Documentation

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)

Equivalences

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

Laws for instances of LeftGCDMonoid.

Includes the following laws:

Reductivity

isJust (stripPrefix (commonPrefix a b) a)

isJust (stripPrefix (commonPrefix a b) b)

Uniqueness

all isJust
    [ stripPrefix c a
    , stripPrefix c b
    , stripPrefix (commonPrefix a b) c
    ]
==>
    (c == commonPrefix a b)

Idempotence

commonPrefix a a == a

Identity

commonPrefix mempty a == mempty

commonPrefix a mempty == mempty

Commutativity

commonPrefix a b == commonPrefix b a

Associativity

commonPrefix (commonPrefix a b) c
==
commonPrefix a (commonPrefix b c)

Equivalences

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

Laws for instances of RightGCDMonoid.

Includes the following laws:

Reductivity

isJust (stripSuffix (commonSuffix a b) a)

isJust (stripSuffix (commonSuffix a b) b)

Uniqueness

all isJust
    [ stripSuffix c a
    , stripSuffix c b
    , stripSuffix (commonSuffix a b) c
    ]
==>
    (c == commonSuffix a b)

Idempotence

commonSuffix a a == a

Identity

commonSuffix mempty a == mempty

commonSuffix a mempty == mempty

Commutativity

commonSuffix a b == commonSuffix b a

Associativity

commonSuffix (commonSuffix a b) c
==
commonSuffix a (commonSuffix b c)

Equivalences

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

Laws for instances of OverlappingGCDMonoid.

Includes the following laws:

Reductivity

isJust (stripSuffix (overlap a b) a)

isJust (stripPrefix (overlap a b) b)

Idempotence

overlap a a == a

Identity

overlap mempty a == mempty

overlap a mempty == mempty

Equivalences

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

Laws for instances of DistributiveGCDMonoid.

Includes the following laws:

Left-distributivity

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

Right-distributivity

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

Note that the following superclass laws are not included:

• gcdMonoidLaws
• leftDistributiveGCDMonoidLaws
• rightDistributiveGCDMonoidLaws

Laws for instances of LeftDistributiveGCDMonoid.

Includes the following law:

Left-distributivity

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

Note that the following superclass laws are not included:

• leftGCDMonoidLaws

Laws for instances of RightDistributiveGCDMonoid.

Includes the following law:

Right-distributivity

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

Note that the following superclass laws are not included:

• rightGCDMonoidLaws