| Copyright | © 2022–2024 Jonathan Knowles |
|---|---|
| License | Apache-2.0 |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.MonoidMap
Description
Synopsis
- data MonoidMap k v
- empty :: MonoidMap k v
- fromList :: (Ord k, MonoidNull v) => [(k, v)] -> MonoidMap k v
- fromListWith :: (Ord k, MonoidNull v) => (v -> v -> v) -> [(k, v)] -> MonoidMap k v
- fromMap :: MonoidNull v => Map k v -> MonoidMap k v
- singleton :: (Ord k, MonoidNull v) => k -> v -> MonoidMap k v
- toList :: MonoidMap k v -> [(k, v)]
- toMap :: MonoidMap k v -> Map k v
- get :: (Ord k, Monoid v) => k -> MonoidMap k v -> v
- set :: (Ord k, MonoidNull v) => k -> v -> MonoidMap k v -> MonoidMap k v
- adjust :: (Ord k, MonoidNull v) => (v -> v) -> k -> MonoidMap k v -> MonoidMap k v
- nullify :: Ord k => k -> MonoidMap k v -> MonoidMap k v
- null :: MonoidMap k v -> Bool
- nullKey :: Ord k => k -> MonoidMap k v -> Bool
- nonNull :: MonoidMap k v -> Bool
- nonNullCount :: MonoidMap k v -> Int
- nonNullKey :: Ord k => k -> MonoidMap k v -> Bool
- nonNullKeys :: MonoidMap k v -> Set k
- take :: Int -> MonoidMap k v -> MonoidMap k v
- drop :: Int -> MonoidMap k v -> MonoidMap k v
- splitAt :: Int -> MonoidMap k a -> (MonoidMap k a, MonoidMap k a)
- filter :: (v -> Bool) -> MonoidMap k v -> MonoidMap k v
- filterKeys :: (k -> Bool) -> MonoidMap k v -> MonoidMap k v
- filterWithKey :: (k -> v -> Bool) -> MonoidMap k v -> MonoidMap k v
- partition :: (v -> Bool) -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v)
- partitionKeys :: (k -> Bool) -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v)
- partitionWithKey :: (k -> v -> Bool) -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v)
- map :: MonoidNull v2 => (v1 -> v2) -> MonoidMap k v1 -> MonoidMap k v2
- mapKeys :: (Ord k2, MonoidNull v) => (k1 -> k2) -> MonoidMap k1 v -> MonoidMap k2 v
- mapKeysWith :: (Ord k2, MonoidNull v) => (v -> v -> v) -> (k1 -> k2) -> MonoidMap k1 v -> MonoidMap k2 v
- append :: (Ord k, MonoidNull v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- minus :: (Ord k, MonoidNull v, Group v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- minusMaybe :: (Ord k, MonoidNull v, Reductive v) => MonoidMap k v -> MonoidMap k v -> Maybe (MonoidMap k v)
- monus :: (Ord k, MonoidNull v, Monus v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- invert :: (MonoidNull v, Group v) => MonoidMap k v -> MonoidMap k v
- power :: (Integral i, MonoidNull v, Group v) => MonoidMap k v -> i -> MonoidMap k v
- isSubmapOf :: (Ord k, Monoid v, Reductive v) => MonoidMap k v -> MonoidMap k v -> Bool
- isSubmapOfBy :: (Ord k, Monoid v1, Monoid v2) => (v1 -> v2 -> Bool) -> MonoidMap k v1 -> MonoidMap k v2 -> Bool
- disjoint :: (Ord k, GCDMonoid v, MonoidNull v) => MonoidMap k v -> MonoidMap k v -> Bool
- disjointBy :: (Ord k, Monoid v1, Monoid v2) => (v1 -> v2 -> Bool) -> MonoidMap k v1 -> MonoidMap k v2 -> Bool
- intersection :: (Ord k, MonoidNull v, GCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- intersectionWith :: (Ord k, MonoidNull v3) => (v1 -> v2 -> v3) -> MonoidMap k v1 -> MonoidMap k v2 -> MonoidMap k v3
- intersectionWithA :: (Applicative f, Ord k, MonoidNull v3) => (v1 -> v2 -> f v3) -> MonoidMap k v1 -> MonoidMap k v2 -> f (MonoidMap k v3)
- union :: (Ord k, MonoidNull v, LCMMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- unionWith :: (Ord k, Monoid v1, Monoid v2, MonoidNull v3) => (v1 -> v2 -> v3) -> MonoidMap k v1 -> MonoidMap k v2 -> MonoidMap k v3
- unionWithA :: (Applicative f, Ord k, Monoid v1, Monoid v2, MonoidNull v3) => (v1 -> v2 -> f v3) -> MonoidMap k v1 -> MonoidMap k v2 -> f (MonoidMap k v3)
- isPrefixOf :: (Ord k, Monoid v, LeftReductive v) => MonoidMap k v -> MonoidMap k v -> Bool
- stripPrefix :: (Ord k, MonoidNull v, LeftReductive v) => MonoidMap k v -> MonoidMap k v -> Maybe (MonoidMap k v)
- commonPrefix :: (Ord k, MonoidNull v, LeftGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripCommonPrefix :: (Ord k, MonoidNull v, LeftGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v, MonoidMap k v)
- isSuffixOf :: (Ord k, Monoid v, RightReductive v) => MonoidMap k v -> MonoidMap k v -> Bool
- stripSuffix :: (Ord k, MonoidNull v, RightReductive v) => MonoidMap k v -> MonoidMap k v -> Maybe (MonoidMap k v)
- commonSuffix :: (Ord k, MonoidNull v, RightGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripCommonSuffix :: (Ord k, MonoidNull v, RightGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v, MonoidMap k v)
- overlap :: (Ord k, MonoidNull v, OverlappingGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripPrefixOverlap :: (Ord k, MonoidNull v, OverlappingGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripSuffixOverlap :: (Ord k, MonoidNull v, OverlappingGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripOverlap :: (Ord k, MonoidNull v, OverlappingGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v, MonoidMap k v)
Introduction
This module provides the MonoidMap type, which:
- models a total function with
+
Data.MonoidMap monoidmap-0.0.1.4: Monoidal map typeCopyright © 2022–2024 Jonathan Knowles License Apache-2.0 Safe Haskell None Language Haskell2010 Data.MonoidMap
Description
Synopsis
- data MonoidMap k v
- empty :: MonoidMap k v
- fromList :: (Ord k, MonoidNull v) => [(k, v)] -> MonoidMap k v
- fromListWith :: (Ord k, MonoidNull v) => (v -> v -> v) -> [(k, v)] -> MonoidMap k v
- fromMap :: MonoidNull v => Map k v -> MonoidMap k v
- singleton :: (Ord k, MonoidNull v) => k -> v -> MonoidMap k v
- toList :: MonoidMap k v -> [(k, v)]
- toMap :: MonoidMap k v -> Map k v
- get :: (Ord k, Monoid v) => k -> MonoidMap k v -> v
- set :: (Ord k, MonoidNull v) => k -> v -> MonoidMap k v -> MonoidMap k v
- adjust :: (Ord k, MonoidNull v) => (v -> v) -> k -> MonoidMap k v -> MonoidMap k v
- nullify :: Ord k => k -> MonoidMap k v -> MonoidMap k v
- null :: MonoidMap k v -> Bool
- nullKey :: Ord k => k -> MonoidMap k v -> Bool
- nonNull :: MonoidMap k v -> Bool
- nonNullCount :: MonoidMap k v -> Int
- nonNullKey :: Ord k => k -> MonoidMap k v -> Bool
- nonNullKeys :: MonoidMap k v -> Set k
- take :: Int -> MonoidMap k v -> MonoidMap k v
- drop :: Int -> MonoidMap k v -> MonoidMap k v
- splitAt :: Int -> MonoidMap k a -> (MonoidMap k a, MonoidMap k a)
- filter :: (v -> Bool) -> MonoidMap k v -> MonoidMap k v
- filterKeys :: (k -> Bool) -> MonoidMap k v -> MonoidMap k v
- filterWithKey :: (k -> v -> Bool) -> MonoidMap k v -> MonoidMap k v
- partition :: (v -> Bool) -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v)
- partitionKeys :: (k -> Bool) -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v)
- partitionWithKey :: (k -> v -> Bool) -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v)
- map :: MonoidNull v2 => (v1 -> v2) -> MonoidMap k v1 -> MonoidMap k v2
- mapKeys :: (Ord k2, MonoidNull v) => (k1 -> k2) -> MonoidMap k1 v -> MonoidMap k2 v
- mapKeysWith :: (Ord k2, MonoidNull v) => (v -> v -> v) -> (k1 -> k2) -> MonoidMap k1 v -> MonoidMap k2 v
- append :: (Ord k, MonoidNull v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- minus :: (Ord k, MonoidNull v, Group v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- minusMaybe :: (Ord k, MonoidNull v, Reductive v) => MonoidMap k v -> MonoidMap k v -> Maybe (MonoidMap k v)
- monus :: (Ord k, MonoidNull v, Monus v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- invert :: (MonoidNull v, Group v) => MonoidMap k v -> MonoidMap k v
- power :: (Integral i, MonoidNull v, Group v) => MonoidMap k v -> i -> MonoidMap k v
- isSubmapOf :: (Ord k, Monoid v, Reductive v) => MonoidMap k v -> MonoidMap k v -> Bool
- isSubmapOfBy :: (Ord k, Monoid v1, Monoid v2) => (v1 -> v2 -> Bool) -> MonoidMap k v1 -> MonoidMap k v2 -> Bool
- disjoint :: (Ord k, GCDMonoid v, MonoidNull v) => MonoidMap k v -> MonoidMap k v -> Bool
- disjointBy :: (Ord k, Monoid v1, Monoid v2) => (v1 -> v2 -> Bool) -> MonoidMap k v1 -> MonoidMap k v2 -> Bool
- intersection :: (Ord k, MonoidNull v, GCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- intersectionWith :: (Ord k, MonoidNull v3) => (v1 -> v2 -> v3) -> MonoidMap k v1 -> MonoidMap k v2 -> MonoidMap k v3
- intersectionWithA :: (Applicative f, Ord k, MonoidNull v3) => (v1 -> v2 -> f v3) -> MonoidMap k v1 -> MonoidMap k v2 -> f (MonoidMap k v3)
- union :: (Ord k, MonoidNull v, LCMMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- unionWith :: (Ord k, Monoid v1, Monoid v2, MonoidNull v3) => (v1 -> v2 -> v3) -> MonoidMap k v1 -> MonoidMap k v2 -> MonoidMap k v3
- unionWithA :: (Applicative f, Ord k, Monoid v1, Monoid v2, MonoidNull v3) => (v1 -> v2 -> f v3) -> MonoidMap k v1 -> MonoidMap k v2 -> f (MonoidMap k v3)
- isPrefixOf :: (Ord k, Monoid v, LeftReductive v) => MonoidMap k v -> MonoidMap k v -> Bool
- stripPrefix :: (Ord k, MonoidNull v, LeftReductive v) => MonoidMap k v -> MonoidMap k v -> Maybe (MonoidMap k v)
- commonPrefix :: (Ord k, MonoidNull v, LeftGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripCommonPrefix :: (Ord k, MonoidNull v, LeftGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v, MonoidMap k v)
- isSuffixOf :: (Ord k, Monoid v, RightReductive v) => MonoidMap k v -> MonoidMap k v -> Bool
- stripSuffix :: (Ord k, MonoidNull v, RightReductive v) => MonoidMap k v -> MonoidMap k v -> Maybe (MonoidMap k v)
- commonSuffix :: (Ord k, MonoidNull v, RightGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripCommonSuffix :: (Ord k, MonoidNull v, RightGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v, MonoidMap k v)
- overlap :: (Ord k, MonoidNull v, OverlappingGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripPrefixOverlap :: (Ord k, MonoidNull v, OverlappingGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripSuffixOverlap :: (Ord k, MonoidNull v, OverlappingGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v
- stripOverlap :: (Ord k, MonoidNull v, OverlappingGCDMonoid v) => MonoidMap k v -> MonoidMap k v -> (MonoidMap k v, MonoidMap k v, MonoidMap k v)
Introduction
This module provides the
MonoidMaptype, which:- models a total function with
finite support
from keys to monoidal values, with a default value
of
mempty. - encodes key-value mappings with a minimal encoding that
@@ -12,38 +12,38 @@
possible key of type
kwith a value of typev:get:: (Ordk,Monoidv) => k ->MonoidMapk v -> vThe
emptymap associates every keykwith a default value ofmempty:∀ k.
getkempty==mempty-Comparison with standard
MaptypeThe
MonoidMaptype differs from the standardMaptype in how it relates - keys to values:Type Models a total function with finite support Mapk v+Comparison with standard
MaptypeThe
MonoidMaptype differs from the standardMaptype in how it relates + keys to values:Type Models a total function with finite support Mapk vfrom keys of type kto values of typeMaybevMonoidMapk vfrom keys of type kto values of typev.This difference can be illustrated by comparing the type signatures of - operations to query a key for its value, for both types:
Map.lookup:: k ->Mapk v ->Maybev + operations to query a key for its value, for both types:Map.lookup:: k ->Mapk v ->MaybevMonoidMap.get::Monoidv => k ->MonoidMapk v -> v -Whereas a standard
Maphas a default value ofNothing, aMonoidMaphas - a default value ofmempty:∀ k.
Map.lookupkMap.empty==Nothing+Whereas a standard
Maphas a default value ofNothing, aMonoidMaphas + a default value ofmempty:∀ k.
Map.lookupkMap.empty==Nothing∀ k.MonoidMap.getkMonoidMap.empty==mempty-In practice, the standard
Maptype usesMaybeto indicate the presence +In practice, the standard
Maptype usesMaybeto indicate the presence or absence of a value for a particular key. This representation is - necessary because theMaptype imposes no constraints on value types.However, monoidal types already have a natural way to represent null or + necessary because the
Maptype imposes no constraints on value types.However, monoidal types already have a natural way to represent null or empty values: the
memptyconstant, which represents the neutral or - identity element of aMonoid.Consequently, using a standard
Mapwith a monoidal value type gives rise + identity element of aMonoid.Consequently, using a standard
Mapwith a monoidal value type gives rise to two distinct representations for null or empty values:-Map.lookupk m +Map.lookupk mInterpretation Nothing-Mapmhas no entry +Mapmhas no entry for keyk.Justmempty-Mapmhas an entry +Mapmhas an entry for keyk, but the value is empty.In constrast, the
MonoidMaptype provides a single, canonical representation for null or empty values, according to the following conceptual mapping:-Map.lookupk m +Map.lookupk m@@ -107,14 +107,14 @@ function.Satisfies the following property for all possible keys
k:getk (fromListWithf kvs)==maybemempty(foldl1f) (nonEmpty(snd<$>filter((==k) . fst) kvs)) -fromMap :: MonoidNull v => Map k v -> MonoidMap k v #
fromMap :: MonoidNull v => Map k v -> MonoidMap k v #
singleton :: (Ord k, MonoidNull v) => k -> v -> MonoidMap k v #
Deconstruction
toList :: MonoidMap k v -> [(k, v)] #
\(O(n)\). Converts a
MonoidMapto a list of key-value pairs, where the keys are in ascending order.The result only includes entries with values that are not
null.Satisfies the following round-trip property:
fromList(toListm)==mThe resulting list is sorted in ascending key order:
sortOnfst(toListm)==toListm -Lookup
Modification
nonNullCount :: MonoidMap k v -> Int #
\(O(1)\). Returns a count of all values in the map that are not
null.Satisfies the following property:
nonNullCountm==size(nonNullKeysm)nonNullKey :: Ord k => k -> MonoidMap k v -> Bool #
nonNullKeys :: MonoidMap k v -> Set k #
\(O(n)\). Returns the set of keys associated with values that are not +
nonNullKeys :: MonoidMap k v -> Set k #
\(O(n)\). Returns the set of keys associated with values that are not
null.Satisfies the following property:
k
`member`(nonNullKeysm)==nonNullKeyk mSlicing
take :: Int -> MonoidMap k v -> MonoidMap k v #
\(O(\log n)\). Takes a slice from a map.
This function takes a given number of non-
nullentries from a map, producing a new map from the entries that were taken.Entries are taken in key order, beginning with the smallest keys.
Satifies the following property:
taken==fromList.taken .toList@@ -247,7 +247,7 @@ (\r ->Just(getk r)==getk m1</>getk m2) (m1`minusMaybe`m2)This function provides the definition of
(</>)for theMonoidMap- instance ofReductive.Examples
monus :: (Ord k, MonoidNull v, Monus v) => MonoidMap k v -> MonoidMap k v -> MonoidMap k v #
Performs monus subtraction of the second map from the first.
Uses the
Monussubtraction operator(<\>)to subtract each value in the second map from its matching value in the first map.Satisfies the following property for all possible keys
k:getk (m1`monus`m2)==getk m1<\>getk m2This function provides the definition of
(<\>)for theMonoidMap- instance ofMonus.Examples
With
SetNaturalvalues, this function performs set + instance ofMonus.Examples
With
SetNaturalvalues, this function performs set subtraction of matching values:f xs =
fromList(fromList<$>xs)>>> m1 = f [("a", [0,1,2]), ("b", [0,1,2])] >>> m2 = f [("a", [ ]), ("b", [0,1,2])] @@ -394,7 +394,7 @@ >>> m3 =fromList[("a", 0), ("b", 1), ("c", 1), ("d", 0)]>>>
intersectionm1 m2==m3True-With
SetNaturalvalues, this function computes the +With
SetNaturalvalues, this function computes the set intersection of each pair of matching values:f xs =
fromList(fromList<$>xs)>>> m1 = f [("a", [0,1,2]), ("b", [0,1,2 ]), ("c", [0,1,2 ])] >>> m2 = f [("a", [0,1,2]), ("b", [ 1,2,3]), ("c", [ 2,3,4])] @@ -445,7 +445,7 @@ >>> m3 =fromList[("a", 3), ("b", 2), ("c", 2), ("d", 3)]>>>
unionm1 m2==m3True-With
SetNaturalvalues, this function computes the +With
SetNaturalvalues, this function computes the set union of each pair of matching values:f xs =
fromList(fromList<$>xs)>>> m1 = f [("a", [0,1,2]), ("b", [0,1,2 ]), ("c", [0,1,2 ])] >>> m2 = f [("a", [0,1,2]), ("b", [ 1,2,3]), ("c", [ 2,3,4])]