src/index.ts
import {
IDENTITY,
COMPARE,
} from "extra-function";
import {
MapFunction as IterableMapFunction,
} from "extra-iterable";
import {
last as arrayLast,
some as arraySome,
subsequences as arraySubsequences,
randomValue as arrayRandomValue,
randomSubsequence as arrayRandomSubsequence,
} from "extra-array";
// TYPES
// =====
/** Entries is a list of key-value pairs, with unique keys. */
export type Entries<K, V> = Iterable<[K, V]>;
/** Lists is a pair of key list and value list, with unique keys. */
export type Lists<K, V> = [Iterable<K>, Iterable<V>];
/**
* Handle reading of a single value.
* @returns value
*/
export type ReadFunction<V> = () => V;
/**
* Handle combining of two values.
* @param a a value
* @param b another value
* @returns combined value
*/
export type CombineFunction<V> = (a: V, b: V) => V;
/**
* Handle comparison of two values.
* @param a a value
* @param b another value
* @returns a<b: -ve, a=b: 0, a>b: +ve
*/
export type CompareFunction<V> = (a: V, b: V) => number;
/**
* Handle processing of values in a map.
* @param v value in map
* @param k key of value in map
* @param x map containing the value
*/
export type ProcessFunction<K, V> = (v: V, k: K, x: Map<K, V>) => void;
/**
* Handle selection of values in a map.
* @param v value in map
* @param k key of value in map
* @param x map containing the value
* @returns selected?
*/
export type TestFunction<K, V> = (v: V, k: K, x: Map<K, V>) => boolean;
/**
* Handle transformation of a value to another.
* @param v value in map
* @param k key of value in map
* @param x map containing the value
* @returns transformed value
*/
export type MapFunction<K, V, W> = (v: V, k: K, x: Map<K, V>) => W;
/**
* Handle reduction of multiple values into a single value.
* @param acc accumulator (temporary result)
* @param v value in map
* @param k key of value in map
* @param x map containing the value
* @returns reduced value
*/
export type ReduceFunction<K, V, W> = (acc: W, v: V, k: K, x: Map<K, V>) => W;
/**
* Handle ending of a combined map.
* @param dones iᵗʰ map done?
* @returns combined map done?
*/
export type EndFunction = (dones: boolean[]) => boolean;
// METHODS
// =======
// ABOUT
// -----
/**
* Check if value is a map.
* @param v value
* @returns v is a map?
*/
export function is(v: any): v is Map<any, any> {
return v instanceof Map;
}
/**
* List all keys.
* @param x a map
* @returns k₀, k₁, ... | [kᵢ, vᵢ] ∈ x
*/
export function keys<K, V>(x: Map<K, V>): IterableIterator<K> {
return x.keys();
}
/**
* List all values.
* @param x a map
* @returns v₀, v₁, ... | [kᵢ, vᵢ] ∈ x
*/
export function values<K, V>(x: Map<K, V>): IterableIterator<V> {
return x.values();
}
/**
* List all key-value pairs.
* @param x a map
* @returns [k₀, v₀], [k₁, v₁], ... | [kᵢ, vᵢ] ∈ x
*/
export function entries<K, V>(x: Map<K, V>): IterableIterator<[K, V]> {
return x.entries();
}
// GENERATE
// --------
/**
* Convert entries to map.
* @param x entries
* @returns x as map
*/
export function from<K, V>(x: Entries<K, V>): Map<K, V> {
return new Map(x);
}
export {from as fromEntries};
/**
* Convert entries to map.
* @param x entries (updateable is map!)
* @returns x as map
*/
export function from$<K, V>(x: Entries<K, V>): Map<K, V> {
return x instanceof Map? x : new Map(x);
}
export {from$ as fromEntries$};
/**
* Convert lists to map.
* @param x lists, i.e. [keys, values]
* @returns x as map
*/
export function fromLists<K, V>(x: Lists<K, V>): Map<K, V> {
var [ks, vs] = x;
var iv = vs[Symbol.iterator]();
var a = new Map<K, V>();
for (var k of ks)
a.set(k, iv.next().value);
return a;
}
/**
* Create a map from keys.
* @param x keys
* @param fm map function for values (v, i, x)
* @returns x as map
*/
export function fromKeys<K, V=K>(x: Iterable<K>, fm: IterableMapFunction<K, K|V> | null=null): Map<K, K|V> {
var fm = fm || IDENTITY;
var a = new Map<K, K|V>(), i = -1;
for (var k of x)
a.set(k, fm(k, ++i, x));
return a;
}
/**
* Create a map from values.
* @param x values
* @param fm map function for keys (v, i, x)
* @returns x as map
*/
export function fromValues<V, K=V>(x: Iterable<V>, fm: IterableMapFunction<V, V|K> | null=null): Map<V|K, V> {
var fm = fm || IDENTITY;
var a = new Map<V|K, V>(), i = -1;
for (var v of x)
a.set(fm(v, ++i, x), v);
return a;
}
// COMPARE
// -------
/**
* Compare two maps.
* @param x a map
* @param y another map
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns x=y: 0, otherwise: -ve/+ve
*/
export function compare<K, V, W=V>(x: Map<K, V>, y: Map<K, V>, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): number {
var fc = fc || COMPARE;
var fm = fm || IDENTITY;
var ks = unionKeys(x, y);
for (var k of ks) {
if (!x.has(k)) return -1;
if (!y.has(k)) return 1;
var vx = fm(x.get(k), k, x);
var vy = fm(y.get(k), k, y);
var c = fc(vx, vy);
if (c!==0) return c;
}
return 0;
}
/**
* Check if two maps are equal.
* @param x a map
* @param y another map
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns x = y?
*/
export function isEqual<K, V, W=V>(x: Map<K, V>, y: Map<K, V>, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): boolean {
return x.size===y.size && compare(x, y, fc, fm)===0;
}
// SIZE
// ----
/**
* Find the size of a map.
* @param x a map
* @returns |x|
*/
export function size<K, V>(x: Map<K, V>): number {
return x.size;
}
export {size as length};
/**
* Check if a map is empty.
* @param x a map
* @returns |x| = 0?
*/
export function isEmpty<K, V>(x: Map<K, V>): boolean {
return x.size===0;
}
// GET/SET
// -------
/**
* Get value at key.
* @param x a map
* @param k key
* @returns x[k]
*/
export function get<K, V>(x: Map<K, V>, k: K): V {
return x.get(k);
}
/**
* Get values at keys.
* @param x a map
* @param ks keys
* @returns [x[k₀], x[k₁], ...] | [k₀, k₁, ...] = ks
*/
export function getAll<K, V>(x: Map<K, V>, ks: K[]): V[] {
return ks.map(k => x.get(k));
}
/**
* Get value at path in a nested map.
* @param x a nested map
* @param p path
* @returns x[k₀][k₁][...] | [k₀, k₁, ...] = p
*/
export function getPath<K>(x: Map<K, any>, p: K[]): any {
for (var k of p)
x = is(x)? x.get(k) : undefined;
return x;
}
/**
* Check if nested map has a path.
* @param x a nested map
* @param p path
* @returns x[k₀][k₁][...] exists? | [k₀, k₁, ...] = p
*/
export function hasPath<K>(x: Map<K, any>, p: K[]): boolean {
for (var k of p) {
if (!is(x)) return false;
x = x.get(k);
}
return true;
}
/**
* Set value at key.
* @param x a map
* @param k key
* @param v value
* @returns x' | x' = x; x'[k] = v
*/
export function set<K, V>(x: Entries<K, V>, k: K, v: V): Map<K, V> {
return new Map(x).set(k, v);
}
/**
* Set value at key.
* @param x a map (updated)
* @param k key
* @param v value
* @returns x | x[k] = v
*/
export function set$<K, V>(x: Map<K, V>, k: K, v: V): Map<K, V> {
return x.set(k, v);
}
/**
* Set value at path in a nested map.
* @param x a nested map (updated)
* @param p path
* @param v value
* @returns x | x[k₀][k₁][...] = v; [k₀, k₁, ...] = p
*/
export function setPath$<K>(x: Map<K, any>, p: K[], v: any): Map<K, any> {
var y = getPath(x, p.slice(0, -1));
if (is(y)) y.set(arrayLast(p), v);
return x;
}
/**
* Exchange two values.
* @param x a map
* @param k a key
* @param l another key
* @returns x' | x' = x; x'[k] = x[l]; x'[l] = x[k]
*/
export function swap<K, V>(x: Entries<K, V>, k: K, l: K): Map<K, V> {
return swap$(new Map(x), k, l);
}
/**
* Exchange two values.
* @param x a map (updated)
* @param k a key
* @param l another key
* @returns x | x[i] ↔ x[j]
*/
export function swap$<K, V>(x: Map<K, V>, k: K, l: K): Map<K, V> {
var t = x.get(k);
x.set(k, x.get(l));
x.set(l, t);
return x;
}
/**
* Remove value at key.
* @param x a map
* @param k key
* @returns x \\: [k]
*/
export function remove<K, V>(x: Entries<K, V>, k: K): Map<K, V> {
return remove$(new Map(x), k);
}
/**
* Remove value at key.
* @param x a map (updated)
* @param k key
* @returns x = x \\: [k]
*/
export function remove$<K, V>(x: Map<K, V>, k: K): Map<K, V> {
x.delete(k);
return x;
}
/**
* Remove value at path in a nested map.
* @param x a nested map (updated)
* @param p path
* @returns x = x \\: [k₀][k₁][...] | [k₀, k₁, ...] = p
*/
export function removePath$<K>(x: Map<K, any>, p: K[]): Map<K, any> {
var y = getPath(x, p.slice(0, -1));
if (is(y)) y.delete(arrayLast(p));
return x;
}
// PROPERTY
// --------
/**
* Count values which satisfy a test.
* @param x a map
* @param ft test function (v, k, x)
* @returns Σtᵢ | tᵢ = 1 if ft(vᵢ) else 0; [kᵢ, vᵢ] ∈ x
*/
export function count<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): number {
var a = 0;
for (var [k, v] of x)
if (ft(v, k, x)) ++a;
return a;
}
/**
* Count occurrences of values.
* @param x a map
* @param fm map function (v, k, x)
* @returns Map \{value ⇒ count\}
*/
export function countAs<K, V, W=V>(x: Map<K, V>, fm: MapFunction<K, V, V|W> | null=null): Map<V|W, number> {
var fm = fm || IDENTITY;
var a = new Map();
for (var [k, v] of x) {
var w = fm(v, k, x);
var n = a.get(w) || 0;
a.set(w, n+1);
}
return a;
}
/**
* Find smallest value.
* @param x a map
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns v | v ≤ vᵢ; [kᵢ, vᵢ] ∈ x
*/
export function min<K, V, W=V>(x: Map<K, V>, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): V {
return rangeEntries(x, fc, fm)[0][1];
}
/**
* Find smallest entry.
* @param x a map
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns [min_key, min_value]
*/
export function minEntry<K, V, W=V>(x: Map<K, V>, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): [K, V] {
return rangeEntries(x, fc, fm)[0];
}
/**
* Find largest value.
* @param x a map
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns v | v ≥ vᵢ; [kᵢ, vᵢ] ∈ x
*/
export function max<K, V, W=V>(x: Map<K, V>, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): V {
return rangeEntries(x, fc, fm)[1][1];
}
/**
* Find largest entry.
* @param x a map
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns [max_key, max_value]
*/
export function maxEntry<K, V, W=V>(x: Map<K, V>, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): [K, V] {
return rangeEntries(x, fc, fm)[1];
}
/**
* Find smallest and largest values.
* @param x a map
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns [min_value, max_value]
*/
export function range<K, V, W=V>(x: Map<K, V>, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): [V, V] {
var [a, b] = rangeEntries(x, fc, fm);
return [a[1], b[1]];
}
/**
* Find smallest and largest entries.
* @param x a map
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns [min_entry, max_entry]
*/
export function rangeEntries<K, V, W=V>(x: Map<K, V>, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): [[K, V], [K, V]] {
var fc = fc || COMPARE;
var fm = fm || IDENTITY;
var mk: K, mu: V, mv: V|W;
var nk: K, nu: V, nv: V|W;
var i = 0;
for (var [k, u] of x) {
var v = fm(u, k, x);
if (i===0 || fc(v, mv)<0) { mk = k; mu = u; mv = v; }
if (i===0 || fc(v, nv)>0) { nk = k; nu = u; nv = v; }
++i;
}
return [[mk, mu], [nk, nu]];
}
// PART
// ----
/**
* Get first entry from map (default order).
* @param x a map
* @param ed default entry
* @returns [k₀, v₀] if x ≠ Φ else ed | [k₀, v₀] ∈ x
*/
export function head<K, V>(x: Entries<K, V>, ed: [K, V]=[] as any): [K, V] {
for (var e of x)
return e;
return ed;
}
/**
* Get a map without its first entry (default order).
* @param x a map
* @returns x \\ \{[k₀, v₀]\} if x ≠ Φ else x | [k₀, v₀] ∈ x
*/
export function tail<K, V>(x: Map<K, V>): Map<K, V> {
return drop(x, 1);
}
/**
* Keep first n entries only (default order).
* @param x a map
* @param n number of entries [1]
* @returns \{[k₀, v₀], [k₁, v₁], ...\} | [kᵢ, vᵢ] ∈ x and |\{[k₀, v₀], [k₁, v₁], ...\}| ≤ n
*/
export function take<K, V>(x: Map<K, V>, n: number=1): Map<K, V> {
var a = new Map(), i = -1;
for (var [k, v] of x) {
if (++i>=n) break;
a.set(k, v);
}
return a;
}
/**
* Keep first n entries only (default order).
* @param x a map (updated)
* @param n number of entries [1]
* @returns x = \{[k₀, v₀], [k₁, v₁], ...\} | [kᵢ, vᵢ] ∈ x and |\{[k₀, v₀], [k₁, v₁], ...\}| ≤ n
*/
export function take$<K, V>(x: Map<K, V>, n: number=1): Map<K, V> {
var i = -1;
for (var k of x.keys())
if (++i>=n) x.delete(k);
return x;
}
/**
* Remove first n entries (default order).
* @param x a map
* @param n number of entries [1]
* @returns \{[kₙ, vₙ], [kₙ₊₁, vₙ₊₁], ...\} | [kᵢ, vᵢ] ∈ x and |\{[kₙ, vₙ], [kₙ₊₁, vₙ₊₁], ...\}| ≤ max(|x| - n, 0)
*/
export function drop<K, V>(x: Map<K, V>, n: number=1): Map<K, V> {
var a = new Map(), i = -1;
for (var [k, v] of x)
if (++i>=n) a.set(k, v);
return a;
}
/**
* Remove first n entries (default order).
* @param x a map (updated)
* @param n number of entries [1]
* @returns x = \{[kₙ, vₙ], [kₙ₊₁, vₙ₊₁], ...\} | [kᵢ, vᵢ] ∈ x and |\{[kₙ, vₙ], [kₙ₊₁, vₙ₊₁], ...\}| ≤ max(|x| - n, 0)
*/
export function drop$<K, V>(x: Map<K, V>, n: number=1): Map<K, V> {
var i = -1;
for (var k of x.keys()) {
if (++i>=n) break;
x.delete(k);
}
return x;
}
// ARRANGEMENTS
// ------------
/**
* List all possible subsets.
* @param x a map
* @param n number of entries [-1 ⇒ any]
* @returns entries selected by bit from 0..2^|x| if n<0; only of length n otherwise
*/
export function* subsets<K, V>(x: Map<K, V>, n: number=-1): IterableIterator<Map<K, V>> {
for (var ks of arraySubsequences([...x.keys()], n))
yield filterAt(x, ks);
}
/**
* Pick an arbitrary key.
* @param x a map
* @param fr random number generator ([0, 1))
* @returns kᵢ | [kᵢ, vᵢ] ∈ x
*/
export function randomKey<K, V>(x: Map<K, V>, fr: ReadFunction<number>=Math.random): K {
return arrayRandomValue([...x.keys()], fr);
}
export {randomKey as key};
/**
* Pick an arbitrary entry.
* @param x a map
* @param fr random number generator ([0, 1))
* @returns [kᵢ, vᵢ] | [kᵢ, vᵢ] ∈ x
*/
export function randomEntry<K, V>(x: Entries<K, V>, fr: ReadFunction<number>=Math.random): [K, V] {
return arrayRandomValue([...x], fr);
}
export {randomEntry as entry};
/**
* Pick an arbitrary subset.
* @param x a map
* @param n number of entries [-1 ⇒ any]
* @param fr random number generator ([0, 1))
* @returns \{[kᵢ, vᵢ], [kⱼ, vⱼ], ...\} | [kᵢ, vᵢ], [kⱼ, vⱼ], ... ∈ x; |\{[kᵢ, vᵢ], [kⱼ, vⱼ], ...\}| = |x| if n<0 else n
*/
export function randomSubset<K, V>(x: Map<K, V>, n: number=-1, fr: ReadFunction<number> | null=Math.random): Map<K, V> {
var ks = arrayRandomSubsequence([...x.keys()], n, fr);
return filterAt(x, ks);
}
export {randomSubset as subset};
// FIND
// ----
/**
* Check if map has a key.
* @param x a map
* @param k search key
* @returns [k, *] ∈ x?
*/
export function has<K, V>(x: Map<K, V>, k: K): boolean {
return x.has(k);
}
export {has as hasKey};
/**
* Check if map has a value.
* @param x a map
* @param v search value
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns [*, v] ∈ x?
*/
export function hasValue<K, V, W=V>(x: Map<K, V>, v: V, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): boolean {
return searchValue(x, v, fc, fm)!==undefined;
}
/**
* Check if map has an entry.
* @param x a map
* @param e search entry ([k, v])
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns [k, v] ∈ x? | [k, v] = e
*/
export function hasEntry<K, V, W=V>(x: Map<K, V>, e: [K, V], fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): boolean {
var fc = fc || COMPARE;
var fm = fm || IDENTITY;
var [k, v] = e;
return x.has(k) && fc(fm(x.get(k), k, x), v)===0;
}
/**
* Check if map has a subset.
* @param x a map
* @param y search subset
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns y ⊆ x?
*/
export function hasSubset<K, V, W=V>(x: Map<K, V>, y: Map<K, V>, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): boolean {
var fc = fc || COMPARE;
var fm = fm || IDENTITY;
for (var [k, v] of y) {
if (!x.has(k)) return false;
var wx = fm(x.get(k), k, x);
var wy = fm(v, k, y);
if (fc(wx, wy)!==0) return false;
}
return true;
}
/**
* Find first value passing a test (default order).
* @param x a map
* @param ft test function (v, k, x)
* @returns first v | ft(v) = true; [k, v] ∈ x
*/
export function find<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): V {
for (var [k, v] of x)
if (ft(v, k, x)) return v;
}
/**
* Find values passing a test.
* @param x a map
* @param ft test function (v, k, x)
* @returns [v₀, v₁, ...] | ft(vᵢ) = true; [kᵢ, vᵢ] ∈ x
*/
export function findAll<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): V[] {
var a = [];
for (var [k, v] of x)
if (ft(v, k, x)) a.push(v);
return a;
}
/**
* Find key of an entry passing a test.
* @param x a map
* @param ft test function (v, k, x)
* @returns key of entry
*/
export function search<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): K {
for (var [k, v] of x)
if (ft(v, k, x)) return k;
}
/**
* Find keys of entries passing a test.
* @param x a map
* @param ft test function (v, k, x)
* @returns keys of entries
*/
export function searchAll<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): K[] {
var a = [];
for (var [k, v] of x)
if (ft(v, k, x)) a.push(k);
return a;
}
/**
* Find a key with given value.
* @param x a map
* @param v search value
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns key of value
*/
export function searchValue<K, V, W=V>(x: Map<K, V>, v: V, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): K {
var fc = fc || COMPARE;
var fm = fm || IDENTITY;
var w = fm(v, null, null);
for (var [k, u] of x) {
var wx = fm(u, k, x);
if (fc(wx, w)===0) return k;
}
}
/**
* Find keys with given value.
* @param x a map
* @param v search value
* @param fc compare function (a, b)
* @param fm map function (v, k, x)
* @returns keys of value
*/
export function searchValueAll<K, V, W=V>(x: Map<K, V>, v: V, fc: CompareFunction<V|W> | null=null, fm: MapFunction<K, V, V|W> | null=null): K[] {
var fc = fc || COMPARE;
var fm = fm || IDENTITY;
var w = fm(v, null, null), a = [];
for(var [k, u] of x) {
var wx = fm(u, k, x);
if (fc(wx, w)===0) a.push(k);
}
return a;
}
// FUNCTIONAL
// ----------
/**
* Call a function for each value.
* @param x a map
* @param fp process function (v, k, x)
*/
export function forEach<K, V>(x: Map<K, V>, fp: ProcessFunction<K, V>): void {
for (var [k, v] of x)
fp(v, k, x);
}
/**
* Check if any value satisfies a test.
* @param x a map
* @param ft test function (v, k, x)
* @returns true if ft(vᵢ) = true for some [kᵢ, vᵢ] ∈ x
*/
export function some<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): boolean {
for (var [k, v] of x)
if (ft(v, k, x)) return true;
return false;
}
/**
* Check if all values satisfy a test.
* @param x a map
* @param ft test function (v, k, x)
* @returns true if ft(vᵢ) = true for all [kᵢ, vᵢ] ∈ x
*/
export function every<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): boolean {
for (var [k, v] of x)
if (!ft(v, k, x)) return false;
return true;
}
/**
* Transform values of a map.
* @param x a map
* @param fm map function (v, k, x)
* @returns \{[k₀, fm(v₀)], [k₁, fm(v₁)], ...\} | [kᵢ, vᵢ] ∈ x
*/
export function map<K, V, W=V>(x: Map<K, V>, fm: MapFunction<K, V, V|W>): Map<K, V|W> {
var a = new Map();
for (var [k, v] of x)
a.set(k, fm(v, k, x));
return a;
}
/**
* Transform values of a map.
* @param x a map (updated)
* @param fm map function (v, k, x)
* @returns x = \{[k₀, fm(v₀)], [k₁, fm(v₁)], ...\} | [kᵢ, vᵢ] ∈ x
*/
export function map$<K, V>(x: Map<K, V>, fm: MapFunction<K, V, V>): Map<K, V> {
for (var [k, v] of x)
x.set(k, fm(v, k, x));
return x;
}
/**
* Reduce values of set to a single value.
* @param x a map
* @param fr reduce function (acc, v, k, x)
* @param acc initial value
* @returns fr(fr(acc, v₀), v₁)... | fr(acc, v₀) = v₀ if acc not given
*/
export function reduce<K, V, W=V>(x: Map<K, V>, fr: ReduceFunction<K, V, V|W>, acc?: V|W): V|W {
var init = arguments.length <= 2;
for (var [k, v] of x) {
if (init) { acc = v; init = false; }
else acc = fr(acc, v, k, x);
}
return acc;
}
/**
* Keep entries which pass a test.
* @param x a map
* @param ft test function (v, k, x)
* @returns \{[k₀, v₀], [k₁, v₁], ...\} | ft(vᵢ) = true; [kᵢ, vᵢ] ∈ x
*/
export function filter<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): Map<K, V> {
var a = new Map();
for (var [k, v] of x)
if (ft(v, k, x)) a.set(k, v);
return a;
}
/**
* Keep entries which pass a test.
* @param x an map (updated)
* @param ft test function (v, k, x)
* @returns x = \{[k₀, v₀], [k₁, v₁], ...\} | ft(vᵢ) = true; [kᵢ, vᵢ] ∈ x
*/
export function filter$<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): Map<K, V> {
for (var [k, v] of x)
if (!ft(v, k, x)) x.delete(k);
return x;
}
/**
* Keep values at given keys.
* @param x a map
* @param ks keys
* @returns \{[k₀, v₀], [k₁, v₁], ...\} | kᵢ ∈ ks; [kᵢ, vᵢ] ∈ x
*/
export function filterAt<K, V>(x: Map<K, V>, ks: K[]): Map<K, V> {
var a = new Map();
for (var k of ks)
a.set(k, x.get(k));
return a;
}
/**
* Keep values at given keys.
* @param x a map (updated)
* @param ks keys
* @returns x = \{[k₀, v₀], [k₁, v₁], ...\} | kᵢ ∈ ks; [kᵢ, vᵢ] ∈ x
*/
export function filterAt$<K, V>(x: Map<K, V>, ks: K[]): Map<K, V> {
for (var k of x.keys())
if (!ks.includes(k)) x.delete(k);
return x;
}
/**
* Discard entries which pass a test.
* @param x a map
* @param ft test function (v, k, x)
* @returns \{[k₀, v₀], [k₁, v₁], ...\} | ft(vᵢ) = false; [kᵢ, vᵢ] ∈ x
*/
export function reject<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): Map<K, V> {
var a = new Map();
for (var [k, v] of x)
if (!ft(v, k, x)) a.set(k, v);
return a;
}
/**
* Discard entries which pass a test.
* @param x a map (updated)
* @param ft test function (v, k, x)
* @returns x = \{[k₀, v₀], [k₁, v₁], ...\} | ft(vᵢ) = false; [kᵢ, vᵢ] ∈ x
*/
export function reject$<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): Map<K, V> {
for (var [k, v] of x)
if (ft(v, k, x)) x.delete(k);
return x;
}
/**
* Discard values at given keys.
* @param x a map
* @param ks keys
* @returns \{[k₀, v₀], [k₁, v₁], ...\} | kᵢ ∉ ks; [kᵢ, vᵢ] ∈ x
*/
export function rejectAt<K, V>(x: Map<K, V>, ks: K[]): Map<K, V> {
return rejectAt$(new Map(x), ks);
}
/**
* Discard values at given keys.
* @param x a map (updated)
* @param ks keys
* @returns x = \{[k₀, v₀], [k₁, v₁], ...\} | kᵢ ∉ ks; [kᵢ, vᵢ] ∈ x
*/
export function rejectAt$<K, V>(x: Map<K, V>, ks: K[]): Map<K, V> {
for (var k of ks)
x.delete(k);
return x;
}
/**
* Flatten nested map to given depth.
* @param x a nested map
* @param n maximum depth [-1 ⇒ all]
* @param fm map function (v, k, x)
* @param ft test function for flatten (v, k, x) [is]
* @returns flat map
*/
export function flat<K>(x: Map<K, any>, n: number=-1, fm: MapFunction<K, any, any> | null=null, ft: TestFunction<K, any> | null=null): Map<K, any> {
var fm = fm || IDENTITY;
var ft = ft || is;
return flatTo$(new Map(), x, n, fm, ft);
}
function flatTo$<K>(a: Map<K, any>, x: Map<K, any>, n: number, fm: MapFunction<K, any, any>, ft: TestFunction<K, any>): Map<K, any> {
for (var [k, v] of x) {
var w = fm(v, k, x);
if (n!==0 && ft(w, k, x)) flatTo$(a, w, n-1, fm, ft);
else a.set(k, w);
}
return a;
}
/**
* Flatten nested map, based on map function.
* @param x a nested map
* @param fm map function (v, k, x)
* @param ft test function for flatten (v, k, x) [is]
* @returns flat map
*/
export function flatMap<K>(x: Map<K, any>, fm: MapFunction<K, any, any> | null=null, ft: TestFunction<K, any> | null=null): Map<K, any> {
var fm = fm || IDENTITY;
var ft = ft || is;
var a = new Map();
for (var [k, v] of x) {
var w = fm(v, k, x);
if (ft(w, k, x)) concat$(a, w);
else a.set(k, w);
}
return a;
}
/**
* Combine matching entries from maps.
* @param xs maps
* @param fm map function (vs, k)
* @param fe end function (dones) [array.some]
* @param vd default value
* @returns [fm([x₀[k₀], x₁[k₀], ...]), fm([x₀[k₁], x₁[k₁], ...]), ...]
*/
export function zip<K, V, W=V>(xs: Map<K, V>[], fm: MapFunction<K, V[], V[]|W> | null=null, fe: EndFunction=null, vd?: V): Map<K, V[]|W> {
var fm = fm || IDENTITY;
var fe = fe || arraySome as EndFunction;
var ks = unionKeys(...xs), a = new Map();
for (var k of ks) {
var ds = xs.map(x => !x.has(k));
if (fe(ds)) break;
var vs = xs.map(x => !x.has(k)? vd : x.get(k));
a.set(k, fm(vs, k, null));
}
return a;
}
// MANIPULATION
// ------------
/**
* Segregate entries by test result.
* @param x a map
* @param ft test function (v, k, x)
* @returns [satisfies, doesnt]
*/
export function partition<K, V>(x: Map<K, V>, ft: TestFunction<K, V>): [Map<K, V>, Map<K, V>] {
var t = new Map();
var f = new Map();
for (var [k, v] of x) {
if (ft(v, k, x)) t.set(k, v);
else f.set(k, v);
}
return [t, f];
}
/**
* Segregate entries by similarity.
* @param x a map
* @param fm map function (v, k, x)
* @returns Map \{key ⇒ values\}
*/
export function partitionAs<K, V, W=V>(x: Map<K, V>, fm: MapFunction<K, V, V|W>): Map<V|W, Map<K, V>> {
var fm = fm || IDENTITY;
var a = new Map();
for (var [k, v] of x) {
var w = fm(v, k, x);
if (!a.has(w)) a.set(w, new Map());
a.get(w).set(k, v);
}
return a;
}
/**
* Break map into chunks of given size.
* @param x a map
* @param n chunk size [1]
* @param s chunk step [n]
* @returns [x[0..n], x[s..s+n], x[2s..2s+n], ...]
*/
export function chunk<K, V>(x: Map<K, V>, n: number=1, s: number=n): Map<K, V>[] {
var ks = [...x.keys()], a = [];
for (var i=0, I=ks.length; i<I; i+=s)
a.push(filterAt(x, ks.slice(i, i+n)));
return a;
}
// COMBINE
// -------
/**
* Append entries from maps, preferring last.
* @param xs maps
* @returns x₀ ∪ x₁ ∪ ... | [x₀, x₁, ...] = xs
*/
export function concat<K, V>(...xs: Entries<K, V>[]): Map<K, V> {
return concat$(new Map(), ...xs);
}
/**
* Append entries from maps, preferring last.
* @param x a map (updated)
* @param ys other maps
* @returns x = x ∪ y₀ ∪ y₁ ∪ ... | [y₀, y₁, ...] = ys
*/
export function concat$<K, V>(x: Map<K, V>, ...ys: Entries<K, V>[]): Map<K, V> {
for (var y of ys) {
for (var [k, v] of y)
x.set(k, v);
}
return x;
}
/**
* Join entries together into a string.
* @param x a map
* @param sep separator [,]
* @param asc associator [=]
* @returns "$\{k₀\}=$\{v₀\},$\{k₁\}=$\{v₁\}..." | [kᵢ, vᵢ] ∈ x
*/
export function join<K, V>(x: Entries<K, V>, sep: string=",", asc: string="="): string {
var a = "";
for (var [k, v] of x)
a += k + asc + v + sep;
return a.slice(0, -sep.length);
}
// SET OPERATIONS
// --------------
/**
* Check if maps have no common keys.
* @param x a map
* @param y another map
* @returns x ∩ y = Φ?
*/
export function isDisjoint<K, V>(x: Map<K, V>, y: Entries<K, V>): boolean {
for (var [k] of y)
if (x.has(k)) return false;
return true;
}
/**
* Obtain keys present in any map.
* @param xs maps
* @returns [k₀, k₁, ...] | [kᵢ, vᵢ] ∈ x₀ ∪ x₁, ...; [x₀, x₁, ...] = xs
*/
export function unionKeys<K, V>(...xs: Entries<K, V>[]): Set<K> {
var a = new Set<K>();
for (var x of xs) {
for (var [k] of x)
a.add(k);
}
return a;
}
/**
* Obtain entries present in any map.
* @param x a map
* @param y another map
* @param fc combine function (a, b)
* @returns x ∪ y = \{[kᵢ, vᵢ] | [kᵢ, vᵢ] ∈ x or [kᵢ, vᵢ] ∈ y\}
*/
export function union<K, V>(x: Entries<K, V>, y: Entries<K, V>, fc: CombineFunction<V> | null=null): Map<K, V> {
return union$(new Map(x), y, fc);
}
/**
* Obtain entries present in any map.
* @param x a map (updated)
* @param y another map
* @param fc combine function (a, b)
* @returns x = x ∪ y = \{[kᵢ, vᵢ] | [kᵢ, vᵢ] ∈ x or [kᵢ, vᵢ] ∈ y\}
*/
export function union$<K, V>(x: Map<K, V>, y: Entries<K, V>, fc: CombineFunction<V> | null=null): Map<K, V> {
var fc = fc || IDENTITY;
for (var [k, v] of y) {
if (!x.has(k)) x.set(k, v);
else x.set(k, fc(x.get(k), v));
}
return x;
}
/**
* Obtain keys present in all maps.
* @param xs maps
* @returns [k₀, k₁, ...] | [kᵢ, vᵢ] ∈ x₀ ∩ x₁, ...; [x₀, x₁, ...] = xs
*/
export function intersectionKeys<K, V>(...xs: Map<K, V>[]): Set<K> {
var a = new Set<K>();
if (xs.length===0) return a;
var x = xs[0], ys = xs.slice(1);
LOOPX: for (var k of x.keys()) {
for (var y of ys)
if (!y.has(k)) continue LOOPX;
a.add(k);
}
return a;
}
/**
* Obtain entries present in both maps.
* @param x a map
* @param y another map
* @param fc combine function (a, b)
* @returns x ∩ y = \{[kᵢ, vᵢ] | [kᵢ, vᵢ] ∈ x and [kᵢ, vᵢ] ∈ y\}
*/
export function intersection<K, V>(x: Map<K, V>, y: Entries<K, V>, fc: CombineFunction<V> | null=null): Map<K, V> {
var fc = fc || IDENTITY;
var a = new Map();
for (var [k, v] of y)
if (x.has(k)) a.set(k, fc(x.get(k), v));
return a;
}
/**
* Obtain entries present in both maps.
* @param x a map (updated)
* @param y another map
* @param fc combine function (a, b)
* @returns x = x ∩ y = \{[kᵢ, vᵢ] | [kᵢ, vᵢ] ∈ x and [kᵢ, vᵢ] ∈ y\}
*/
export function intersection$<K, V>(x: Map<K, V>, y: Map<K, V>, fc: CombineFunction<V> | null=null): Map<K, V> {
var fc = fc || IDENTITY, ks = [];
for (var [k, u] of [...x]) {
if (!y.has(k)) ks.push(k);
x.set(k, fc(u, y.get(k)));
}
return rejectAt$(x, ks);
}
/**
* Obtain entries not present in another map.
* @param x a map
* @param y another map
* @returns x - y = \{[kᵢ, vᵢ] | [kᵢ, vᵢ] ∈ x, [kᵢ, *] ∉ y\}
*/
export function difference<K, V>(x: Entries<K, V>, y: Entries<K, V>): Map<K, V> {
return difference$(new Map(x), y);
}
/**
* Obtain entries not present in another map.
* @param x a map (updated)
* @param y another map
* @returns x = x - y = \{[kᵢ, vᵢ] | [kᵢ, vᵢ] ∈ x, [kᵢ, *] ∉ y\}
*/
export function difference$<K, V>(x: Map<K, V>, y: Entries<K, V>): Map<K, V> {
for (var [k] of y)
x.delete(k);
return x;
}
/**
* Obtain entries not present in both maps.
* @param x a map
* @param y another map
* @returns x-y ∪ y-x
*/
export function symmetricDifference<K, V>(x: Entries<K, V>, y: Entries<K, V>): Map<K, V> {
return symmetricDifference$(new Map(x), y);
}
/**
* Obtain entries not present in both maps.
* @param x a map (updated)
* @param y another map
* @returns x = x-y ∪ y-x
*/
export function symmetricDifference$<K, V>(x: Map<K, V>, y: Entries<K, V>): Map<K, V> {
for (var [k, v] of y) {
if (x.has(k)) x.delete(k);
else x.set(k, v);
}
return x;
}
/**
* List cartesian product of maps.
* @param xs maps
* @param fm map function (vs, i)
* @returns x₀ × x₁ × ... = \{\{[k₀, v₀], [k₁, v₁], ...\} | [k₀, v₀] ∈ x₀, [k₁, v₁] ∈ x₁, ...]\}
*/
export function* cartesianProduct<K, V, W=Map<K, V>>(xs: Map<K, V>[], fm: MapFunction<number, Map<K, V>, Map<K, V>|W> | null=null): IterableIterator<Map<K, V>|W> {
var fm = fm || IDENTITY;
var XS = xs.length;
var kx = xs.map(x => [...x.keys()]);
var ls = kx.map(ks => ks.length);
var is = kx.map(ks => 0);
for (var j=0;; ++j) {
var a = new Map<K, V>();
for (var n=0; n<XS; ++n) {
var i = is[n], x = xs[n];
var ks = kx[n], k = ks[i];
a.set(k, x.get(k));
}
yield fm(a, j, null);
for (var r=XS-1; r>=0; --r) {
if (++is[r] < ls[r]) break;
is[r] = 0;
}
if (r<0) break;
}
}