;;; 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/base

(require syntax/parse/define
         (for-syntax racket/base
                     racket/match
                     racket/list
                     racket/syntax
                     syntax/parse))

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

(module+ test
  (require typed/rackunit))

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

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

(define-for-syntax (make-compose-type n)
  (with-syntax* ([(t ...) (generate-temporaries (make-list n 't))]
                 [(_ ... t₀) #'(a t ...)]
                 [(F ...)
                  (let step ([u #'a] [ts (syntax->list #'(t ...))])
                    (match ts
                      ['() '()]
                      [(cons t ts*) (cons #`(#,t → #,u) (step t ts*))]))])
    #'(∀ (a t ...) (F ... → t₀ → a))))

(define-syntax-parser make-compose
  [(_ n:nat)
     (with-syntax* ([(f ...) (generate-temporaries (make-list (syntax-e #'n) 'f))]
                    [T (make-compose-type (syntax-e #'n))]
                    [body (foldr (λ (fᵢ res) #`(#,fᵢ #,res)) #'x (syntax->list #'(f ...)))])
       #'(ann (λ (f ...) (λ (x) body)) T))])

(define compose-3 (make-compose 3))
(define compose-4 (make-compose 4))
(define compose-5 (make-compose 5))
(define compose-6 (make-compose 6))
(define compose-7 (make-compose 7))
(define compose-8 (make-compose 8))
(define compose-9 (make-compose 9))

(module+ test
  (test-case "compose-3 to compose-9"
    (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
  (test-case "multi-compose"
    (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
  (require racket/port)
  (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")))