrary,
  )
where

import Data.GenValidity
import Test.QuickCheck

-- |
--
-- \[
--   Antireflexive(\prec)
--   \quad\equiv\quad
--   \forall a: \neg (a \prec a)
-- \]
antireflexiveOnElem ::
  -- | A relation
  (a -> a -> Bool) ->
  -- | An element
  a ->
  Bool
antireflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
antireflexiveOnElem a -> a -> Bool
func a
a = Bool -> Bool
not (Bool -> Bool) -> Bool -> Bool
forall a b. (a -> b) -> a -> b
$ a -> a -> Bool
func a
a a
a

antireflexivityOnGen ::
  Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
antireflexivityOnGen :: (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
antireflexivityOnGen 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
antireflexiveOnElem a -> a -> Bool
func

-- |
--
-- prop> antireflexivity ((<) :: Int -> Int -> Bool)
-- prop> antireflexivity ((/=) :: Int -> Int -> Bool)
-- prop> antireflexivity ((>) :: Int -> Int -> Bool)
antireflexivity :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
antireflexivity :: (a -> a -> Bool) -> Property
antireflexivity a -> a -> Bool
func = (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
forall a.
Show a =>
(a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
antireflexivityOnGen a -> a -> Bool
func Gen a
forall a. GenValid a => Gen a
genValid a -> [a]
forall a. GenValid a => a -> [a]
shrinkValid

-- |
--
-- prop> antireflexivityOnArbitrary ((<) :: Int -> Int -> Bool)
-- prop> antireflexivityOnArbitrary ((/=) :: Int -> Int -> Bool)
-- prop> antireflexivityOnArbitrary ((>) :: Int -> Int -> Bool)
antireflexivityOnArbitrary ::
  (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
antireflexivityOnArbitrary :: (a -> a -> Bool) -> Property
antireflexivityOnArbitrary a -> a -> Bool
func = (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
forall a.
Show a =>
(a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
antireflexivityOnGen a -> a -> Bool
func Gen a
forall a. Arbitrary a => Gen a
arbitrary a -> [a]
forall a. Arbitrary a => a -> [a]
shrink