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

module Test.Validity.Relations.Transitivity
  ( transitiveOnElems,
    transitivityOnGens,
    transitivity,
    transitivityOnArbitrary,
  )
where

import Data.GenValidity
import Test.QuickCheck
import Test.Validity.Property.Utils

-- |
--
-- \[
--   Transitive(\prec)
--   \quad\equiv\quad
--   \forall a, b, c: ((a \prec b) \wedge (b \prec c)) \Rightarrow (a \prec c)
-- \]
transitiveOnElems ::
  -- | A relation
  (a -> a -> Bool) ->
  a ->
  a ->
  -- | Three elements
  a ->
  Bool
transitiveOnElems :: (a -> a -> Bool) -> a -> a -> a -> Bool
transitiveOnElems a -> a -> Bool
func a
a a
b a
c = (a -> a -> Bool
func a
a a
b Bool -> Bool -> Bool
&& a -> a -> Bool
func a
b a
c) Bool -> Bool -> Bool
===> a -> a -> Bool
func a
a a
c

transitivityOnGens ::
  Show a => (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property
transitivityOnGens :: (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property
transitivityOnGens a -> a -> Bool
func Gen (a, a, a)
gen a -> [a]
s =
  Gen (a, a, a)
-> ((a, a, a) -> [(a, a, a)]) -> ((a, a, a) -> Bool) -> Property
forall a prop.
(Show a, Testable prop) =>
Gen a -> (a -> [a]) -> (a -> prop) -> Property
forAllShrink Gen (a, a, a)
gen ((a -> [a]) -> (a, a, a) -> [(a, a, a)]
forall a. (a -> [a]) -> (a, a, a) -> [(a, a, a)]
shrinkT3 a -> [a]
s) (((a, a, a) -> Bool) -> Property)
-> ((a, a, a) -> Bool) -> Property
forall a b. (a -> b) -> a -> b
$ \(a
a, a
b, a
c) -> (a -> a -> Bool) -> a -> a -> a -> Bool
forall a. (a -> a -> Bool) -> a -> a -> a -> Bool
transitiveOnElems a -> a -> Bool
func a
a a
b a
c

-- |
--
-- prop> transitivity ((>) :: Int -> Int -> Bool)
-- prop> transitivity ((>=) :: Int -> Int -> Bool)
-- prop> transitivity ((==) :: Int -> Int -> Bool)
-- prop> transitivity ((<=) :: Int -> Int -> Bool)
-- prop> transitivity ((<) :: Int -> Int -> Bool)
-- prop> transitivity (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
-- prop> transitivity (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
-- prop> transitivity (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
transitivity :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
transitivity :: (a -> a -> Bool) -> Property
transitivity a -> a -> Bool
func = (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property
forall a.
Show a =>
(a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property
transitivityOnGens a -> a -> Bool
func Gen (a, a, a)
forall a. GenValid a => Gen a
genValid a -> [a]
forall a. GenValid a => a -> [a]
shrinkValid

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