monoid-subclasses-1.2.4.1: Subclasses of Monoid

Safe Haskell | Trustworthy
Language | Haskell2010

Data.Monoid.GCD

Description

This module defines the `GCDMonoid` subclass of the `Monoid` class.

The `GCDMonoid` subclass adds the `gcd` operation which takes two monoidal arguments and finds their greatest common divisor, or (more generally) the greatest monoid that can be extracted with the `</>` operation from both.

The `GCDMonoid` class is for Abelian, i.e., `Commutative` monoids.

## Non-commutative GCD monoids

Since most practical monoids in Haskell are not Abelian, the `GCDMonoid` class has three symmetric superclasses:

- `LeftGCDMonoid`

  Class of monoids for which it is possible to find the greatest common prefix of two monoidal values.

- `RightGCDMonoid`

  Class of monoids for which it is possible to find the greatest common suffix of two monoidal values.

- `OverlappingGCDMonoid`

  Class of monoids for which it is possible to find the greatest common overlap of two monoidal values.

## Distributive GCD monoids

Since some (but not all) GCD monoids are also distributive, there are three subclasses that add distributivity:

- `DistributiveGCDMonoid`

  Subclass of `GCDMonoid` with symmetric distributivity.

- `LeftDistributiveGCDMonoid`

  Subclass of `LeftGCDMonoid` with left-distributivity.

- `RightDistributiveGCDMonoid`

  Subclass of `RightGCDMonoid` with right-distributivity.

Synopsis

- class (Monoid m, Commutative m, Reductive m, LeftGCDMonoid m, RightGCDMonoid m, OverlappingGCDMonoid m) => GCDMonoid m where
  - gcd :: m -> m -> m
- class (Monoid m, LeftReductive m) => LeftGCDMonoid m where
  - commonPrefix :: m -> m -> m
  - stripCommonPrefix :: m -> m -> (m, m, m)
- class (Monoid m, RightReductive m) => RightGCDMonoid m where
  - commonSuffix :: m -> m -> m
  - stripCommonSuffix :: m -> m -> (m, m, m)
- class (Monoid m, LeftReductive m, RightReductive m) => OverlappingGCDMonoid m where
  - stripPrefixOverlap :: m -> m -> m
  - stripSuffixOverlap :: m -> m -> m
  - overlap :: m -> m -> m
  - stripOverlap :: m -> m -> (m, m, m)
- class (LeftDistributiveGCDMonoid m, RightDistributiveGCDMonoid m, GCDMonoid m) => DistributiveGCDMonoid m
- class LeftGCDMonoid m => LeftDistributiveGCDMonoid m
- class RightGCDMonoid m => RightDistributiveGCDMonoid m

# Documentation

class (Monoid m, Commutative m, Reductive m, LeftGCDMonoid m, RightGCDMonoid m, OverlappingGCDMonoid m) => GCDMonoid m where #

Class of Abelian monoids that allow the greatest common divisor to be found for any two given values. The operations must satisfy the following laws:

    gcd a b == commonPrefix a b == commonSuffix a b
    Just a' = a </> p && Just b' = b </> p
       where p = gcd a b

In addition, the `gcd` operation must satisfy the following properties:

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)

Methods

gcd :: m -> m -> m #

#### Instances

Instances details

GCDMonoid IntSet # | O(m+n)
Instance details Defined in Data.Monoid.GCD Methods gcd :: IntSet -> IntSet -> IntSet #
GCDMonoid () # | O(1)
Instance details Defined in Data.Monoid.GCD Methods gcd :: () -> () -> () #
GCDMonoid a => GCDMonoid (Dual a) # |
Instance details Defined in Data.Monoid.GCD Methods gcd :: Dual a -> Dual a -> Dual a #
GCDMonoid (Product Natural) # | O(1)
Instance details Defined in Data.Monoid.GCD Methods gcd :: Product Natural -> Product Natural -> Product Natural #
GCDMonoid (Sum Natural) # | O(1)
Instance details Defined in Data.Monoid.GCD Methods gcd :: Sum Natural -> Sum Natural -> Sum Natural #
Ord a => GCDMonoid (Set a) # | O(m*log(n/m + 1)), m <= n
Instance details Defined in Data.Monoid.GCD Methods gcd :: Set a -> Set a -> Set a #
(GCDMonoid a, GCDMonoid b) => GCDMonoid (a, b) # |
Instance details Defined in Data.Monoid.GCD Methods gcd :: (a, b) -> (a, b) -> (a, b) #
(GCDMonoid a, GCDMonoid b, GCDMonoid c) => GCDMonoid (a, b, c) # |
Instance details Defined in Data.Monoid.GCD Methods gcd :: (a, b, c) -> (a, b, c) -> (a, b, c) #
(GCDMonoid a, GCDMonoid b, GCDMonoid c, GCDMonoid d) => GCDMonoid (a, b, c, d) # |
Instance details Defined in Data.Monoid.GCD Methods gcd :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #

class (Monoid m, LeftReductive m) => LeftGCDMonoid m where #

Class of monoids capable of finding the equivalent of greatest common divisor on the left side of two monoidal values. The following laws must be respected:

    stripCommonPrefix a b == (p, a', b')
       where p = commonPrefix a b
             Just a' = stripPrefix p a
             Just b' = stripPrefix p b
    p == commonPrefix a b && p <> a' == a && p <> b' == b
       where (p, a', b') = stripCommonPrefix a b

Furthermore, `commonPrefix` must return the unique greatest common prefix that contains, as its prefix, any other prefix `x` of both values:

    not (x `isPrefixOf` a && x `isPrefixOf` b) || x `isPrefixOf` commonPrefix a b

and it cannot itself be a suffix of any other common prefix `y` of both values:

    not (y `isPrefixOf` a && y `isPrefixOf` b && commonPrefix a b `isSuffixOf` y)

In addition, the `commonPrefix` operation must satisfy the following properties:

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)

Minimal complete definition

commonPrefix | stripCommonPrefix

Methods

commonPrefix :: m -> m -> m #

stripCommonPrefix :: m -> m -> (m, m, m) #

#### Instances

Instances details

LeftGCDMonoid ByteString # | O(prefixLength)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: ByteString -> ByteString -> ByteString # stripCommonPrefix :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) #
LeftGCDMonoid ByteString # | O(prefixLength)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: ByteString -> ByteString -> ByteString # stripCommonPrefix :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) #
LeftGCDMonoid IntSet # | O(m+n)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: IntSet -> IntSet -> IntSet # stripCommonPrefix :: IntSet -> IntSet -> (IntSet, IntSet, IntSet) #
LeftGCDMonoid ByteStringUTF8 # | O(prefixLength)
Instance details Defined in Data.Monoid.Instances.ByteString.UTF8 Methods commonPrefix :: ByteStringUTF8 -> ByteStringUTF8 -> ByteStringUTF8 # stripCommonPrefix :: ByteStringUTF8 -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8, ByteStringUTF8) #
LeftGCDMonoid Text # | O(prefixLength)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Text -> Text -> Text # stripCommonPrefix :: Text -> Text -> (Text, Text, Text) #
LeftGCDMonoid Text # | O(prefixLength)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Text -> Text -> Text # stripCommonPrefix :: Text -> Text -> (Text, Text, Text) #
LeftGCDMonoid () # | O(1)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: () -> () -> () # stripCommonPrefix :: () -> () -> ((), (), ()) #
RightGCDMonoid a => LeftGCDMonoid (Dual a) # |
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Dual a -> Dual a -> Dual a # stripCommonPrefix :: Dual a -> Dual a -> (Dual a, Dual a, Dual a) #
LeftGCDMonoid (Product Natural) # | O(1)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Product Natural -> Product Natural -> Product Natural # stripCommonPrefix :: Product Natural -> Product Natural -> (Product Natural, Product Natural, Product Natural) #
LeftGCDMonoid (Sum Natural) # | O(1)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Sum Natural -> Sum Natural -> Sum Natural # stripCommonPrefix :: Sum Natural -> Sum Natural -> (Sum Natural, Sum Natural, Sum Natural) #
Eq a => LeftGCDMonoid (IntMap a) # | O(m+n)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: IntMap a -> IntMap a -> IntMap a # stripCommonPrefix :: IntMap a -> IntMap a -> (IntMap a, IntMap a, IntMap a) #
Eq a => LeftGCDMonoid (Seq a) # | O(prefixLength)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Seq a -> Seq a -> Seq a # stripCommonPrefix :: Seq a -> Seq a -> (Seq a, Seq a, Seq a) #
Ord a => LeftGCDMonoid (Set a) # | O(m*log(n/m + 1)), m <= n
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Set a -> Set a -> Set a # stripCommonPrefix :: Set a -> Set a -> (Set a, Set a, Set a) #
(LeftGCDMonoid a, StableFactorial a, PositiveMonoid a) => LeftGCDMonoid (Concat a) # |
Instance details Defined in Data.Monoid.Instances.Concat Methods commonPrefix :: Concat a -> Concat a -> Concat a # stripCommonPrefix :: Concat a -> Concat a -> (Concat a, Concat a, Concat a) #
(LeftGCDMonoid a, StableFactorial a) => LeftGCDMonoid (Measured a) # |
Instance details Defined in Data.Monoid.Instances.Measured Methods commonPrefix :: Measured a -> Measured a -> Measured a # stripCommonPrefix :: Measured a -> Measured a -> (Measured a, Measured a, Measured a) #
(StableFactorial m, TextualMonoid m, LeftGCDMonoid m) => LeftGCDMonoid (LinePositioned m) # |
Instance details Defined in Data.Monoid.Instances.Positioned Methods commonPrefix :: LinePositioned m -> LinePositioned m -> LinePositioned m # stripCommonPrefix :: LinePositioned m -> LinePositioned m -> (LinePositioned m, LinePositioned m, LinePositioned m) #
(StableFactorial m, FactorialMonoid m, LeftGCDMonoid m) => LeftGCDMonoid (OffsetPositioned m) # |
Instance details Defined in Data.Monoid.Instances.Positioned Methods commonPrefix :: OffsetPositioned m -> OffsetPositioned m -> OffsetPositioned m # stripCommonPrefix :: OffsetPositioned m -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m, OffsetPositioned m) #
(Eq m, StableFactorial m, FactorialMonoid m, LeftGCDMonoid m) => LeftGCDMonoid (Shadowed m) # |
Instance details Defined in Data.Monoid.Instances.PrefixMemory Methods commonPrefix :: Shadowed m -> Shadowed m -> Shadowed m # stripCommonPrefix :: Shadowed m -> Shadowed m -> (Shadowed m, Shadowed m, Shadowed m) #
Eq a => LeftGCDMonoid (Vector a) # | O(prefixLength)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Vector a -> Vector a -> Vector a # stripCommonPrefix :: Vector a -> Vector a -> (Vector a, Vector a, Vector a) #
LeftGCDMonoid x => LeftGCDMonoid (Maybe x) # |
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Maybe x -> Maybe x -> Maybe x # stripCommonPrefix :: Maybe x -> Maybe x -> (Maybe x, Maybe x, Maybe x) #
Eq x => LeftGCDMonoid [x] # | O(prefixLength)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: [x] -> [x] -> [x] # stripCommonPrefix :: [x] -> [x] -> ([x], [x], [x]) #
(Ord k, Eq a) => LeftGCDMonoid (Map k a) # | O(m+n)
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: Map k a -> Map k a -> Map k a # stripCommonPrefix :: Map k a -> Map k a -> (Map k a, Map k a, Map k a) #
(LeftGCDMonoid a, LeftGCDMonoid b) => LeftGCDMonoid (Stateful a b) # |
Instance details Defined in Data.Monoid.Instances.Stateful Methods commonPrefix :: Stateful a b -> Stateful a b -> Stateful a b # stripCommonPrefix :: Stateful a b -> Stateful a b -> (Stateful a b, Stateful a b, Stateful a b) #
(LeftGCDMonoid a, LeftGCDMonoid b) => LeftGCDMonoid (a, b) # |
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: (a, b) -> (a, b) -> (a, b) # stripCommonPrefix :: (a, b) -> (a, b) -> ((a, b), (a, b), (a, b)) #
(LeftGCDMonoid a, LeftGCDMonoid b, LeftGCDMonoid c) => LeftGCDMonoid (a, b, c) # |
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: (a, b, c) -> (a, b, c) -> (a, b, c) # stripCommonPrefix :: (a, b, c) -> (a, b, c) -> ((a, b, c), (a, b, c), (a, b, c)) #
(LeftGCDMonoid a, LeftGCDMonoid b, LeftGCDMonoid c, LeftGCDMonoid d) => LeftGCDMonoid (a, b, c, d) # |
Instance details Defined in Data.Monoid.GCD Methods commonPrefix :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # stripCommonPrefix :: (a, b, c, d) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), (a, b, c, d)) #

class (Monoid m, RightReductive m) => RightGCDMonoid m where #

Class of monoids capable of finding the equivalent of greatest common divisor on the right side of two monoidal values. The following laws must be respected:

    stripCommonSuffix a b == (a', b', s)
       where s = commonSuffix a b
             Just a' = stripSuffix p a
             Just b' = stripSuffix p b
    s == commonSuffix a b && a' <> s == a && b' <> s == b
       where (a', b', s) = stripCommonSuffix a b

Furthermore, `commonSuffix` must return the unique greatest common suffix that contains, as its suffix, any other suffix `x` of both values:

    not (x `isSuffixOf` a && x `isSuffixOf` b) || x `isSuffixOf` commonSuffix a b

and it cannot itself be a prefix of any other common suffix `y` of both values:

    not (y `isSuffixOf` a && y `isSuffixOf` b && commonSuffix a b `isPrefixOf` y)

In addition, the `commonSuffix` operation must satisfy the following properties:

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)

Minimal complete definition

commonSuffix | stripCommonSuffix

Methods

commonSuffix :: m -> m -> m #

stripCommonSuffix :: m -> m -> (m, m, m) #

#### Instances

Instances details

RightGCDMonoid ByteString # | O(suffixLength)
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: ByteString -> ByteString -> ByteString # stripCommonSuffix :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) #
RightGCDMonoid ByteString # | O(suffixLength)
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: ByteString -> ByteString -> ByteString # stripCommonSuffix :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) #
RightGCDMonoid IntSet # | O(m+n)
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: IntSet -> IntSet -> IntSet # stripCommonSuffix :: IntSet -> IntSet -> (IntSet, IntSet, IntSet) #
RightGCDMonoid Text # | O(suffixLength), except on GHCjs where it is O(m+n) Since: 1.0
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: Text -> Text -> Text # stripCommonSuffix :: Text -> Text -> (Text, Text, Text) #
RightGCDMonoid Text # | O(m+n) Since: 1.0
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: Text -> Text -> Text # stripCommonSuffix :: Text -> Text -> (Text, Text, Text) #
RightGCDMonoid () # | O(1)
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: () -> () -> () # stripCommonSuffix :: () -> () -> ((), (), ()) #
LeftGCDMonoid a => RightGCDMonoid (Dual a) # |
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: Dual a -> Dual a -> Dual a # stripCommonSuffix :: Dual a -> Dual a -> (Dual a, Dual a, Dual a) #
RightGCDMonoid (Product Natural) # | O(1)
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: Product Natural -> Product Natural -> Product Natural # stripCommonSuffix :: Product Natural -> Product Natural -> (Product Natural, Product Natural, Product Natural) #
RightGCDMonoid (Sum Natural) # | O(1)
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: Sum Natural -> Sum Natural -> Sum Natural # stripCommonSuffix :: Sum Natural -> Sum Natural -> (Sum Natural, Sum Natural, Sum Natural) #
Eq a => RightGCDMonoid (Seq a) # | O(suffixLength)
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: Seq a -> Seq a -> Seq a # stripCommonSuffix :: Seq a -> Seq a -> (Seq a, Seq a, Seq a) #
Ord a => RightGCDMonoid (Set a) # | O(m*log(n/m + 1)), m <= n
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: Set a -> Set a -> Set a # stripCommonSuffix :: Set a -> Set a -> (Set a, Set a, Set a) #
(RightGCDMonoid a, StableFactorial a, PositiveMonoid a) => RightGCDMonoid (Concat a) # |
Instance details Defined in Data.Monoid.Instances.Concat Methods commonSuffix :: Concat a -> Concat a -> Concat a # stripCommonSuffix :: Concat a -> Concat a -> (Concat a, Concat a, Concat a) #
(RightGCDMonoid a, StableFactorial a) => RightGCDMonoid (Measured a) # |
Instance details Defined in Data.Monoid.Instances.Measured Methods commonSuffix :: Measured a -> Measured a -> Measured a # stripCommonSuffix :: Measured a -> Measured a -> (Measured a, Measured a, Measured a) #
(StableFactorial m, TextualMonoid m, RightGCDMonoid m) => RightGCDMonoid (LinePositioned m) # |
Instance details Defined in Data.Monoid.Instances.Positioned Methods commonSuffix :: LinePositioned m -> LinePositioned m -> LinePositioned m # stripCommonSuffix :: LinePositioned m -> LinePositioned m -> (LinePositioned m, LinePositioned m, LinePositioned m) #
(StableFactorial m, FactorialMonoid m, RightGCDMonoid m) => RightGCDMonoid (OffsetPositioned m) # |
Instance details Defined in Data.Monoid.Instances.Positioned Methods commonSuffix :: OffsetPositioned m -> OffsetPositioned m -> OffsetPositioned m # stripCommonSuffix :: OffsetPositioned m -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m, OffsetPositioned m) #
(StableFactorial m, FactorialMonoid m, RightGCDMonoid m) => RightGCDMonoid (Shadowed m) # |
Instance details Defined in Data.Monoid.Instances.PrefixMemory Methods commonSuffix :: Shadowed m -> Shadowed m -> Shadowed m # stripCommonSuffix :: Shadowed m -> Shadowed m -> (Shadowed m, Shadowed m, Shadowed m) #
Eq a => RightGCDMonoid (Vector a) # | O(suffixLength)
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: Vector a -> Vector a -> Vector a # stripCommonSuffix :: Vector a -> Vector a -> (Vector a, Vector a, Vector a) #
RightGCDMonoid x => RightGCDMonoid (Maybe x) # |
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: Maybe x -> Maybe x -> Maybe x # stripCommonSuffix :: Maybe x -> Maybe x -> (Maybe x, Maybe x, Maybe x) #
Eq x => RightGCDMonoid [x] # | O(m+n) Since: 1.0
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: [x] -> [x] -> [x] # stripCommonSuffix :: [x] -> [x] -> ([x], [x], [x]) #
(RightGCDMonoid a, RightGCDMonoid b) => RightGCDMonoid (Stateful a b) # |
Instance details Defined in Data.Monoid.Instances.Stateful Methods commonSuffix :: Stateful a b -> Stateful a b -> Stateful a b # stripCommonSuffix :: Stateful a b -> Stateful a b -> (Stateful a b, Stateful a b, Stateful a b) #
(RightGCDMonoid a, RightGCDMonoid b) => RightGCDMonoid (a, b) # |
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: (a, b) -> (a, b) -> (a, b) # stripCommonSuffix :: (a, b) -> (a, b) -> ((a, b), (a, b), (a, b)) #
(RightGCDMonoid a, RightGCDMonoid b, RightGCDMonoid c) => RightGCDMonoid (a, b, c) # |
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: (a, b, c) -> (a, b, c) -> (a, b, c) # stripCommonSuffix :: (a, b, c) -> (a, b, c) -> ((a, b, c), (a, b, c), (a, b, c)) #
(RightGCDMonoid a, RightGCDMonoid b, RightGCDMonoid c, RightGCDMonoid d) => RightGCDMonoid (a, b, c, d) # |
Instance details Defined in Data.Monoid.GCD Methods commonSuffix :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # stripCommonSuffix :: (a, b, c, d) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), (a, b, c, d)) #

class (Monoid m, LeftReductive m, RightReductive m) => OverlappingGCDMonoid m where #

Class of monoids for which the greatest overlap can be found between any two values, such that

    a == a' <> overlap a b
    b == overlap a b <> b'

The methods must satisfy the following laws:

    stripOverlap a b == (stripSuffixOverlap b a, overlap a b, stripPrefixOverlap a b)
    stripSuffixOverlap b a <> overlap a b == a
    overlap a b <> stripPrefixOverlap a b == b

The result of `overlap a b` must be the largest prefix of `b` and suffix of `a`, in the sense that it contains any other value `x` that satifies the property `(x `isPrefixOf` b) && (x `isSuffixOf` a)`:

    ∀x. (x `isPrefixOf` b && x `isSuffixOf` a) => (x `isPrefixOf` overlap a b && x `isSuffixOf` overlap a b)

and it must be unique so there's no other value `y` that satisfies the same properties for every such `x`:

    ∀y. ((∀x. (x `isPrefixOf` b && x `isSuffixOf` a) => x `isPrefixOf` y && x `isSuffixOf` y) => y == overlap a b)

In addition, the `overlap` operation must satisfy the following properties:

Idempotence

    overlap a a == a

Identity

    overlap mempty a == mempty

    overlap a mempty == mempty

Since: 1.0

Minimal complete definition

stripOverlap

Methods

stripPrefixOverlap :: m -> m -> m #

stripSuffixOverlap :: m -> m -> m #

overlap :: m -> m -> m #

stripOverlap :: m -> m -> (m, m, m) #

#### Instances

Instances details

OverlappingGCDMonoid ByteString # | O(min(m,n)^2)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: ByteString -> ByteString -> ByteString # stripSuffixOverlap :: ByteString -> ByteString -> ByteString # overlap :: ByteString -> ByteString -> ByteString # stripOverlap :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) #
OverlappingGCDMonoid ByteString # | O(m*n)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: ByteString -> ByteString -> ByteString # stripSuffixOverlap :: ByteString -> ByteString -> ByteString # overlap :: ByteString -> ByteString -> ByteString # stripOverlap :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) #
OverlappingGCDMonoid IntSet # | O(m+n)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: IntSet -> IntSet -> IntSet # stripSuffixOverlap :: IntSet -> IntSet -> IntSet # overlap :: IntSet -> IntSet -> IntSet # stripOverlap :: IntSet -> IntSet -> (IntSet, IntSet, IntSet) #
OverlappingGCDMonoid Text # | O(min(m,n)^2)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Text -> Text -> Text # stripSuffixOverlap :: Text -> Text -> Text # overlap :: Text -> Text -> Text # stripOverlap :: Text -> Text -> (Text, Text, Text) #
OverlappingGCDMonoid Text # | O(m*n)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Text -> Text -> Text # stripSuffixOverlap :: Text -> Text -> Text # overlap :: Text -> Text -> Text # stripOverlap :: Text -> Text -> (Text, Text, Text) #
OverlappingGCDMonoid () # | O(1)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: () -> () -> () # stripSuffixOverlap :: () -> () -> () # overlap :: () -> () -> () # stripOverlap :: () -> () -> ((), (), ()) #
OverlappingGCDMonoid a => OverlappingGCDMonoid (Dual a) # |
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Dual a -> Dual a -> Dual a # stripSuffixOverlap :: Dual a -> Dual a -> Dual a # overlap :: Dual a -> Dual a -> Dual a # stripOverlap :: Dual a -> Dual a -> (Dual a, Dual a, Dual a) #
OverlappingGCDMonoid (Product Natural) # | O(1)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Product Natural -> Product Natural -> Product Natural # stripSuffixOverlap :: Product Natural -> Product Natural -> Product Natural # overlap :: Product Natural -> Product Natural -> Product Natural # stripOverlap :: Product Natural -> Product Natural -> (Product Natural, Product Natural, Product Natural) #
OverlappingGCDMonoid (Sum Natural) # | O(1)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Sum Natural -> Sum Natural -> Sum Natural # stripSuffixOverlap :: Sum Natural -> Sum Natural -> Sum Natural # overlap :: Sum Natural -> Sum Natural -> Sum Natural # stripOverlap :: Sum Natural -> Sum Natural -> (Sum Natural, Sum Natural, Sum Natural) #
Eq a => OverlappingGCDMonoid (IntMap a) # | O(m+n)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: IntMap a -> IntMap a -> IntMap a # stripSuffixOverlap :: IntMap a -> IntMap a -> IntMap a # overlap :: IntMap a -> IntMap a -> IntMap a # stripOverlap :: IntMap a -> IntMap a -> (IntMap a, IntMap a, IntMap a) #
Eq a => OverlappingGCDMonoid (Seq a) # | O(min(m,n)^2)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Seq a -> Seq a -> Seq a # stripSuffixOverlap :: Seq a -> Seq a -> Seq a # overlap :: Seq a -> Seq a -> Seq a # stripOverlap :: Seq a -> Seq a -> (Seq a, Seq a, Seq a) #
Ord a => OverlappingGCDMonoid (Set a) # | O(m*log(nm + 1)), m <= n/
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Set a -> Set a -> Set a # stripSuffixOverlap :: Set a -> Set a -> Set a # overlap :: Set a -> Set a -> Set a # stripOverlap :: Set a -> Set a -> (Set a, Set a, Set a) #
Eq a => OverlappingGCDMonoid (Vector a) # | O(min(m,n)^2)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Vector a -> Vector a -> Vector a # stripSuffixOverlap :: Vector a -> Vector a -> Vector a # overlap :: Vector a -> Vector a -> Vector a # stripOverlap :: Vector a -> Vector a -> (Vector a, Vector a, Vector a) #
(OverlappingGCDMonoid a, MonoidNull a) => OverlappingGCDMonoid (Maybe a) # |
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Maybe a -> Maybe a -> Maybe a # stripSuffixOverlap :: Maybe a -> Maybe a -> Maybe a # overlap :: Maybe a -> Maybe a -> Maybe a # stripOverlap :: Maybe a -> Maybe a -> (Maybe a, Maybe a, Maybe a) #
Eq a => OverlappingGCDMonoid [a] # | O(m*n)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: [a] -> [a] -> [a] # stripSuffixOverlap :: [a] -> [a] -> [a] # overlap :: [a] -> [a] -> [a] # stripOverlap :: [a] -> [a] -> ([a], [a], [a]) #
(Ord k, Eq v) => OverlappingGCDMonoid (Map k v) # | O(m+n)
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Map k v -> Map k v -> Map k v # stripSuffixOverlap :: Map k v -> Map k v -> Map k v # overlap :: Map k v -> Map k v -> Map k v # stripOverlap :: Map k v -> Map k v -> (Map k v, Map k v, Map k v) #
(OverlappingGCDMonoid a, OverlappingGCDMonoid b) => OverlappingGCDMonoid (a, b) # |
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: (a, b) -> (a, b) -> (a, b) # stripSuffixOverlap :: (a, b) -> (a, b) -> (a, b) # overlap :: (a, b) -> (a, b) -> (a, b) # stripOverlap :: (a, b) -> (a, b) -> ((a, b), (a, b), (a, b)) #
(OverlappingGCDMonoid a, OverlappingGCDMonoid b, OverlappingGCDMonoid c) => OverlappingGCDMonoid (a, b, c) # |
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: (a, b, c) -> (a, b, c) -> (a, b, c) # stripSuffixOverlap :: (a, b, c) -> (a, b, c) -> (a, b, c) # overlap :: (a, b, c) -> (a, b, c) -> (a, b, c) # stripOverlap :: (a, b, c) -> (a, b, c) -> ((a, b, c), (a, b, c), (a, b, c)) #
(OverlappingGCDMonoid a, OverlappingGCDMonoid b, OverlappingGCDMonoid c, OverlappingGCDMonoid d) => OverlappingGCDMonoid (a, b, c, d) # |
Instance details Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # stripSuffixOverlap :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # overlap :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # stripOverlap :: (a, b, c, d) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), (a, b, c, d)) #

class (LeftDistributiveGCDMonoid m, RightDistributiveGCDMonoid m, GCDMonoid m) => DistributiveGCDMonoid m #

Class of commutative GCD monoids with symmetric distributivity.

In addition to the general `GCDMonoid` laws, instances of this class must also satisfy the following laws:

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

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

#### Instances

Instances details

DistributiveGCDMonoid IntSet # |
Instance details Defined in Data.Monoid.GCD
DistributiveGCDMonoid () # |
Instance details Defined in Data.Monoid.GCD
DistributiveGCDMonoid a => DistributiveGCDMonoid (Dual a) # |
Instance details Defined in Data.Monoid.GCD
DistributiveGCDMonoid (Product Natural) # |
Instance details Defined in Data.Monoid.GCD
DistributiveGCDMonoid (Sum Natural) # |
Instance details Defined in Data.Monoid.GCD
Ord a => DistributiveGCDMonoid (Set a) # |
Instance details Defined in Data.Monoid.GCD

class LeftGCDMonoid m => LeftDistributiveGCDMonoid m #

Class of left GCD monoids with left-distributivity.

In addition to the general `LeftGCDMonoid` laws, instances of this class must also satisfy the following law:

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

#### Instances

Instances details

LeftDistributiveGCDMonoid ByteString # |
Instance details Defined in Data.Monoid.GCD
LeftDistributiveGCDMonoid ByteString # |
Instance details Defined in Data.Monoid.GCD
LeftDistributiveGCDMonoid IntSet # |
Instance details Defined in Data.Monoid.GCD
LeftDistributiveGCDMonoid Text # |
Instance details Defined in Data.Monoid.GCD
LeftDistributiveGCDMonoid Text # |
Instance details Defined in Data.Monoid.GCD
LeftDistributiveGCDMonoid () # |
Instance details Defined in Data.Monoid.GCD
RightDistributiveGCDMonoid a => LeftDistributiveGCDMonoid (Dual a) # |
Instance details Defined in Data.Monoid.GCD
LeftDistributiveGCDMonoid (Product Natural) # |
Instance details Defined in Data.Monoid.GCD
LeftDistributiveGCDMonoid (Sum Natural) # |
Instance details Defined in Data.Monoid.GCD
Eq a => LeftDistributiveGCDMonoid (Seq a) # |
Instance details Defined in Data.Monoid.GCD
Ord a => LeftDistributiveGCDMonoid (Set a) # |
Instance details Defined in Data.Monoid.GCD
Eq a => LeftDistributiveGCDMonoid (Vector a) # |
Instance details Defined in Data.Monoid.GCD
Eq a => LeftDistributiveGCDMonoid [a] # |
Instance details Defined in Data.Monoid.GCD

class RightGCDMonoid m => RightDistributiveGCDMonoid m #

Class of right GCD monoids with right-distributivity.

In addition to the general `RightGCDMonoid` laws, instances of this class must also satisfy the following law:

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

#### Instances

Instances details

RightDistributiveGCDMonoid ByteString # |
Instance details Defined in Data.Monoid.GCD
RightDistributiveGCDMonoid ByteString # |
Instance details Defined in Data.Monoid.GCD
RightDistributiveGCDMonoid IntSet # |
Instance details Defined in Data.Monoid.GCD
RightDistributiveGCDMonoid Text # |
Instance details Defined in Data.Monoid.GCD
RightDistributiveGCDMonoid Text # |
Instance details Defined in Data.Monoid.GCD
RightDistributiveGCDMonoid () # |
Instance details Defined in Data.Monoid.GCD
LeftDistributiveGCDMonoid a => RightDistributiveGCDMonoid (Dual a) # |
Instance details Defined in Data.Monoid.GCD
RightDistributiveGCDMonoid (Product Natural) # |
Instance details Defined in Data.Monoid.GCD
RightDistributiveGCDMonoid (Sum Natural) # |
Instance details Defined in Data.Monoid.GCD
Eq a => RightDistributiveGCDMonoid (Seq a) # |
Instance details Defined in Data.Monoid.GCD
Ord a => RightDistributiveGCDMonoid (Set a) # |
Instance details Defined in Data.Monoid.GCD
Eq a => RightDistributiveGCDMonoid (Vector a) # |
Instance details Defined in Data.Monoid.GCD
Eq a => RightDistributiveGCDMonoid [a] # |
Instance details Defined in Data.Monoid.GCD