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

module Test.Validity.Operations.Commutativity
    ( commutativeOnGens
    , commutativeOnValids
    , commutative
    , commutativeOnArbitrary
    ) where

import Data.GenValidity

import Test.Hspec
import Test.QuickCheck

-- |
--
-- \[
--     Commutative(\star)
--     \quad\equiv\quad
--     \forall a, b:
--     a \star b = b \star a
-- \]
commutativeOnGens ::
       (Show a, Eq a)
    => (a -> a -> a)
    -> Gen (a, a)
    -> ((a, a) -> [(a, a)])
    -> Property
commutativeOnGens :: (a -> a -> a) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property
commutativeOnGens op :: a -> a -> a
op gen :: Gen (a, a)
gen s :: (a, a) -> [(a, a)]
s =
    Gen (a, a)
-> ((a, a) -> [(a, a)]) -> ((a, a) -> Expectation) -> Property
forall a prop.
(Show a, Testable prop) =>
Gen a -> (a -> [a]) -> (a -> prop) -> Property
forAllShrink Gen (a, a)
gen (a, a) -> [(a, a)]
s (((a, a) -> Expectation) -> Property)
-> ((a, a) -> Expectation) -> Property
forall a b. (a -> b) -> a -> b
$ \(a :: a
a, b :: a
b) -> (a
a a -> a -> a
`op` a
b) a -> a -> Expectation
forall a. (HasCallStack, Show a, Eq a) => a -> a -> Expectation
`shouldBe` (a
b a -> a -> a
`op` a
a)

-- |
--
-- prop> commutativeOnValids ((+) :: Rational -> Rational -> Rational)
-- prop> commutativeOnValids ((*) :: Rational -> Rational -> Rational)
commutativeOnValids :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> Property
commutativeOnValids :: (a -> a -> a) -> Property
commutativeOnValids op :: a -> a -> a
op = (a -> a -> a) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property
forall a.
(Show a, Eq a) =>
(a -> a -> a) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property
commutativeOnGens a -> a -> a
op Gen (a, a)
forall a. GenValid a => Gen a
genValid (a, a) -> [(a, a)]
forall a. GenValid a => a -> [a]
shrinkValid

-- |
--
-- prop> commutative ((+) :: Int -> Int -> Int)
-- prop> commutative ((*) :: Int -> Int -> Int)
commutative :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> Property
commutative :: (a -> a -> a) -> Property
commutative op :: a -> a -> a
op = (a -> a -> a) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property
forall a.
(Show a, Eq a) =>
(a -> a -> a) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property
commutativeOnGens a -> a -> a
op Gen (a, a)
forall a. GenUnchecked a => Gen a
genUnchecked (a, a) -> [(a, a)]
forall a. GenUnchecked a => a -> [a]
shrinkUnchecked

-- |
--
-- prop> commutativeOnArbitrary ((+) :: Int -> Int -> Int)
-- prop> commutativeOnArbitrary ((*) :: Int -> Int -> Int)
commutativeOnArbitrary ::
       (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> Property
commutativeOnArbitrary :: (a -> a -> a) -> Property
commutativeOnArbitrary op :: a -> a -> a
op = (a -> a -> a) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property
forall a.
(Show a, Eq a) =>
(a -> a -> a) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property
commutativeOnGens a -> a -> a
op Gen (a, a)
forall a. Arbitrary a => Gen a
arbitrary (a, a) -> [(a, a)]
forall a. Arbitrary a => a -> [a]
shrink