typed-compose/typed-compose.rkt

;;; typed-compose.rkt
;;;
;;; Copyright 2020 Sergiu Ivanov <sivanov@colimite.fr>
;;;
;;; This program is free software: you can redistribute it and/or
;;; modify it under the terms of the GNU General Public License as
;;; published by the Free Software Foundation, either version 3 of the
;;; License, or (at your option) any later version.
;;;
;;; This program is distributed in the hope that it will be useful,
;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
;;; General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License
;;; along with this program.  If not, see
;;; <https://www.gnu.org/licenses/>.

#lang typed/racket

(require (for-syntax syntax/parse))

(module+ test
  (require typed/rackunit))

(provide compose-n
         compose-3 compose-4 compose-5 compose-6 compose-7 compose-8 compose-9
         multi-compose multi-chain)

(: compose-n (All (a) (-> (-> a a) * (-> a a))))
(define (compose-n . funcs)
  (λ (x)
    (for/foldr ([x x]) ([f funcs])
      (f x))))

(module+ test
  (check-equal? ((compose-n add1 add1 add1) 3) 6))

(: compose-3 (All (a b c d)
                  (-> (-> c d)
                      (-> b c)
                      (-> a b)
                      (-> a d))))
(define (compose-3 f1 f2 f3)
  (λ (x) (f1 (f2 (f3 x)))))

(: compose-4 (All (a b c d e)
                  (-> (-> d e)
                      (-> c d)
                      (-> b c)
                      (-> a b)
                      (-> a e))))
(define (compose-4 f1 f2 f3 f4)
  (λ (x) (f1 (f2 (f3 (f4 x))))))

(: compose-5 (All (a b c d e f)
                  (-> (-> e f)
                      (-> d e)
                      (-> c d)
                      (-> b c)
                      (-> a b)
                      (-> a f))))
(define (compose-5 f1 f2 f3 f4 f5)
  (λ (x) (f1 (f2 (f3 (f4 (f5 x)))))))

(: compose-6 (All (a b c d e f g)
                  (-> (-> f g)
                      (-> e f)
                      (-> d e)
                      (-> c d)
                      (-> b c)
                      (-> a b)
                      (-> a g))))
(define (compose-6 f1 f2 f3 f4 f5 f6)
  (λ (x) (f1 (f2 (f3 (f4 (f5 (f6 x))))))))

(: compose-7 (All (a b c d e f g h)
                  (-> (-> g h)
                      (-> f g)
                      (-> e f)
                      (-> d e)
                      (-> c d)
                      (-> b c)
                      (-> a b)
                      (-> a h))))
(define (compose-7 f1 f2 f3 f4 f5 f6 f7)
  (λ (x) (f1 (f2 (f3 (f4 (f5 (f6 (f7 x)))))))))

(: compose-8 (All (a b c d e f g h i)
                  (-> (-> h i)
                      (-> g h)
                      (-> f g)
                      (-> e f)
                      (-> d e)
                      (-> c d)
                      (-> b c)
                      (-> a b)
                      (-> a i))))
(define (compose-8 f1 f2 f3 f4 f5 f6 f7 f8)
  (λ (x) (f1 (f2 (f3 (f4 (f5 (f6 (f7 (f8 x))))))))))

(: compose-9 (All (a b c d e f g h i j)
                  (-> (-> i j)
                      (-> h i)
                      (-> g h)
                      (-> f g)
                      (-> e f)
                      (-> d e)
                      (-> c d)
                      (-> b c)
                      (-> a b)
                      (-> a j))))
(define (compose-9 f1 f2 f3 f4 f5 f6 f7 f8 f9)
  (λ (x) (f1 (f2 (f3 (f4 (f5 (f6 (f7 (f8 (f9 x)))))))))))

(module+ test
  (define (s->n [s : String]) (cast (string->number s) Number))
  (define (n->s [n : Number]) (number->string n))
  (check-equal? ((compose-3 n->s add1 s->n) "3") "4")
  (check-equal? ((compose-4 n->s add1 add1 s->n) "3") "5")
  (check-equal? ((compose-5 n->s add1 add1 add1 s->n) "3") "6")
  (check-equal? ((compose-6 n->s add1 add1 add1 add1 s->n) "3") "7")
  (check-equal? ((compose-7 n->s add1 add1 add1 add1 add1 s->n) "3") "8")
  (check-equal?
   ((compose-8 n->s add1 add1 add1 add1 add1 add1 s->n) "3") "9")
  (check-equal?
   ((compose-9 n->s add1 add1 add1 add1 add1 add1 add1 s->n) "3") "10"))

(define-syntax (multi-compose stx)
  ;; Implementation by Sorawee Porncharoenwase.
  (syntax-parse stx
    [(_ f:expr g:expr)
     #'(compose f g)]
    [(_ f:expr funcs:expr ...)
     #'(compose f (multi-compose funcs ...))]))

(module+ test
  (check-equal? ((multi-compose add1
                                (λ ([x : Number]) (* x 3))
                                add1
                                (λ ([x : Number]) (+ x 2)))
                 3)
                19))

(define-syntax (multi-chain stx)
  (syntax-parse stx
    [(_ funcs:expr ...)
     (define rev-funcs (reverse (syntax->list #'(funcs ...))))
     #`(multi-compose #,@rev-funcs)]))

(module+ test
  (test-case "multi-chain and multi-compose"
    (define f1 (λ ([x : Number]) (displayln "f1") (+ x 1)))
    (define f2 (λ ([x : Number]) (displayln "f2") (+ x 1)))
    (define f3 (λ ([x : Number]) (displayln "f3") (+ x 1)))
    (check-equal?
     (with-output-to-string (λ () (displayln ((multi-chain f1 f2 f3) 3))))
     "f1\nf2\nf3\n6\n")
    (check-equal?
     (with-output-to-string (λ () (displayln ((multi-compose f1 f2 f3) 3))))
     "f3\nf2\nf1\n6\n")))