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|
;;; set.el --- Working with mathematical sets -*- lexical-binding: t -*-
;; Author: William Carroll <wpcarro@gmail.com>
;;; Commentary:
;; The set data structure is a collection that deduplicates its elements.
;;; Code:
(require 'ht) ;; friendlier API for hash-tables
(require 'dotted)
(require 'struct)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Wish List
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; - TODO: Support enum protocol for set.
;; - TODO: Prefer a different hash-table library that doesn't rely on mutative
;; code.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Library
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(cl-defstruct set xs)
(defconst set/enable-testing? t
"Run tests when t.")
(defun set/from-list (xs)
"Create a new set from the list XS."
(make-set :xs (->> xs
(list/map #'dotted/new)
ht-from-alist)))
(defun set/new (&rest args)
"Create a new set from ARGS."
(set/from-list args))
(defun set/to-list (xs)
"Map set XS into a list."
(->> xs
set-xs
ht-keys))
(defun set/add (x xs)
"Add X to set XS."
(struct/update set
xs
(lambda (table)
(let ((table-copy (ht-copy table)))
(ht-set table-copy x nil)
table-copy))
xs))
;; TODO: Ensure all `*/reduce' functions share the same API.
(defun set/reduce (acc f xs)
"Return a new set by calling F on each element of XS and ACC."
(->> xs
set/to-list
(list/reduce acc f)))
(defun set/intersection (a b)
"Return the set intersection between sets A and B."
(set/reduce (set/new)
(lambda (x acc)
(if (set/contains? x b)
(set/add x acc)
acc))
a))
(defun set/count (xs)
"Return the number of elements in XS."
(->> xs
set-xs
ht-size))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Predicates
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun set/empty? (xs)
"Return t if XS has no elements in it."
(= 0 (set/count xs)))
(defun set/contains? (x xs)
"Return t if set XS has X."
(ht-contains? (set-xs xs) x))
;; TODO: Prefer using `ht.el' functions for this.
(defun set/equal? (a b)
"Return t if A and B share the name members."
(ht-equal? (set-xs a)
(set-xs b)))
(defun set/distinct? (a b)
"Return t if sets A and B have no shared members."
(set/empty? (set/intersection a b)))
(defun set/superset? (a b)
"Return t if set A contains all of the members of set B."
(->> b
set/to-list
(list/all? (lambda (x) (set/contains? x a)))))
(defun set/subset? (a b)
"Return t if each member of set A is present in set B."
(set/superset? b a))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Tests
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(when set/enable-testing?
;; set/distinct?
(prelude-assert
(set/distinct? (set/new 'one 'two 'three)
(set/new 'a 'b 'c)))
(prelude-refute
(set/distinct? (set/new 1 2 3)
(set/new 3 4 5)))
(prelude-refute
(set/distinct? (set/new 1 2 3)
(set/new 1 2 3)))
;; set/equal?
(prelude-refute
(set/equal? (set/new 'a 'b 'c)
(set/new 'x 'y 'z)))
(prelude-refute
(set/equal? (set/new 'a 'b 'c)
(set/new 'a 'b)))
(prelude-assert
(set/equal? (set/new 'a 'b 'c)
(set/new 'a 'b 'c)))
;; set/intersection
(prelude-assert
(set/equal? (set/new 2 3)
(set/intersection (set/new 1 2 3)
(set/new 2 3 4))))
;; set/{from,to}-list
(prelude-assert (equal '(1 2 3)
(->> '(1 1 2 2 3 3)
set/from-list
set/to-list)))
(let ((primary-colors (set/new "red" "green" "blue")))
;; set/subset?
(prelude-refute
(set/subset? (set/new "black" "grey")
primary-colors))
(prelude-assert
(set/subset? (set/new "red")
primary-colors))
;; set/superset?
(prelude-refute
(set/superset? primary-colors
(set/new "black" "grey")))
(prelude-assert
(set/superset? primary-colors
(set/new "red" "green" "blue")))
(prelude-assert
(set/superset? primary-colors
(set/new "red" "blue"))))
;; set/empty?
(prelude-assert (set/empty? (set/new)))
(prelude-refute (set/empty? (set/new 1 2 3)))
;; set/count
(prelude-assert (= 0 (set/count (set/new))))
(prelude-assert (= 2 (set/count (set/new 1 1 2 2)))))
(provide 'set)
;;; set.el ends here
|
