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. Since most practical monoids in Haskell are not
Abelian, there are also its three symmetric superclasses:
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)
Documentation
class (Monoid m, Commutative m, Reductive m, LeftGCDMonoid m, RightGCDMonoid m, OverlappingGCDMonoid m) => GCDMonoid m where Source #
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
If a GCDMonoid
happens to also be Cancellative
, it should additionally satisfy the following laws:
gcd (a <> b) (a <> c) == a <> gcd b c gcd (a <> c) (b <> c) == gcd a b <> c
Instances
GCDMonoid () Source # | O(1) |
Defined in Data.Monoid.GCD | |
GCDMonoid IntSet Source # | O(m+n) |
Defined in Data.Monoid.GCD | |
GCDMonoid a => GCDMonoid (Dual a) Source # | |
Defined in Data.Monoid.GCD | |
GCDMonoid (Product Natural) Source # | O(1) |
Defined in Data.Monoid.GCD | |
GCDMonoid (Sum Natural) Source # | O(1) |
Defined in Data.Monoid.GCD | |
Ord a => GCDMonoid (Set a) Source # | O(m*log(n/m + 1)), m <= n |
Defined in Data.Monoid.GCD | |
(GCDMonoid a, GCDMonoid b) => GCDMonoid (a, b) Source # | |
Defined in Data.Monoid.GCD | |
(GCDMonoid a, GCDMonoid b, GCDMonoid c) => GCDMonoid (a, b, c) Source # | |
Defined in Data.Monoid.GCD | |
(GCDMonoid a, GCDMonoid b, GCDMonoid c, GCDMonoid d) => GCDMonoid (a, b, c, d) Source # | |
Defined in Data.Monoid.GCD |
class (Monoid m, LeftReductive m) => LeftGCDMonoid m where Source #
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)
Minimal complete definition
Instances
LeftGCDMonoid () Source # | O(1) |
Defined in Data.Monoid.GCD Methods commonPrefix :: () -> () -> () Source # stripCommonPrefix :: () -> () -> ((), (), ()) Source # | |
LeftGCDMonoid ByteString Source # | O(prefixLength) |
Defined in Data.Monoid.GCD Methods commonPrefix :: ByteString -> ByteString -> ByteString Source # stripCommonPrefix :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) Source # | |
LeftGCDMonoid ByteString Source # | O(prefixLength) |
Defined in Data.Monoid.GCD Methods commonPrefix :: ByteString -> ByteString -> ByteString Source # stripCommonPrefix :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) Source # | |
LeftGCDMonoid Text Source # | O(prefixLength) |
Defined in Data.Monoid.GCD Methods commonPrefix :: Text -> Text -> Text Source # stripCommonPrefix :: Text -> Text -> (Text, Text, Text) Source # | |
LeftGCDMonoid Text Source # | O(prefixLength) |
Defined in Data.Monoid.GCD Methods commonPrefix :: Text -> Text -> Text Source # stripCommonPrefix :: Text -> Text -> (Text, Text, Text) Source # | |
LeftGCDMonoid IntSet Source # | O(m+n) |
Defined in Data.Monoid.GCD Methods commonPrefix :: IntSet -> IntSet -> IntSet Source # stripCommonPrefix :: IntSet -> IntSet -> (IntSet, IntSet, IntSet) Source # | |
LeftGCDMonoid ByteStringUTF8 Source # | O(prefixLength) |
Defined in Data.Monoid.Instances.ByteString.UTF8 Methods commonPrefix :: ByteStringUTF8 -> ByteStringUTF8 -> ByteStringUTF8 Source # stripCommonPrefix :: ByteStringUTF8 -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8, ByteStringUTF8) Source # | |
Eq x => LeftGCDMonoid [x] Source # | O(prefixLength) |
Defined in Data.Monoid.GCD Methods commonPrefix :: [x] -> [x] -> [x] Source # stripCommonPrefix :: [x] -> [x] -> ([x], [x], [x]) Source # | |
LeftGCDMonoid x => LeftGCDMonoid (Maybe x) Source # | |
Defined in Data.Monoid.GCD Methods commonPrefix :: Maybe x -> Maybe x -> Maybe x Source # stripCommonPrefix :: Maybe x -> Maybe x -> (Maybe x, Maybe x, Maybe x) Source # | |
Eq a => LeftGCDMonoid (Vector a) Source # | O(prefixLength) |
Defined in Data.Monoid.GCD | |
RightGCDMonoid a => LeftGCDMonoid (Dual a) Source # | |
Defined in Data.Monoid.GCD Methods commonPrefix :: Dual a -> Dual a -> Dual a Source # stripCommonPrefix :: Dual a -> Dual a -> (Dual a, Dual a, Dual a) Source # | |
LeftGCDMonoid (Product Natural) Source # | O(1) |
Defined in Data.Monoid.GCD Methods commonPrefix :: Product Natural -> Product Natural -> Product Natural Source # stripCommonPrefix :: Product Natural -> Product Natural -> (Product Natural, Product Natural, Product Natural) Source # | |
LeftGCDMonoid (Sum Natural) Source # | O(1) |
Defined in Data.Monoid.GCD Methods commonPrefix :: Sum Natural -> Sum Natural -> Sum Natural Source # stripCommonPrefix :: Sum Natural -> Sum Natural -> (Sum Natural, Sum Natural, Sum Natural) Source # | |
Eq a => LeftGCDMonoid (IntMap a) Source # | O(m+n) |
Defined in Data.Monoid.GCD Methods commonPrefix :: IntMap a -> IntMap a -> IntMap a Source # stripCommonPrefix :: IntMap a -> IntMap a -> (IntMap a, IntMap a, IntMap a) Source # | |
Eq a => LeftGCDMonoid (Seq a) Source # | O(prefixLength) |
Defined in Data.Monoid.GCD Methods commonPrefix :: Seq a -> Seq a -> Seq a Source # stripCommonPrefix :: Seq a -> Seq a -> (Seq a, Seq a, Seq a) Source # | |
Ord a => LeftGCDMonoid (Set a) Source # | O(m*log(n/m + 1)), m <= n |
Defined in Data.Monoid.GCD Methods commonPrefix :: Set a -> Set a -> Set a Source # stripCommonPrefix :: Set a -> Set a -> (Set a, Set a, Set a) Source # | |
(StableFactorial m, TextualMonoid m, LeftGCDMonoid m) => LeftGCDMonoid (LinePositioned m) Source # | |
Defined in Data.Monoid.Instances.Positioned Methods commonPrefix :: LinePositioned m -> LinePositioned m -> LinePositioned m Source # stripCommonPrefix :: LinePositioned m -> LinePositioned m -> (LinePositioned m, LinePositioned m, LinePositioned m) Source # | |
(StableFactorial m, FactorialMonoid m, LeftGCDMonoid m) => LeftGCDMonoid (OffsetPositioned m) Source # | |
Defined in Data.Monoid.Instances.Positioned Methods commonPrefix :: OffsetPositioned m -> OffsetPositioned m -> OffsetPositioned m Source # stripCommonPrefix :: OffsetPositioned m -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m, OffsetPositioned m) Source # | |
(LeftGCDMonoid a, StableFactorial a) => LeftGCDMonoid (Measured a) Source # | |
Defined in Data.Monoid.Instances.Measured | |
(LeftGCDMonoid a, StableFactorial a, PositiveMonoid a) => LeftGCDMonoid (Concat a) Source # | |
Defined in Data.Monoid.Instances.Concat | |
(LeftGCDMonoid a, LeftGCDMonoid b) => LeftGCDMonoid (a, b) Source # | |
Defined in Data.Monoid.GCD Methods commonPrefix :: (a, b) -> (a, b) -> (a, b) Source # stripCommonPrefix :: (a, b) -> (a, b) -> ((a, b), (a, b), (a, b)) Source # | |
(Ord k, Eq a) => LeftGCDMonoid (Map k a) Source # | O(m+n) |
Defined in Data.Monoid.GCD Methods commonPrefix :: Map k a -> Map k a -> Map k a Source # stripCommonPrefix :: Map k a -> Map k a -> (Map k a, Map k a, Map k a) Source # | |
(LeftGCDMonoid a, LeftGCDMonoid b) => LeftGCDMonoid (Stateful a b) Source # | |
Defined in Data.Monoid.Instances.Stateful | |
(LeftGCDMonoid a, LeftGCDMonoid b, LeftGCDMonoid c) => LeftGCDMonoid (a, b, c) Source # | |
Defined in Data.Monoid.GCD Methods commonPrefix :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # stripCommonPrefix :: (a, b, c) -> (a, b, c) -> ((a, b, c), (a, b, c), (a, b, c)) Source # | |
(LeftGCDMonoid a, LeftGCDMonoid b, LeftGCDMonoid c, LeftGCDMonoid d) => LeftGCDMonoid (a, b, c, d) Source # | |
Defined in Data.Monoid.GCD Methods commonPrefix :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # stripCommonPrefix :: (a, b, c, d) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), (a, b, c, d)) Source # |
class (Monoid m, RightReductive m) => RightGCDMonoid m where Source #
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)
Minimal complete definition
Instances
RightGCDMonoid () Source # | O(1) |
Defined in Data.Monoid.GCD Methods commonSuffix :: () -> () -> () Source # stripCommonSuffix :: () -> () -> ((), (), ()) Source # | |
RightGCDMonoid ByteString Source # | O(suffixLength) |
Defined in Data.Monoid.GCD Methods commonSuffix :: ByteString -> ByteString -> ByteString Source # stripCommonSuffix :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) Source # | |
RightGCDMonoid ByteString Source # | O(suffixLength) |
Defined in Data.Monoid.GCD Methods commonSuffix :: ByteString -> ByteString -> ByteString Source # stripCommonSuffix :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) Source # | |
RightGCDMonoid Text Source # | O(suffixLength) Since: 1.0 |
Defined in Data.Monoid.GCD Methods commonSuffix :: Text -> Text -> Text Source # stripCommonSuffix :: Text -> Text -> (Text, Text, Text) Source # | |
RightGCDMonoid Text Source # | O(m+n) Since: 1.0 |
Defined in Data.Monoid.GCD Methods commonSuffix :: Text -> Text -> Text Source # stripCommonSuffix :: Text -> Text -> (Text, Text, Text) Source # | |
RightGCDMonoid IntSet Source # | O(m+n) |
Defined in Data.Monoid.GCD Methods commonSuffix :: IntSet -> IntSet -> IntSet Source # stripCommonSuffix :: IntSet -> IntSet -> (IntSet, IntSet, IntSet) Source # | |
Eq x => RightGCDMonoid [x] Source # | O(m+n) Since: 1.0 |
Defined in Data.Monoid.GCD Methods commonSuffix :: [x] -> [x] -> [x] Source # stripCommonSuffix :: [x] -> [x] -> ([x], [x], [x]) Source # | |
RightGCDMonoid x => RightGCDMonoid (Maybe x) Source # | |
Defined in Data.Monoid.GCD Methods commonSuffix :: Maybe x -> Maybe x -> Maybe x Source # stripCommonSuffix :: Maybe x -> Maybe x -> (Maybe x, Maybe x, Maybe x) Source # | |
Eq a => RightGCDMonoid (Vector a) Source # | O(suffixLength) |
Defined in Data.Monoid.GCD | |
LeftGCDMonoid a => RightGCDMonoid (Dual a) Source # | |
Defined in Data.Monoid.GCD Methods commonSuffix :: Dual a -> Dual a -> Dual a Source # stripCommonSuffix :: Dual a -> Dual a -> (Dual a, Dual a, Dual a) Source # | |
RightGCDMonoid (Product Natural) Source # | O(1) |
Defined in Data.Monoid.GCD Methods commonSuffix :: Product Natural -> Product Natural -> Product Natural Source # stripCommonSuffix :: Product Natural -> Product Natural -> (Product Natural, Product Natural, Product Natural) Source # | |
RightGCDMonoid (Sum Natural) Source # | O(1) |
Defined in Data.Monoid.GCD Methods commonSuffix :: Sum Natural -> Sum Natural -> Sum Natural Source # stripCommonSuffix :: Sum Natural -> Sum Natural -> (Sum Natural, Sum Natural, Sum Natural) Source # | |
Eq a => RightGCDMonoid (Seq a) Source # | O(suffixLength) |
Defined in Data.Monoid.GCD Methods commonSuffix :: Seq a -> Seq a -> Seq a Source # stripCommonSuffix :: Seq a -> Seq a -> (Seq a, Seq a, Seq a) Source # | |
Ord a => RightGCDMonoid (Set a) Source # | O(m*log(n/m + 1)), m <= n |
Defined in Data.Monoid.GCD Methods commonSuffix :: Set a -> Set a -> Set a Source # stripCommonSuffix :: Set a -> Set a -> (Set a, Set a, Set a) Source # | |
(StableFactorial m, TextualMonoid m, RightGCDMonoid m) => RightGCDMonoid (LinePositioned m) Source # | |
Defined in Data.Monoid.Instances.Positioned Methods commonSuffix :: LinePositioned m -> LinePositioned m -> LinePositioned m Source # stripCommonSuffix :: LinePositioned m -> LinePositioned m -> (LinePositioned m, LinePositioned m, LinePositioned m) Source # | |
(StableFactorial m, FactorialMonoid m, RightGCDMonoid m) => RightGCDMonoid (OffsetPositioned m) Source # | |
Defined in Data.Monoid.Instances.Positioned Methods commonSuffix :: OffsetPositioned m -> OffsetPositioned m -> OffsetPositioned m Source # stripCommonSuffix :: OffsetPositioned m -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m, OffsetPositioned m) Source # | |
(RightGCDMonoid a, StableFactorial a) => RightGCDMonoid (Measured a) Source # | |
Defined in Data.Monoid.Instances.Measured | |
(RightGCDMonoid a, StableFactorial a, PositiveMonoid a) => RightGCDMonoid (Concat a) Source # | |
Defined in Data.Monoid.Instances.Concat | |
(RightGCDMonoid a, RightGCDMonoid b) => RightGCDMonoid (a, b) Source # | |
Defined in Data.Monoid.GCD Methods commonSuffix :: (a, b) -> (a, b) -> (a, b) Source # stripCommonSuffix :: (a, b) -> (a, b) -> ((a, b), (a, b), (a, b)) Source # | |
(RightGCDMonoid a, RightGCDMonoid b) => RightGCDMonoid (Stateful a b) Source # | |
Defined in Data.Monoid.Instances.Stateful | |
(RightGCDMonoid a, RightGCDMonoid b, RightGCDMonoid c) => RightGCDMonoid (a, b, c) Source # | |
Defined in Data.Monoid.GCD Methods commonSuffix :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # stripCommonSuffix :: (a, b, c) -> (a, b, c) -> ((a, b, c), (a, b, c), (a, b, c)) Source # | |
(RightGCDMonoid a, RightGCDMonoid b, RightGCDMonoid c, RightGCDMonoid d) => RightGCDMonoid (a, b, c, d) Source # | |
Defined in Data.Monoid.GCD Methods commonSuffix :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # stripCommonSuffix :: (a, b, c, d) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), (a, b, c, d)) Source # |
class (Monoid m, LeftReductive m, RightReductive m) => OverlappingGCDMonoid m where Source #
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 is contained
in any other value x
that satifies the property (x
:isPrefixOf
b) && (x isSuffixOf
a)
(x `isPrefixOf` overlap a b) && (x `isSuffixOf` overlap a b)
and it must be unique so it's not contained in any other value y
that satisfies the same property (y
:isPrefixOf
b) && (y isSuffixOf
a)
not ((y `isPrefixOf` overlap a b) && (y `isSuffixOf` overlap a b) && y /= overlap a b)
Since: 1.0
Minimal complete definition
Methods
stripPrefixOverlap :: m -> m -> m Source #
stripSuffixOverlap :: m -> m -> m Source #
overlap :: m -> m -> m Source #
stripOverlap :: m -> m -> (m, m, m) Source #
Instances
OverlappingGCDMonoid () Source # | O(1) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: () -> () -> () Source # stripSuffixOverlap :: () -> () -> () Source # overlap :: () -> () -> () Source # stripOverlap :: () -> () -> ((), (), ()) Source # | |
OverlappingGCDMonoid ByteString Source # | O(min(m,n)^2) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: ByteString -> ByteString -> ByteString Source # stripSuffixOverlap :: ByteString -> ByteString -> ByteString Source # overlap :: ByteString -> ByteString -> ByteString Source # stripOverlap :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) Source # | |
OverlappingGCDMonoid ByteString Source # | O(m*n) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: ByteString -> ByteString -> ByteString Source # stripSuffixOverlap :: ByteString -> ByteString -> ByteString Source # overlap :: ByteString -> ByteString -> ByteString Source # stripOverlap :: ByteString -> ByteString -> (ByteString, ByteString, ByteString) Source # | |
OverlappingGCDMonoid Text Source # | O(min(m,n)^2) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Text -> Text -> Text Source # stripSuffixOverlap :: Text -> Text -> Text Source # overlap :: Text -> Text -> Text Source # stripOverlap :: Text -> Text -> (Text, Text, Text) Source # | |
OverlappingGCDMonoid Text Source # | O(m*n) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Text -> Text -> Text Source # stripSuffixOverlap :: Text -> Text -> Text Source # overlap :: Text -> Text -> Text Source # stripOverlap :: Text -> Text -> (Text, Text, Text) Source # | |
OverlappingGCDMonoid IntSet Source # | O(m+n) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: IntSet -> IntSet -> IntSet Source # stripSuffixOverlap :: IntSet -> IntSet -> IntSet Source # overlap :: IntSet -> IntSet -> IntSet Source # stripOverlap :: IntSet -> IntSet -> (IntSet, IntSet, IntSet) Source # | |
Eq a => OverlappingGCDMonoid [a] Source # | O(m*n) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: [a] -> [a] -> [a] Source # stripSuffixOverlap :: [a] -> [a] -> [a] Source # overlap :: [a] -> [a] -> [a] Source # stripOverlap :: [a] -> [a] -> ([a], [a], [a]) Source # | |
(OverlappingGCDMonoid a, MonoidNull a) => OverlappingGCDMonoid (Maybe a) Source # | |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Maybe a -> Maybe a -> Maybe a Source # stripSuffixOverlap :: Maybe a -> Maybe a -> Maybe a Source # overlap :: Maybe a -> Maybe a -> Maybe a Source # stripOverlap :: Maybe a -> Maybe a -> (Maybe a, Maybe a, Maybe a) Source # | |
Eq a => OverlappingGCDMonoid (Vector a) Source # | O(min(m,n)^2) |
OverlappingGCDMonoid a => OverlappingGCDMonoid (Dual a) Source # | |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Dual a -> Dual a -> Dual a Source # stripSuffixOverlap :: Dual a -> Dual a -> Dual a Source # overlap :: Dual a -> Dual a -> Dual a Source # stripOverlap :: Dual a -> Dual a -> (Dual a, Dual a, Dual a) Source # | |
OverlappingGCDMonoid (Product Natural) Source # | O(1) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Product Natural -> Product Natural -> Product Natural Source # stripSuffixOverlap :: Product Natural -> Product Natural -> Product Natural Source # overlap :: Product Natural -> Product Natural -> Product Natural Source # stripOverlap :: Product Natural -> Product Natural -> (Product Natural, Product Natural, Product Natural) Source # | |
OverlappingGCDMonoid (Sum Natural) Source # | O(1) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Sum Natural -> Sum Natural -> Sum Natural Source # stripSuffixOverlap :: Sum Natural -> Sum Natural -> Sum Natural Source # overlap :: Sum Natural -> Sum Natural -> Sum Natural Source # stripOverlap :: Sum Natural -> Sum Natural -> (Sum Natural, Sum Natural, Sum Natural) Source # | |
Eq a => OverlappingGCDMonoid (IntMap a) Source # | O(m+n) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: IntMap a -> IntMap a -> IntMap a Source # stripSuffixOverlap :: IntMap a -> IntMap a -> IntMap a Source # overlap :: IntMap a -> IntMap a -> IntMap a Source # stripOverlap :: IntMap a -> IntMap a -> (IntMap a, IntMap a, IntMap a) Source # | |
Eq a => OverlappingGCDMonoid (Seq a) Source # | O(min(m,n)^2) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Seq a -> Seq a -> Seq a Source # stripSuffixOverlap :: Seq a -> Seq a -> Seq a Source # overlap :: Seq a -> Seq a -> Seq a Source # stripOverlap :: Seq a -> Seq a -> (Seq a, Seq a, Seq a) Source # | |
Ord a => OverlappingGCDMonoid (Set a) Source # | O(m*log(nm + 1)), m <= n/ |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Set a -> Set a -> Set a Source # stripSuffixOverlap :: Set a -> Set a -> Set a Source # overlap :: Set a -> Set a -> Set a Source # stripOverlap :: Set a -> Set a -> (Set a, Set a, Set a) Source # | |
(OverlappingGCDMonoid a, OverlappingGCDMonoid b) => OverlappingGCDMonoid (a, b) Source # | |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: (a, b) -> (a, b) -> (a, b) Source # stripSuffixOverlap :: (a, b) -> (a, b) -> (a, b) Source # overlap :: (a, b) -> (a, b) -> (a, b) Source # stripOverlap :: (a, b) -> (a, b) -> ((a, b), (a, b), (a, b)) Source # | |
(Ord k, Eq v) => OverlappingGCDMonoid (Map k v) Source # | O(m+n) |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: Map k v -> Map k v -> Map k v Source # stripSuffixOverlap :: Map k v -> Map k v -> Map k v Source # overlap :: Map k v -> Map k v -> Map k v Source # stripOverlap :: Map k v -> Map k v -> (Map k v, Map k v, Map k v) Source # | |
(OverlappingGCDMonoid a, OverlappingGCDMonoid b, OverlappingGCDMonoid c) => OverlappingGCDMonoid (a, b, c) Source # | |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # stripSuffixOverlap :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # overlap :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # stripOverlap :: (a, b, c) -> (a, b, c) -> ((a, b, c), (a, b, c), (a, b, c)) Source # | |
(OverlappingGCDMonoid a, OverlappingGCDMonoid b, OverlappingGCDMonoid c, OverlappingGCDMonoid d) => OverlappingGCDMonoid (a, b, c, d) Source # | |
Defined in Data.Monoid.Monus Methods stripPrefixOverlap :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # stripSuffixOverlap :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # overlap :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # stripOverlap :: (a, b, c, d) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), (a, b, c, d)) Source # |