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

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

import Data.GenValidity

import Test.QuickCheck

-- |
--
-- \[
--   Antireflexive(\prec)
--   \quad\equiv\quad
--   \forall a: \neg (a \prec a)
-- \]
antireflexiveOnElem ::
       (a -> a -> Bool) -- ^ A relation
    -> a -- ^ An element
    -> 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> antireflexivityOnValid ((<) :: Rational -> Rational -> Bool)
-- prop> antireflexivityOnValid ((/=) :: Rational -> Rational -> Bool)
-- prop> antireflexivityOnValid ((>) :: Rational -> Rational -> Bool)
antireflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
antireflexivityOnValid :: (a -> a -> Bool) -> Property
antireflexivityOnValid 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> antireflexivity ((<) :: Int -> Int -> Bool)
-- prop> antireflexivity ((/=) :: Int -> Int -> Bool)
-- prop> antireflexivity ((>) :: Int -> Int -> Bool)
antireflexivity :: (Show a, GenUnchecked 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. GenUnchecked a => Gen a
genUnchecked a -> [a]
forall a. GenUnchecked a => a -> [a]
shrinkUnchecked

-- |
--
-- 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