Test.QuickCheck.Classes.Monoid.GCD

This module provides Laws definitions for classes exported by Data.Monoid.GCD.

Documentation

gcdMonoidLaws :: forall a. (Arbitrary a, Show a, Eq a, GCDMonoid a) => Proxy a -> Laws

Laws for instances of GCDMonoid.

Includes the following laws:

Reductivity

isJust (a </> gcd a b)

isJust (b </> gcd a b)

Uniqueness

all isJust
    [ a </> c
    , b </> c
    , c </> gcd a b
    ]
==>
    (c == gcd a b)

Idempotence

gcd a a == a

Identity

gcd mempty a == mempty

gcd a mempty == mempty

Commutativity

gcd a b == gcd b a

Associativity

gcd (gcd a b) c == gcd a (gcd b c)

Distributivity

gcd (a <> b) (a <> c) == a <> gcd b c

gcd (a <> c) (b <> c) == gcd a b <> c

Equivalence

gcd a b == commonPrefix a b

gcd a b == commonSuffix a b

Note that the following superclass laws are not included:

• monoidLaws
• commutativeLaws
• reductiveLaws
• leftGCDMonoidLaws
• rightGCDMonoidLaws
• overlappingGCDMonoidLaws

cancellativeGCDMonoidLaws :: forall a. (Arbitrary a, Show a, Eq a, Cancellative a, GCDMonoid a) => Proxy a -> Laws

Laws for instances of Cancellative and GCDMonoid.

Includes 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:

• cancellativeLaws
• gcdMonoidLaws

leftGCDMonoidLaws :: forall a. (Arbitrary a, Show a, Eq a, LeftGCDMonoid a) => Proxy a -> Laws

Laws for instances of LeftGCDMonoid.

Includes 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:

• monoidLaws
• leftReductiveLaws

rightGCDMonoidLaws :: forall a. (Arbitrary a, Show a, Eq a, RightGCDMonoid a) => Proxy a -> Laws

Laws for instances of RightGCDMonoid.

Includes 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:

• monoidLaws
• rightReductiveLaws

overlappingGCDMonoidLaws :: forall a. (Arbitrary a, Show a, Eq a, OverlappingGCDMonoid a) => Proxy a -> Laws

Laws for instances of OverlappingGCDMonoid.

Includes 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:

• monoidLaws
• leftReductiveLaws
• rightReductiveLaws