brag/parser-tools/private-lex/deriv.rkt

#lang racket/base
(require (prefix-in is: data/integer-set)
         racket/list
         yaragg/parser-tools/private-lex/re
         yaragg/parser-tools/private-lex/util)

(provide build-dfa print-dfa (struct-out dfa))

(define e (build-epsilon))
(define z (build-zero))
  
  
;; Don't do anything with this one but extract the chars
(define all-chars (->re `(char-complement (union)) (make-cache)))
  
;; get-char-groups : re bool -> (list-of char-setR?)
;; Collects the char-setRs in r that could be used in
;; taking the derivative of r.
(define (get-char-groups r found-negation)
  (cond
    [(or (eq? r e) (eq? r z)) '()]
    [(char-setR? r) (list r)]
    [(concatR? r)
     (if (re-nullable? (concatR-re1 r))
         (append (get-char-groups (concatR-re1 r) found-negation)
                 (get-char-groups (concatR-re2 r) found-negation))
         (get-char-groups (concatR-re1 r) found-negation))]
    [(repeatR? r)
     (get-char-groups (repeatR-re r) found-negation)]
    [(orR? r)
     (append-map (λ (x) (get-char-groups x found-negation)) (orR-res r))]
    [(andR? r)
     (append-map (λ (x) (get-char-groups x found-negation)) (andR-res r))]
    [(negR? r)
     (if found-negation
         (get-char-groups (negR-re r) #t)
         (cons all-chars (get-char-groups (negR-re r) #t)))]))

(test-block ((c (make-cache))
             (r1 (->re #\1 c))
             (r2 (->re #\2 c)))
            ((get-char-groups e #f) '())
            ((get-char-groups z #f) '())
            ((get-char-groups r1 #f) (list r1))
            ((get-char-groups (->re `(concatenation ,r1 ,r2) c) #f)
             (list r1))
            ((get-char-groups (->re `(concatenation ,e ,r2) c) #f) 
             (list r2))
            ((get-char-groups (->re `(concatenation (repetition 0 +inf.0 ,r1) ,r2) c) #f) 
             (list r1 r2))
            ((get-char-groups (->re `(repetition 0 +inf.0 ,r1) c) #f) 
             (list r1))
            ((get-char-groups
              (->re `(union (repetition 0 +inf.0 ,r1) 
                            (concatenation (repetition 0 +inf.0 ,r2) "3") "4") c) #f)
             (list r1 r2 (->re "3" c) (->re "4" c)))
            ((get-char-groups (->re `(complement ,r1) c) #f) 
             (list all-chars r1))
            ((get-char-groups 
              (->re `(intersection (repetition 0 +inf.0 ,r1)
                                   (concatenation (repetition 0 +inf.0 ,r2) "3") "4") c) #f)
             (list r1 r2 (->re "3" c) (->re "4" c)))
            )
(define loc:member? is:member?)
  
;; deriveR : re char cache -> re
(define (deriveR r c cache)
  (cond
    [(or (eq? r e) (eq? r z)) z]
    [(char-setR? r)
     (if (loc:member? c (char-setR-chars r)) e z)]
    [(concatR? r)
     (define r1 (concatR-re1 r))
     (define r2 (concatR-re2 r))
     (define d (build-concat (deriveR r1 c cache) r2 cache))
     (if (re-nullable? r1)
         (build-or (list d (deriveR r2 c cache)) cache)
         d)]
    [(repeatR? r)
     (build-concat (deriveR (repeatR-re r) c cache)
                   (build-repeat (sub1 (repeatR-low r))
                                 (sub1 (repeatR-high r))
                                 (repeatR-re r) cache)
                   cache)]
    [(orR? r)
     (build-or (map (λ (x) (deriveR x c cache))
                    (orR-res r))
               cache)]
    [(andR? r)
     (build-and (map (λ (x) (deriveR x c cache))
                     (andR-res r))
                cache)]
    [(negR? r)
     (build-neg (deriveR (negR-re r) c cache) cache)]))

(test-block ((c (make-cache))
             (a (char->integer #\a))
             (b (char->integer #\b))
             (r1 (->re #\a c))
             (r2 (->re `(repetition 0 +inf.0 #\a) c))
             (r3 (->re `(repetition 0 +inf.0 ,r2) c))
             (r4 (->re `(concatenation #\a ,r2) c))
             (r5 (->re `(repetition 0 +inf.0 ,r4) c))
             (r6 (->re `(union ,r5 #\a) c))
             (r7 (->re `(concatenation ,r2 ,r2) c))
             (r8 (->re `(complement ,r4) c))
             (r9 (->re `(intersection ,r2 ,r4) c)))
            ((deriveR e a c) z)
            ((deriveR z a c) z)
            ((deriveR r1 b c) z)
            ((deriveR r1 a c) e)
            ((deriveR r2 a c) r2)
            ((deriveR r2 b c) z)
            ((deriveR r3 a c) r2)
            ((deriveR r3 b c) z)
            ((deriveR r4 a c) r2)
            ((deriveR r4 b c) z)
            ((deriveR r5 a c) (->re `(concatenation ,r2 ,r5) c))
            ((deriveR r5 b c) z)
            ((deriveR r6 a c) (->re `(union (concatenation ,r2 ,r5) "") c))
            ((deriveR r6 b c) z)
            ((deriveR r7 a c) (->re `(union (concatenation ,r2 ,r2) ,r2) c))
            ((deriveR r7 b c) z)
            ((deriveR r8 a c) (->re `(complement, r2) c))
            ((deriveR r8 b c) (->re `(complement ,z) c))
            ((deriveR r9 a c) r2)
            ((deriveR r9 b c) z)
            ((deriveR (->re `(repetition 1 2 "ab") c) a c)
             (->re `(concatenation "b" (repetition 0 1 "ab")) c)))
  
;; An re-action is (cons re action)

;; derive : (list-of re-action) char cache -> (union (list-of re-action) #f)
;; applies deriveR to all the re-actions's re parts.
;; Returns #f if the derived state is equivalent to z.
(define (derive r c cache)
  (define new-r (for/list ([ra (in-list r)])
                          (cons (deriveR (car ra) c cache) (cdr ra))))
  (if (andmap (λ (x) (eq? z (car x))) new-r)
      #f
      new-r))

(test-block ((c (make-cache))
             (r1 (->re #\1 c))
             (r2 (->re #\2 c)))
            ((derive '() (char->integer #\1) c) #f)
            ((derive (list (cons r1 1) (cons r2 2)) (char->integer #\1) c)
             (list (cons e 1) (cons z 2)))
            ((derive (list (cons r1 1) (cons r2 2)) (char->integer #\3) c) #f))
  

;; get-final : (list-of re-action) -> (union #f syntax-object)
;; An re that accepts e represents a final state.  Return the
;; action from the first final state or #f if there is none.
(define (get-final res)
  (cond
    [(null? res) #f]
    [(re-nullable? (caar res)) (cdar res)]
    [else (get-final (cdr res))]))

(test-block ((c->i char->integer)
             (c (make-cache))
             (r1 (->re #\a c))
             (r2 (->re #\b c))
             (b (list (cons z 1) (cons z 2) (cons z 3) (cons e 4) (cons z 5)))
             (a (list (cons r1 1) (cons r2 2))))
            ((derive '() (c->i #\a) c) #f)
            ((derive a (c->i #\a) c) (list (cons e 1) (cons z 2)))
            ((derive a (c->i #\b) c) (list (cons z 1) (cons e 2)))
            ((derive a (c->i #\c) c) #f)
            ((derive (list (cons (->re `(union " " "\n" ",") c) 1)
                           (cons (->re `(concatenation (repetition 0 1 "-")
                                                       (repetition 1 +inf.0 (char-range "0" "9"))) c) 2)
                           (cons (->re `(concatenation "-" (repetition 1 +inf.0 "-")) c) 3)
                           (cons (->re "[" c) 4)
                           (cons (->re "]" c) 5)) (c->i #\[) c)
             b)
            ((get-final a) #f)
            ((get-final (list (cons e 1) (cons e 2))) 1)
            ((get-final b) 4))
  
  
;; A state is (state (list-of re-action) nat)
(struct state (spec index))
        
;; get->key : re-action -> (list-of nat)
;; states are indexed by the list of indexes of their res
(define (get-key s)
  (map (λ (x) (re-index (car x))) s))  
          
(define loc:partition is:partition)
  
;; compute-chars : (list-of state) -> (list-of char-set)
;; Computed the sets of equivalent characters for taking the
;; derivative of the car of st.  Only one derivative per set need to be taken.
(define (compute-chars st)
  (cond
    [(null? st) '()]
    [else
     (loc:partition (map char-setR-chars
                         (append-map (λ (x) (get-char-groups (car x) #f)) (state-spec (car st)))))]))
  
(test-block ((c (make-cache))
             (c->i char->integer)
             (r1 (->re `(char-range #\1 #\4) c))
             (r2 (->re `(char-range #\2 #\3) c)))
            ((compute-chars '()) '())
            ((compute-chars (list (state '() 1))) '())
            ((map is:integer-set-contents
                  (compute-chars (list (state (list (cons r1 1) (cons r2 2)) 2))))
             (list (is:integer-set-contents (is:make-range (c->i #\2) (c->i #\3)))
                   (is:integer-set-contents (is:union (is:make-range (c->i #\1))
                                                      (is:make-range (c->i #\4)))))))
  
  
;; A dfa is (dfa int int
;;                    (list-of (cons int syntax-object))
;;                    (list-of (cons int (list-of (cons char-set int)))))
;; Each transitions is a state and a list of chars with the state to transition to.
;; The finals and transitions are sorted by state number, and duplicate free.
(struct dfa (num-states start-state final-states/actions transitions) #:transparent)
  
(define loc:get-integer is:get-integer)
  
;; build-dfa : (list-of re-action) cache -> dfa
(define (build-dfa rs cache)
  (let* ([transitions (make-hash)]
         [get-state-number (make-counter)]
         [start (state rs (get-state-number))])
    (cache (cons 'state (get-key rs)) (λ () start))
    (let loop ([old-states (list start)]
               [new-states '()]
               [all-states (list start)]
               [cs (compute-chars (list start))])
      (cond
        [(and (null? old-states) (null? new-states))
         (dfa (get-state-number) (state-index start)
                   (sort (for*/list ([state (in-list all-states)]
                                     [val (in-value (cons (state-index state) (get-final (state-spec state))))]
                                     #:when (cdr val))
                                    val)
                         < #:key car)
                   (sort (hash-map transitions
                                   (λ (state trans)
                                     (cons (state-index state)
                                           (for/list ([t (in-list trans)])
                                                     (cons (car t)
                                                           (state-index (cdr t)))))))
                         < #:key car))]
        [(null? old-states)
         (loop new-states '() all-states (compute-chars new-states))]
        [(null? cs)
         (loop (cdr old-states) new-states all-states (compute-chars (cdr old-states)))]
        [else
         (define s (car old-states))
         (define c (car cs))
         (define new-re (derive (state-spec s) (loc:get-integer c) cache))
         (cond
           [new-re
            (let* ([new-state? #f]
                   [new-state (cache (cons 'state (get-key new-re))
                                     (λ ()
                                       (set! new-state? #t)
                                       (state new-re (get-state-number))))]
                   [new-all-states (if new-state? (cons new-state all-states) all-states)])
              (hash-set! transitions 
                         s
                         (cons (cons c new-state)
                               (hash-ref transitions s
                                         (λ () '()))))
              (cond
                [new-state?
                 (loop old-states (cons new-state new-states) new-all-states (cdr cs))]
                [else
                 (loop old-states new-states new-all-states (cdr cs))]))]
           [else (loop old-states new-states all-states (cdr cs))])]))))
  
(define (print-dfa x)
  (printf "number of states: ~a\n" (dfa-num-states x))
  (printf "start state: ~a\n" (dfa-start-state x))
  (printf "final states: ~a\n" (map car (dfa-final-states/actions x)))
  (for ([trans (in-list (dfa-transitions x))])
    (printf "state: ~a\n" (car trans))
    (for ([rule (in-list (cdr trans))])
      (printf "  -~a-> ~a\n"
              (is:integer-set-contents (car rule))
              (cdr rule)))))
 
(define (build-test-dfa rs)
  (define c (make-cache))
  (build-dfa (map (λ (x) (cons (->re x c) 'action)) rs) c))

  
#|
  (define t1 (build-test-dfa null))
  (define t2 (build-test-dfa `(#\a)))
  (define t3 (build-test-dfa `(#\a #\b)))
  (define t4 (build-test-dfa `((repetition 0 +inf.0 #\a)
                               (repetition 0 +inf.0 (concatenation #\a #\b)))))
  (define t5 (build-test-dfa `((concatenation (repetition 0 +inf.0 (union #\0 #\1)) #\1))))
  (define t6 (build-test-dfa `((repetition 0 +inf.0 (repetition 0 +inf.0 #\a))
                               (repetition 0 +inf.0 (concatenation #\b (repetition 1 +inf.0 #\b))))))
  (define t7 (build-test-dfa `((concatenation (repetition 0 +inf.0 #\a) (repetition 0 +inf.0 #\b)
                                              (repetition 0 +inf.0 #\c) (repetition 0 +inf.0 #\d)
                                              (repetition 0 +inf.0 #\e)))))
  (define t8
    (build-test-dfa `((concatenation (repetition 0 +inf.0 (union #\a #\b)) #\a (union #\a #\b)
                                     (union #\a #\b) (union #\a #\b) (union #\a #\b)))))
  (define t9 (build-test-dfa `((concatenation "/*"
                                              (complement (concatenation (intersection) "*/" (intersection)))
                                              "*/"))))
  (define t11 (build-test-dfa `((complement "1"))))
  (define t12 (build-test-dfa `((concatenation (intersection (concatenation (repetition 0 +inf.0 "a") "b")
                                                             (concatenation "a" (repetition 0 +inf.0 "b")))
                                               "ab"))))
  (define x (build-test-dfa `((union " " "\n" ",")
                              (concatenation (repetition 0 1 "-") (repetition 1 +inf.0 (char-range "0" "9")))
                              (concatenation "-" (repetition 1 +inf.0 "-"))
                              "["
                              "]")))
  (define y (build-test-dfa
             `((repetition 1 +inf.0
                           (union (concatenation "|" (repetition 0 +inf.0 (char-complement "|")) "|")
                                  (concatenation "|" (repetition 0 +inf.0 (char-complement "|"))))))))
  (define t13 (build-test-dfa `((intersection (concatenation (intersection) "111" (intersection))
                                              (complement (union (concatenation (intersection) "01")
                                                                 (repetition 1 +inf.0 "1")))))))
  (define t14 (build-test-dfa `((complement "1")))))

  |#