{- HLINT ignore "Use camelCase" -}
{- HLINT ignore "Redundant bracket" -}

-- |
-- Copyright: © 2022 Jonathan Knowles
-- License: Apache-2.0
--
-- This module provides 'Laws' definitions for classes exported by
-- "Data.Monoid.GCD".
--
module Test.QuickCheck.Classes.Monoid.GCD
    ( gcdMonoidLaws
    , cancellativeGCDMonoidLaws
    , leftGCDMonoidLaws
    , rightGCDMonoidLaws
    , overlappingGCDMonoidLaws
    )
    where

import Prelude hiding
    ( gcd )

import Data.Function
    ( (&) )
import Data.Maybe
    ( isJust )
import Data.Monoid.GCD
    ( GCDMonoid (..)
    , LeftGCDMonoid (..)
    , OverlappingGCDMonoid (..)
    , RightGCDMonoid (..)
    )
import Data.Proxy
    ( Proxy (..) )
import Data.Semigroup.Cancellative
    ( Cancellative, LeftReductive (..), Reductive (..), RightReductive (..) )
import Internal
    ( cover, makeLaw2, makeLaw3, makeProperty, report )
import Test.QuickCheck
    ( Arbitrary (..), Property )
import Test.QuickCheck.Classes
    ( Laws (..) )

--------------------------------------------------------------------------------
-- CancellativeGCDMonoid
--------------------------------------------------------------------------------

-- | 'Laws' for instances of 'Cancellative' and 'GCDMonoid'.
--
-- Tests the following laws:
--
-- @
-- 'gcd' (a '<>' b) (a '<>' c) '==' a '<>' 'gcd' b c
-- @
--
-- @
-- 'gcd' (a '<>' c) (b '<>' c) '==' 'gcd' a b '<>' c
-- @
--
-- Note that the following superclass laws are __not__ included:
--
-- * 'Test.QuickCheck.Classes.Semigroup.Cancellative.cancellativeLaws'
-- * 'Test.QuickCheck.Classes.Monoid.GCD.gcdMonoidLaws'
--
cancellativeGCDMonoidLaws
    :: forall a. (Arbitrary a, Show a, Eq a, Cancellative a, GCDMonoid a)
    => Proxy a
    -> Laws
cancellativeGCDMonoidLaws :: forall a.
(Arbitrary a, Show a, Eq a, Cancellative a, GCDMonoid a) =>
Proxy a -> Laws
cancellativeGCDMonoidLaws Proxy a
_ = String -> [(String, Property)] -> Laws
Laws String
"CancellativeGCDMonoid"
    [ forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> a -> t) -> (String, Property)
makeLaw3 @a
        String
"cancellativeGCDMonoidLaw_prefix"
        (forall a.
(Eq a, Show a, Cancellative a, GCDMonoid a) =>
a -> a -> a -> Property
cancellativeGCDMonoidLaw_prefix)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> a -> t) -> (String, Property)
makeLaw3 @a
        String
"cancellativeGCDMonoidLaw_suffix"
        (forall a.
(Eq a, Show a, Cancellative a, GCDMonoid a) =>
a -> a -> a -> Property
cancellativeGCDMonoidLaw_suffix)
    ]

cancellativeGCDMonoidLaw_prefix
    :: (Eq a, Show a, Cancellative a, GCDMonoid a) => a -> a -> a -> Property
cancellativeGCDMonoidLaw_prefix :: forall a.
(Eq a, Show a, Cancellative a, GCDMonoid a) =>
a -> a -> a -> Property
cancellativeGCDMonoidLaw_prefix a
a a
b a
c =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"gcd (a <> b) (a <> c) == a <> gcd b c"
        (forall m. GCDMonoid m => m -> m -> m
gcd (a
a forall a. Semigroup a => a -> a -> a
<> a
b) (a
a forall a. Semigroup a => a -> a -> a
<> a
c) forall a. Eq a => a -> a -> Bool
== a
a forall a. Semigroup a => a -> a -> a
<> forall m. GCDMonoid m => m -> m -> m
gcd a
b a
c)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"a <> b"
        (a
a forall a. Semigroup a => a -> a -> a
<> a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"a <> c"
        (a
a forall a. Semigroup a => a -> a -> a
<> a
c)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"gcd (a <> b) (a <> c)"
        (forall m. GCDMonoid m => m -> m -> m
gcd (a
a forall a. Semigroup a => a -> a -> a
<> a
b) (a
a forall a. Semigroup a => a -> a -> a
<> a
c))
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"gcd b c"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
b a
c)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"a <> gcd b c"
        (a
a forall a. Semigroup a => a -> a -> a
<> forall m. GCDMonoid m => m -> m -> m
gcd a
b a
c)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"a /= mempty && gcd b c /= mempty && a /= gcd b c"
        (a
a forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& forall m. GCDMonoid m => m -> m -> m
gcd a
b a
c forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
a forall a. Eq a => a -> a -> Bool
/= forall m. GCDMonoid m => m -> m -> m
gcd a
b a
c)

cancellativeGCDMonoidLaw_suffix
    :: (Eq a, Show a, Cancellative a, GCDMonoid a) => a -> a -> a -> Property
cancellativeGCDMonoidLaw_suffix :: forall a.
(Eq a, Show a, Cancellative a, GCDMonoid a) =>
a -> a -> a -> Property
cancellativeGCDMonoidLaw_suffix a
a a
b a
c =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"gcd (a <> c) (b <> c) == gcd a b <> c"
        (forall m. GCDMonoid m => m -> m -> m
gcd (a
a forall a. Semigroup a => a -> a -> a
<> a
c) (a
b forall a. Semigroup a => a -> a -> a
<> a
c) forall a. Eq a => a -> a -> Bool
== forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b forall a. Semigroup a => a -> a -> a
<> a
c)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"a <> c"
        (a
a forall a. Semigroup a => a -> a -> a
<> a
c)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"b <> c"
        (a
b forall a. Semigroup a => a -> a -> a
<> a
c)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"gcd (a <> c) (b <> c)"
        (forall m. GCDMonoid m => m -> m -> m
gcd (a
a forall a. Semigroup a => a -> a -> a
<> a
c) (a
b forall a. Semigroup a => a -> a -> a
<> a
c))
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"gcd a b"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"gcd a b <> c"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b forall a. Semigroup a => a -> a -> a
<> a
c)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"c /= mempty && gcd a b /= mempty && c /= gcd a b"
        (a
c forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
c forall a. Eq a => a -> a -> Bool
/= forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b)

--------------------------------------------------------------------------------
-- GCDMonoid
--------------------------------------------------------------------------------

-- | 'Laws' for instances of 'GCDMonoid'.
--
-- Tests the following laws:
--
-- @
-- 'gcd' a b '==' 'commonPrefix' a b
-- @
--
-- @
-- 'gcd' a b '==' 'commonSuffix' a b
-- @
--
-- @
-- 'isJust' (a '</>' 'gcd' a b)
-- @
--
-- @
-- 'isJust' (b '</>' 'gcd' a b)
-- @
--
-- Note that the following superclass laws are __not__ included:
--
-- * 'Test.QuickCheck.Classes.monoidLaws'
-- * 'Test.QuickCheck.Classes.Semigroup.Cancellative.commutativeLaws'
-- * 'Test.QuickCheck.Classes.Semigroup.Cancellative.reductiveLaws'
-- * 'Test.QuickCheck.Classes.Monoid.GCD.leftGCDMonoidLaws'
-- * 'Test.QuickCheck.Classes.Monoid.GCD.rightGCDMonoidLaws'
-- * 'Test.QuickCheck.Classes.Monoid.GCD.overlappingGCDMonoidLaws'
--
gcdMonoidLaws
    :: forall a. (Arbitrary a, Show a, Eq a, GCDMonoid a)
    => Proxy a
    -> Laws
gcdMonoidLaws :: forall a.
(Arbitrary a, Show a, Eq a, GCDMonoid a) =>
Proxy a -> Laws
gcdMonoidLaws Proxy a
_ = String -> [(String, Property)] -> Laws
Laws String
"GCDMonoid"
    [ forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"gcdMonoidLaw_gcd_commonPrefix"
        (forall a. (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_commonPrefix)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"gcdMonoidLaw_gcd_commonSuffix"
        (forall a. (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_commonSuffix)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"gcdMonoidLaw_gcd_reduction_1"
        (forall a. (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_reduction_1)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"gcdMonoidLaw_gcd_reduction_2"
        (forall a. (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_reduction_2)
    ]

gcdMonoidLaw_gcd_commonPrefix
    :: (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_commonPrefix :: forall a. (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_commonPrefix a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"gcd a b == commonPrefix a b"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b forall a. Eq a => a -> a -> Bool
== forall m. LeftGCDMonoid m => m -> m -> m
commonPrefix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"gcd a b /= mempty"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"commonPrefix a b /= mempty"
        (forall m. LeftGCDMonoid m => m -> m -> m
commonPrefix a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"gcd a b"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"commonPrefix a b"
        (forall m. LeftGCDMonoid m => m -> m -> m
commonPrefix a
a a
b)

gcdMonoidLaw_gcd_commonSuffix
    :: (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_commonSuffix :: forall a. (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_commonSuffix a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"gcd a b == commonSuffix a b"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b forall a. Eq a => a -> a -> Bool
== forall m. RightGCDMonoid m => m -> m -> m
commonSuffix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"gcd a b /= mempty"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"commonSuffix a b /= mempty"
        (forall m. RightGCDMonoid m => m -> m -> m
commonSuffix a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"gcd a b"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"commonSuffix a b"
        (forall m. RightGCDMonoid m => m -> m -> m
commonSuffix a
a a
b)

gcdMonoidLaw_gcd_reduction_1
    :: (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_reduction_1 :: forall a. (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_reduction_1 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"isJust (a </> gcd a b)"
        (forall a. Maybe a -> Bool
isJust (a
a forall m. Reductive m => m -> m -> Maybe m
</> forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b))
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"gcd a b /= mempty"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"(a </> gcd a b) /= mempty"
        ((a
a forall m. Reductive m => m -> m -> Maybe m
</> forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b) forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"gcd a b"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"a </> gcd a b"
        (a
a forall m. Reductive m => m -> m -> Maybe m
</> forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b)

gcdMonoidLaw_gcd_reduction_2
    :: (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_reduction_2 :: forall a. (Eq a, Show a, GCDMonoid a) => a -> a -> Property
gcdMonoidLaw_gcd_reduction_2 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"isJust (b </> gcd a b)"
        (forall a. Maybe a -> Bool
isJust (a
b forall m. Reductive m => m -> m -> Maybe m
</> forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b))
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"gcd a b /= mempty"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"(b </> gcd a b) /= mempty"
        ((a
b forall m. Reductive m => m -> m -> Maybe m
</> forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b) forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"gcd a b"
        (forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"b </> gcd a b"
        (a
b forall m. Reductive m => m -> m -> Maybe m
</> forall m. GCDMonoid m => m -> m -> m
gcd a
a a
b)

--------------------------------------------------------------------------------
-- LeftGCDMonoid
--------------------------------------------------------------------------------

-- | 'Laws' for instances of 'LeftGCDMonoid'.
--
-- Tests the following laws:
--
-- @
-- 'stripCommonPrefix' a b '&' \\(p, _, _) -> p '==' 'commonPrefix' a b
-- @
--
-- @
-- 'stripCommonPrefix' a b '&' \\(p, x, _) -> p '<>' x '==' a
-- @
--
-- @
-- 'stripCommonPrefix' a b '&' \\(p, _, x) -> p '<>' x '==' b
-- @
--
-- @
-- 'stripCommonPrefix' a b '&' \\(p, x, _) -> 'Just' x '==' 'stripPrefix' p a
-- @
--
-- @
-- 'stripCommonPrefix' a b '&' \\(p, _, x) -> 'Just' x '==' 'stripPrefix' p b
-- @
--
-- Note that the following superclass laws are __not__ included:
--
-- * 'Test.QuickCheck.Classes.monoidLaws'
-- * 'Test.QuickCheck.Classes.Semigroup.Cancellative.leftReductiveLaws'
--
leftGCDMonoidLaws
    :: forall a. (Arbitrary a, Show a, Eq a, LeftGCDMonoid a)
    => Proxy a
    -> Laws
leftGCDMonoidLaws :: forall a.
(Arbitrary a, Show a, Eq a, LeftGCDMonoid a) =>
Proxy a -> Laws
leftGCDMonoidLaws Proxy a
_ = String -> [(String, Property)] -> Laws
Laws String
"LeftGCDMonoid"
    [ forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"leftGCDMonoidLaw_stripCommonPrefix_commonPrefix"
        (forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_commonPrefix)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"leftGCDMonoidLaw_stripCommonPrefix_mappend_1"
        (forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_mappend_1)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"leftGCDMonoidLaw_stripCommonPrefix_mappend_2"
        (forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_mappend_2)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_1"
        (forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_1)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_2"
        (forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_2)
    ]

leftGCDMonoidLaw_stripCommonPrefix_commonPrefix
    :: (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_commonPrefix :: forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_commonPrefix a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonPrefix a b & λ(p, _, _) -> p == commonPrefix a b"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
_, a
_) -> a
p forall a. Eq a => a -> a -> Bool
== forall m. LeftGCDMonoid m => m -> m -> m
commonPrefix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"commonPrefix a b /= mempty"
        (forall m. LeftGCDMonoid m => m -> m -> m
commonPrefix a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonPrefix a b"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"commonPrefix a b"
        (forall m. LeftGCDMonoid m => m -> m -> m
commonPrefix a
a a
b)

leftGCDMonoidLaw_stripCommonPrefix_mappend_1
    :: (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_mappend_1 :: forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_mappend_1 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonPrefix a b & λ(p, x, _) -> p <> x == a"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
x, a
_) -> a
p forall a. Semigroup a => a -> a -> a
<> a
x forall a. Eq a => a -> a -> Bool
== a
a)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripCommonPrefix a b & λ(p, x, _) -> p /= mempty && x /= mempty"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
x, a
_) -> a
p forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
x forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonPrefix a b"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonPrefix a b & λ(p, x, _) -> p <> x"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
x, a
_) -> a
p forall a. Semigroup a => a -> a -> a
<> a
x)

leftGCDMonoidLaw_stripCommonPrefix_mappend_2
    :: (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_mappend_2 :: forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_mappend_2 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonPrefix a b & λ(p, _, x) -> p <> x == b"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
_, a
x) -> a
p forall a. Semigroup a => a -> a -> a
<> a
x forall a. Eq a => a -> a -> Bool
== a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripCommonPrefix a b & λ(p, _, x) -> p /= mempty && x /= mempty"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
_, a
x) -> a
p forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
x forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonPrefix a b"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonPrefix a b & λ(p, _, x) -> p <> x"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
_, a
x) -> a
p forall a. Semigroup a => a -> a -> a
<> a
x)

leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_1
    :: (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_1 :: forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_1 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonPrefix a b & λ(p, x, _) -> Just x == stripPrefix p a"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
x, a
_) -> forall a. a -> Maybe a
Just a
x forall a. Eq a => a -> a -> Bool
== forall m. LeftReductive m => m -> m -> Maybe m
stripPrefix a
p a
a)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripCommonPrefix a b & λ(p, x, _) -> p /= mempty && x /= mempty"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
x, a
_) -> a
p forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
x forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonPrefix a b"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonPrefix a b & λ(p, _, _) -> stripPrefix p a"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
_, a
_) -> forall m. LeftReductive m => m -> m -> Maybe m
stripPrefix a
p a
a)

leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_2
    :: (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_2 :: forall a. (Eq a, Show a, LeftGCDMonoid a) => a -> a -> Property
leftGCDMonoidLaw_stripCommonPrefix_stripPrefix_2 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonPrefix a b & λ(p, _, x) -> Just x == stripPrefix p b"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
_, a
x) -> forall a. a -> Maybe a
Just a
x forall a. Eq a => a -> a -> Bool
== forall m. LeftReductive m => m -> m -> Maybe m
stripPrefix a
p a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripCommonPrefix a b & λ(p, _, x) -> p /= mempty && x /= mempty"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
_, a
x) -> a
p forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
x forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonPrefix a b"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonPrefix a b & λ(p, _, _) -> stripPrefix p b"
        (forall m. LeftGCDMonoid m => m -> m -> (m, m, m)
stripCommonPrefix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
p, a
_, a
_) -> forall m. LeftReductive m => m -> m -> Maybe m
stripPrefix a
p a
b)

--------------------------------------------------------------------------------
-- OverlappingGCDMonoid
--------------------------------------------------------------------------------

-- | 'Laws' for instances of 'OverlappingGCDMonoid'.
--
-- Tests the following laws:
--
-- @
-- 'overlap' a b '<>' 'stripPrefixOverlap' a b '==' b
-- @
--
-- @
-- 'stripSuffixOverlap' b a '<>' 'overlap' a b '==' a
-- @
--
-- @
-- 'stripOverlap' a b '&' \\(_, x, _) -> x '==' 'overlap' a b
-- @
--
-- @
-- 'stripOverlap' a b '&' \\(_, _, x) -> x '==' 'stripPrefixOverlap' a b
-- @
--
-- @
-- 'stripOverlap' a b '&' \\(x, _, _) -> x '==' 'stripSuffixOverlap' b a
-- @
--
-- Note that the following superclass laws are __not__ included:
--
-- * 'Test.QuickCheck.Classes.monoidLaws'
-- * 'Test.QuickCheck.Classes.Semigroup.Cancellative.leftReductiveLaws'
-- * 'Test.QuickCheck.Classes.Semigroup.Cancellative.rightReductiveLaws'
--
overlappingGCDMonoidLaws
    :: forall a. (Arbitrary a, Show a, Eq a, OverlappingGCDMonoid a)
    => Proxy a
    -> Laws
overlappingGCDMonoidLaws :: forall a.
(Arbitrary a, Show a, Eq a, OverlappingGCDMonoid a) =>
Proxy a -> Laws
overlappingGCDMonoidLaws Proxy a
_ = String -> [(String, Property)] -> Laws
Laws String
"OverlappingGCDMonoid"
    [ forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"overlappingGCDMonoidLaw_overlap_stripPrefixOverlap"
        (forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_overlap_stripPrefixOverlap)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"overlappingGCDMonoidLaw_overlap_stripSuffixOverlap"
        (forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_overlap_stripSuffixOverlap)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"overlappingGCDMonoidLaw_stripOverlap_overlap"
        (forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_stripOverlap_overlap)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"overlappingGCDMonoidLaw_stripOverlap_stripPrefixOverlap"
        (forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_stripOverlap_stripPrefixOverlap)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"overlappingGCDMonoidLaw_stripOverlap_stripSuffixOverlap"
        (forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_stripOverlap_stripSuffixOverlap)
    ]

overlappingGCDMonoidLaw_overlap_stripPrefixOverlap
    :: (Eq a, Show a, OverlappingGCDMonoid a) => a -> a -> Property
overlappingGCDMonoidLaw_overlap_stripPrefixOverlap :: forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_overlap_stripPrefixOverlap a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"overlap a b <> stripPrefixOverlap a b == b"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b forall a. Semigroup a => a -> a -> a
<> forall m. OverlappingGCDMonoid m => m -> m -> m
stripPrefixOverlap a
a a
b forall a. Eq a => a -> a -> Bool
== a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"overlap a b /= mempty && stripPrefixOverlap a b /= mempty"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& forall m. OverlappingGCDMonoid m => m -> m -> m
stripPrefixOverlap a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"overlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripPrefixOverlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
stripPrefixOverlap a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"overlap a b <> stripPrefixOverlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b forall a. Semigroup a => a -> a -> a
<> forall m. OverlappingGCDMonoid m => m -> m -> m
stripPrefixOverlap a
a a
b)

overlappingGCDMonoidLaw_overlap_stripSuffixOverlap
    :: (Eq a, Show a, OverlappingGCDMonoid a) => a -> a -> Property
overlappingGCDMonoidLaw_overlap_stripSuffixOverlap :: forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_overlap_stripSuffixOverlap a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripSuffixOverlap b a <> overlap a b == a"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
stripSuffixOverlap a
b a
a forall a. Semigroup a => a -> a -> a
<> forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b forall a. Eq a => a -> a -> Bool
== a
a)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripSuffixOverlap b a /= mempty && overlap a b /= mempty"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
stripSuffixOverlap a
b a
a forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripSuffixOverlap b a"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
stripSuffixOverlap a
b a
a)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"overlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripSuffixOverlap b a <> overlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
stripSuffixOverlap a
b a
a forall a. Semigroup a => a -> a -> a
<> forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b)

overlappingGCDMonoidLaw_stripOverlap_overlap
    :: (Eq a, Show a, OverlappingGCDMonoid a) => a -> a -> Property
overlappingGCDMonoidLaw_stripOverlap_overlap :: forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_stripOverlap_overlap a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripOverlap a b & λ(_, x, _) -> x == overlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> (m, m, m)
stripOverlap a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
x, a
_) -> a
x forall a. Eq a => a -> a -> Bool
== forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"overlap a b /= mempty"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripOverlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> (m, m, m)
stripOverlap a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"overlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
overlap a
a a
b)

overlappingGCDMonoidLaw_stripOverlap_stripPrefixOverlap
    :: (Eq a, Show a, OverlappingGCDMonoid a) => a -> a -> Property
overlappingGCDMonoidLaw_stripOverlap_stripPrefixOverlap :: forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_stripOverlap_stripPrefixOverlap a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripOverlap a b & λ(_, _, x) -> x == stripPrefixOverlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> (m, m, m)
stripOverlap a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
_, a
x) -> a
x forall a. Eq a => a -> a -> Bool
== forall m. OverlappingGCDMonoid m => m -> m -> m
stripPrefixOverlap a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripPrefixOverlap a b /= mempty"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
stripPrefixOverlap a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripOverlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> (m, m, m)
stripOverlap a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripPrefixOverlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
stripPrefixOverlap a
a a
b)

overlappingGCDMonoidLaw_stripOverlap_stripSuffixOverlap
    :: (Eq a, Show a, OverlappingGCDMonoid a) => a -> a -> Property
overlappingGCDMonoidLaw_stripOverlap_stripSuffixOverlap :: forall a.
(Eq a, Show a, OverlappingGCDMonoid a) =>
a -> a -> Property
overlappingGCDMonoidLaw_stripOverlap_stripSuffixOverlap a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripOverlap a b & λ(x, _, _) -> x == stripSuffixOverlap b a"
        (forall m. OverlappingGCDMonoid m => m -> m -> (m, m, m)
stripOverlap a
a a
b forall a b. a -> (a -> b) -> b
& \(a
x, a
_, a
_) -> a
x forall a. Eq a => a -> a -> Bool
== forall m. OverlappingGCDMonoid m => m -> m -> m
stripSuffixOverlap a
b a
a)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripSuffixOverlap b a /= mempty"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
stripSuffixOverlap a
b a
a forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripOverlap a b"
        (forall m. OverlappingGCDMonoid m => m -> m -> (m, m, m)
stripOverlap a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripSuffixOverlap b a"
        (forall m. OverlappingGCDMonoid m => m -> m -> m
stripSuffixOverlap a
b a
a)

--------------------------------------------------------------------------------
-- RightGCDMonoid
--------------------------------------------------------------------------------

-- | 'Laws' for instances of 'RightGCDMonoid'.
--
-- Tests the following laws:
--
-- @
-- 'stripCommonSuffix' a b '&' \\(_, _, s) -> s '==' 'commonSuffix' a b
-- @
--
-- @
-- 'stripCommonSuffix' a b '&' \\(x, _, s) -> x '<>' s '==' a
-- @
--
-- @
-- 'stripCommonSuffix' a b '&' \\(_, x, s) -> x '<>' s '==' b
-- @
--
-- @
-- 'stripCommonSuffix' a b '&' \\(x, _, s) -> 'Just' x '==' 'stripSuffix' s a
-- @
--
-- @
-- 'stripCommonSuffix' a b '&' \\(_, x, s) -> 'Just' x '==' 'stripSuffix' s b
-- @
--
-- Note that the following superclass laws are __not__ included:
--
-- * 'Test.QuickCheck.Classes.monoidLaws'
-- * 'Test.QuickCheck.Classes.Semigroup.Cancellative.rightReductiveLaws'
--
rightGCDMonoidLaws
    :: forall a. (Arbitrary a, Show a, Eq a, RightGCDMonoid a)
    => Proxy a
    -> Laws
rightGCDMonoidLaws :: forall a.
(Arbitrary a, Show a, Eq a, RightGCDMonoid a) =>
Proxy a -> Laws
rightGCDMonoidLaws Proxy a
_ = String -> [(String, Property)] -> Laws
Laws String
"RightGCDMonoid"
    [ forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"rightGCDMonoidLaw_stripCommonSuffix_commonSuffix"
        (forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_commonSuffix)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"rightGCDMonoidLaw_stripCommonSuffix_mappend_1"
        (forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_mappend_1)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"rightGCDMonoidLaw_stripCommonSuffix_mappend_2"
        (forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_mappend_2)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_1"
        (forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_1)
    , forall a t.
(Arbitrary a, Show a, Eq a, Semigroup a, Testable t) =>
String -> (a -> a -> t) -> (String, Property)
makeLaw2 @a
        String
"rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_2"
        (forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_2)
    ]

rightGCDMonoidLaw_stripCommonSuffix_commonSuffix
    :: (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_commonSuffix :: forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_commonSuffix a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonSuffix a b & λ(_, _, s) -> s == commonSuffix a b"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
_, a
s) -> a
s forall a. Eq a => a -> a -> Bool
== forall m. RightGCDMonoid m => m -> m -> m
commonSuffix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"commonSuffix a b /= mempty"
        (forall m. RightGCDMonoid m => m -> m -> m
commonSuffix a
a a
b forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonSuffix a b"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"commonSuffix a b"
        (forall m. RightGCDMonoid m => m -> m -> m
commonSuffix a
a a
b)

rightGCDMonoidLaw_stripCommonSuffix_mappend_1
    :: (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_mappend_1 :: forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_mappend_1 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonSuffix a b & λ(x, _, s) -> x <> s == a"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
x, a
_, a
s) -> a
x forall a. Semigroup a => a -> a -> a
<> a
s forall a. Eq a => a -> a -> Bool
== a
a)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripCommonSuffix a b & λ(x, _, s) -> x /= mempty && s /= mempty"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
x, a
_, a
s) -> a
x forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
s forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonSuffix a b"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonSuffix a b & λ(x, _, s) -> x <> s"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
x, a
_, a
s) -> a
x forall a. Semigroup a => a -> a -> a
<> a
s)

rightGCDMonoidLaw_stripCommonSuffix_mappend_2
    :: (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_mappend_2 :: forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_mappend_2 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonSuffix a b & λ(_, x, s) -> x <> s == b"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
x, a
s) -> a
x forall a. Semigroup a => a -> a -> a
<> a
s forall a. Eq a => a -> a -> Bool
== a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripCommonSuffix a b & λ(_, x, s) -> x /= mempty && s /= mempty"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
x, a
s) -> a
x forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
s forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonSuffix a b"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonSuffix a b & λ(_, x, s) -> x <> s"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
x, a
s) -> a
x forall a. Semigroup a => a -> a -> a
<> a
s)

rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_1
    :: (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_1 :: forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_1 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonSuffix a b & λ(x, _, s) -> Just x == stripSuffix s a"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
x, a
_, a
s) -> forall a. a -> Maybe a
Just a
x forall a. Eq a => a -> a -> Bool
== forall m. RightReductive m => m -> m -> Maybe m
stripSuffix a
s a
a)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripCommonSuffix a b & λ(x, _, s) -> x /= mempty && s /= mempty"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
x, a
_, a
s) -> a
x forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
s forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonSuffix a b"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonSuffix a b & λ(_, _, s) -> stripSuffix s a"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
_, a
s) -> forall m. RightReductive m => m -> m -> Maybe m
stripSuffix a
s a
a)

rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_2
    :: (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_2 :: forall a. (Eq a, Show a, RightGCDMonoid a) => a -> a -> Property
rightGCDMonoidLaw_stripCommonSuffix_stripSuffix_2 a
a a
b =
    forall t. Testable t => String -> t -> Property
makeProperty
        String
"stripCommonSuffix a b & λ(_, x, s) -> Just x == stripSuffix s b"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
x, a
s) -> forall a. a -> Maybe a
Just a
x forall a. Eq a => a -> a -> Bool
== forall m. RightReductive m => m -> m -> Maybe m
stripSuffix a
s a
b)
    forall a b. a -> (a -> b) -> b
& forall t. Testable t => String -> Bool -> t -> Property
cover
        String
"stripCommonSuffix a b & λ(_, x, s) -> x /= mempty && s /= mempty"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
x, a
s) -> a
x forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty Bool -> Bool -> Bool
&& a
s forall a. Eq a => a -> a -> Bool
/= forall a. Monoid a => a
mempty)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonSuffix a b"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b)
    forall a b. a -> (a -> b) -> b
& forall a prop.
(Show a, Testable prop) =>
String -> a -> prop -> Property
report
        String
"stripCommonSuffix a b & λ(_, _, s) -> stripSuffix s b"
        (forall m. RightGCDMonoid m => m -> m -> (m, m, m)
stripCommonSuffix a
a a
b forall a b. a -> (a -> b) -> b
& \(a
_, a
_, a
s) -> forall m. RightReductive m => m -> m -> Maybe m
stripSuffix a
s a
b)