alice
library
manual.
signature MAP
functor MkRedBlackMap (Key : ORDERED) :> MAP where type key = Key.t
The MAP signature provides a functional interface to finite maps. The MkRedBlackMap functor provides an implementation of this interface based on red-black trees.
See also: IMP_MAP, SET, ORDERED
import signature MAP from "x-alice:/lib/data/MAP-sig"
import functor MkRedBlackMap from "x-alice:/lib/data/MkRedBlackMap"
signature MAP =
sig
type key
type 'a map
type 'a t = 'a map
exception Unknown of key
exception Collision of key
val empty : 'a map
val singleton : key * 'a -> 'a map
val fromList : (key * 'a) list -> 'a map
val fromVector : (key * 'a) vector -> 'a map
val toList : 'a map -> (key * 'a) list
val toVector : 'a map -> (key * 'a) vector
val insert : 'a map * key * 'a -> 'a map
val insertDisjoint : 'a map * key * 'a -> 'a map
val insertWith : ('a * 'a -> 'a) -> 'a map * key * 'a -> 'a map
val insertWithi : (key * 'a * 'a -> 'a) -> 'a map * key * 'a -> 'a map
val remove : 'a map * key -> 'a map
val removeExistent : 'a map * key -> 'a map
val removeWith : (key -> unit) -> 'a map * key -> 'a map
val union : 'a map * 'a map -> 'a map
val unionDisjoint : 'a map * 'a map -> 'a map
val unionWith : ('a * 'a -> 'a) -> 'a map * 'a map -> 'a map
val unionWithi : (key * 'a * 'a -> 'a) -> 'a map * 'a map -> 'a map
val intersect : 'a map * 'a map -> 'a map
val intersectWith : ('a * 'a -> 'a) -> 'a map * 'a map -> 'a map
val intersectWithi : (key * 'a * 'a -> 'a) -> 'a map * 'a map -> 'a map
val difference : 'a map * 'a map -> 'a map
val size : 'a map -> int
val isEmpty : 'a map -> bool
val member : 'a map * key -> bool
val lookup : 'a map * key -> 'a option
val lookupExistent : 'a map * key -> 'a
val choose : 'a map -> 'a option
val choosei : 'a map -> (key * 'a) option
val equal : ('a * 'a -> bool) -> 'a map * 'a map -> bool
val submap : ('a * 'a -> bool) -> 'a map * 'a map -> bool
val disjoint : 'a map * 'a map -> bool
val app : ('a -> unit) -> 'a map -> unit
val map : ('a -> 'b) -> 'a map -> 'b map
val mapPartial : ('a -> 'b option) -> 'a map -> 'b map
val fold : ('a * 'b -> 'b) -> 'b -> 'a map -> 'b
val all : ('a -> bool) -> 'a map -> bool
val exists : ('a -> bool) -> 'a map -> bool
val find : ('a -> bool) -> 'a map -> 'a option
val filter : ('a -> bool) -> 'a map -> 'a map
val partition : ('a -> bool) -> 'a map -> 'a map * 'a map
val appi : (key * 'a -> unit) -> 'a map -> unit
val mapi : (key * 'a -> 'b) -> 'a map -> 'b map
val mapPartiali : (key * 'a -> 'b option) -> 'a map -> 'b map
val foldi : (key * 'a * 'b -> 'b) -> 'b -> 'a map -> 'b
val alli : (key * 'a -> bool) -> 'a map -> bool
val existsi : (key * 'a -> bool) -> 'a map -> bool
val findi : (key * 'a -> bool) -> 'a map -> (key * 'a) option
val filteri : (key * 'a -> bool) -> 'a map -> 'a map
val partitioni : (key * 'a -> bool) -> 'a map -> 'a map * 'a map
end
The type of keys.
The type of finite maps from keys of type key to values of type 'a.
Indicates that a key could not be found in the map.
Indicates an attempt to add a key that already is in the map when using functions that disallow replacement.
The empty map.
The map only containing the single entry k->x.
Constructs a map from a list of key/value pairs. Raises Collision k is a key in the list that is followed by at least one other key equal to k.
Constructs a map from a vector of key/value pairs. Raises Collision k if k is a key in the vector that is followed by at least one other entry with a key equal to k. Equivalent to fromList(Vector.toList v).
Returns the list of key/value pairs from map m. For red-black maps, the pairs are delivered in increasing key order.
Returns the vector of key/value pairs from map m. For red-black maps, the pairs are delivered in increasing key order. Equivalent to Vector.fromList(toList m).
Returns the map m extended with the entry k->x. In the first form, if m already contains a key k' equal to k, then the corresponding entry gets replaced by k->x. In the second form, Collision k' will be raised. In the third form, the entry is replaced by k->f(x', x), where x' is the value k' maps to. In the forth form, k' is additionally passed to f. The following equivalences hold:
insert = insertWith #2
insertDisjoint = insertWithi (fn (k,_,_) => raise Collision k)
insertWith f = insertWithi (fn (_,x,y) => f(x, y))
Returns the map m with the entry corresponding to key k removed. In the first form, if no key equal to k is contained in m, then the map is returned unchanged. In the second form, Unknown k will be raised. In the third form, f is applied to k before the map is returned unchanged. The following equivalences hold:
remove = removeWith ignore
removeExistent = removeWith (fn k => raise Unknown k)
Returns the union of maps m1 and m1. In the first form, if m1 and m2 contain entries k1->x1 and k2->x2 with equal keys k1 and k2, respectively, then the resulting map will contain k2->x2. In the second form, Collision k2 will be raised. In the third form, the resulting map will contain k2->f(x1,x2). In the forth form, k2 is additionally passed to f. The following equivalences hold:
union = unionWith #2
unionDisjoint = unionWithi (fn (k,_,_) => raise Collision k)
unionWith f = unionWithi (fn (_,x,y) => f(x, y))
Returns the intersection of maps m1 and m1, i.e. a map whose domain is the intersection of the domains of the two maps. In the first form, if m1 and m2 contain entries k1->x1 and k2->x2 with equal keys k1 and k2, respectively, then the resulting map will contain k2->x2. In the second form, the resulting map will contain k2->f(x1,x2). In the third form, k2 is additionally passed to f. The following equivalences hold:
intersect = intersectWith #2
intersectWith f = intersectWithi (fn (_,x,y) => f(x, y))
Returns the difference of maps m1 and m1, i.e. a map that contains only those entries k1->x1 from m1 for which no key k2 equal to k1 is in the domain of m2.
Returns the cardinality of the map m, i.e. the number of entries it contains.
Returns true if m is the empty map, false otherwise. Equivalent to size m = 0.
Returns true if the map m contains a key equal to k, false otherwise.
In the first form, returns SOME x if the map m contains an entry k'->x, where key k' is equal to k, NONE otherwise. In the second form, returns x unwrapped, or raises Unknown k if no such entry exists.
In the first form, returns SOME x, such that k->x is an entry of the map m. In the second form, returns SOME(k,x). Returns NONE if m is the empty map. For red-black maps, k will be the smallest key in the map.
Returns true if m1 and m2 are maps with equal entries, false otherwise. Two entries k1->x1 and k2->x2 are considered equal if Key.equal(k1, k2) andalso f(x1, x2) evaluates to true.
Returns true if m1 contains an entry k1->x1 for every entry k2->x2 in m2, such that Key.equal(k1, k2) andalso f(x1, x2) evaluates to true.
Returns true if m1 and m2 are maps with disjoint domains, false otherwise.
In the second form, applies f to each entry in the map m. In the first form, applies f to the value in the entry only. For red-black trees, this happens in increasing order. The following equivalences hold:
app f m = appi (f o #2) m
appi f m = List.app f (toList m)
In the second form, returns the map which contains the entries resulting from applying f to each entry in map m. In the first form, only x is passed to f. For red-black trees, the mapping is applied in increasing order. The following equivalences hold:
map f m = mapi (f o #2) m
mapi f m = fromList (List.map f (toList m))
In the second form, applies f to each entry in map m and returns the map of defined results. In the first form, only x is passed to f. For red-black trees, the function is applied in increasing order. The following equivalences hold:
mapPartial f m = mapPartiali (f o #2) m
mapPartiali f m = fromList (List.mapPartial f (toList m))
In the second form, sequentially applies f to the triple of each map entry's key and value and the result of the previous application, starting with initial value a. In the first form, only an entry's value and the previous result are passed to f. For red-black trees, folding is performed in increasing order. The following equivalences hold:
fold f a m = fold (fn (_,x,y) => f (x,y)) a m
foldi f a m = List.foldl f a (toList m)
In the second form, applies f to each entry (k, x) of map ms until f(k, x) delivers false. Returns false if such an entry exists, true otherwise. In the first form, only x is passed to f. For red-black trees, f is applied in increasing order. The following equivalences hold:
all f m = alli (f o #2) m
alli f m = List.all f (toList m)
In the second form, applies f to each entry (k, x) of map ms until f(k, x) delivers true. Returns true if such an entry exists, false otherwise. In the first form, only x is passed to f. For red-black trees, f is applied in increasing order. The following equivalences hold:
exists f m = existsi (f o #2) m
existsi f m = List.exists f (toList m)
In the second form, applies f to each entry (k, x) of map m until f(k, x) delivers true. Returns SOME(k, x) if such an entry exists, NONE otherwise. In the first form, only x is passed to f, and on success SOME x is returned. For red-black trees, f is applied in increasing order. The following equivalences hold:
find f m = Option.map #2 (findi (f o #2) m)
findi f m = List.find f (toList m)
In the second form, applies f to each entry (k, x) of map m and returns the map containing those entries for which f(k, x) delivered true. In the first form, only x is passed to f. For red-black trees, f is applied in increasing order. The following equivalences hold:
filter f m = filteri (f o #2) m
filteri f m = fromList (List.filter f (toList m))
In the second form, applies f to each entry (k, x) of map m and returns the pair (m1, m2) of maps where m1 contains all entries for which f(k, x) delivered true, and m2 all entries for which it delivered false. In the first form, only x is passed to f. For red-black trees, f is applied in increasing order. The following equivalences hold:
partition f m = partitioni (f o #2) m
partitioni f m = Pair.map (fromList, fromList) (List.partition f (toList m))