#lang racket

(require racket/trace)

(struct DISCARD ())
(struct CAPTURE (p))

(define (q p)
  (match p
    [(DISCARD) `(discard)]
    [(CAPTURE p) `(capture ,(q p))]
    [`(discard) `('discard)]
    [`(capture ,p) `('capture ,(q p))]
    [`(quote ,p) `('quote ,(q p))]
    [`(,pa . ,pd) `(,(q pa) . ,(q pd))]
    [a a]))

(define (uq p)
  (match p
    [`(discard) (DISCARD)]
    [`(capture ,p) (CAPTURE (uq p))]
    [`(quote ,p) p]
    [`(,pa . ,pd) `(,(uq pa) . ,(uq pd))]
    [a a]))

;; Goal: (uq (q p)) === p

;; (define (m p v k)
;;   (match* (p v)
;;     [(`(discard) _) (k '())]
;;     [(`(capture ,p) v) (m p v (lambda (bs) (cons v bs)))]
;;     [(`(quote ,p) v) (and (equal? p v) (k '()))]
;;     [(`(,pa . ,pd) `(,va . ,vd)) (m pa va (lambda (bs) (m pd vd (lambda (cs) (k (append bs cs))))))]
;;     [(p v) (and (equal? p v) (k '()))]))

(define (m p v k)
  (match* (p v)
    [((DISCARD) _) (k '())]
    [((CAPTURE p) v) (m p v (lambda (bs) (cons v bs)))]
    [(`(,pa . ,pd) `(,va . ,vd)) (m pa va (lambda (bs) (m pd vd (lambda (cs) (k (append bs cs))))))]
    [(p v) (and (equal? p v) (k '()))]))

;; (trace m)

(module+ test
  (require rackunit)
  ;; (define (M p v) (m p v values))
  (define (M p v) (m (uq p) v values))
  (check-equal? (M `(capture 1) 1) '(1))
  (check-equal? (M `(discard) 1) '())
  (check-equal? (M 1 1) '())
  (check-equal? (M 2 1) #f)
  (check-equal? (M `(capture 2) 1) #f)

  (check-equal? (M `(record (capture (discard))) `(record value)) '(value))
  (check-equal? (M `(record (capture (discard))) `(record 'value)) '('value))
  (check-equal? (M `(record (capture (discard))) `(record (capture (discard))))
                '((capture (discard))))

  (check-equal? (M `(record ('capture (discard))) `(record (capture (discard))))
                '())
  (check-equal? (M `(record (capture ('capture (discard)))) `(record (capture (discard))))
                '((capture (discard))))
  (check-equal? (M `(record (capture ('capture (discard)))) `(record value))
                #f)
  (check-equal? (M `(record (capture ('capture (discard)))) `(record 'value))
                #f)
  (check-equal? (M `(record (capture ('capture (discard)))) `(record ('capture (discard))))
                #f)

  (check-equal? (M `(record '(capture (discard))) `(record (capture (discard))))
                '())
  (check-equal? (M `(record (capture '(capture (discard)))) `(record (capture (discard))))
                '((capture (discard))))
  (check-equal? (M `(record (capture '(capture (discard)))) `(record value))
                #f)
  (check-equal? (M `(record (capture '(capture (discard)))) `(record 'value))
                #f)
  (check-equal? (M `(record (capture '(capture (discard)))) `(record '(capture (discard))))
                #f)

  (check-equal? (M `(record ('quote value)) `(record (capture (discard)))) #f)
  (check-equal? (M `(record (capture ('quote value))) `(record (capture (discard)))) #f)
  (check-equal? (M `(record (capture ('quote value))) `(record value)) #f)
  (check-equal? (M `(record (capture ('quote value))) `(record 'value)) '('value))
  (check-equal? (M `(record (capture ('quote value))) `(record 'notvalue)) #f)
  (check-equal? (M `(record ('quote value)) `(record 'value)) '())
  (check-equal? (M `(record (capture ('quote value))) `(record ('quote value))) #f)

  (check-equal? (M `(record ''value) `(record (capture (discard)))) #f)
  (check-equal? (M `(record (capture ''value)) `(record (capture (discard)))) #f)
  (check-equal? (M `(record (capture ''value)) `(record value)) #f)
  (check-equal? (M `(record (capture ''value)) `(record 'value)) '('value))
  (check-equal? (M `(record (capture ''value)) `(record 'notvalue)) #f)
  (check-equal? (M `(record ''value) `(record 'value)) '())
  (check-equal? (M `(record (capture ''value)) `(record ''value)) #f)

  (check-equal? (q (CAPTURE 1)) `(capture 1))
  (check-equal? (q (DISCARD)) `(discard))
  (check-equal? (q `(capture 1)) `('capture 1))
  (check-equal? (q `(discard)) `('discard))

  )