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340 lines
15 KiB
Racket
340 lines
15 KiB
Racket
(module deriv mzscheme
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(require mzlib/list
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(prefix is: mzlib/integer-set)
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"re.ss"
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"util.ss")
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(provide build-dfa print-dfa (struct dfa (num-states start-state final-states/actions transitions)))
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(define e (build-epsilon))
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(define z (build-zero))
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;; Don't do anything with this one but extract the chars
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(define all-chars (->re `(char-complement (union)) (make-cache)))
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;; get-char-groups : re bool -> (list-of char-setR?)
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;; Collects the char-setRs in r that could be used in
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;; taking the derivative of r.
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(define (get-char-groups r found-negation)
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(cond
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((or (eq? r e) (eq? r z)) null)
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((char-setR? r) (list r))
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((concatR? r)
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(if (re-nullable? (concatR-re1 r))
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(append (get-char-groups (concatR-re1 r) found-negation)
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(get-char-groups (concatR-re2 r) found-negation))
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(get-char-groups (concatR-re1 r) found-negation)))
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((repeatR? r)
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(get-char-groups (repeatR-re r) found-negation))
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((orR? r)
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(apply append (map (lambda (x) (get-char-groups x found-negation)) (orR-res r))))
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((andR? r)
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(apply append (map (lambda (x) (get-char-groups x found-negation)) (andR-res r))))
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((negR? r)
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(if found-negation
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(get-char-groups (negR-re r) #t)
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(cons all-chars (get-char-groups (negR-re r) #t))))))
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(test-block ((c (make-cache))
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(r1 (->re #\1 c))
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(r2 (->re #\2 c)))
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((get-char-groups e #f) null)
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((get-char-groups z #f) null)
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((get-char-groups r1 #f) (list r1))
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((get-char-groups (->re `(concatenation ,r1 ,r2) c) #f)
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(list r1))
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((get-char-groups (->re `(concatenation ,e ,r2) c) #f)
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(list r2))
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((get-char-groups (->re `(concatenation (repetition 0 +inf.0 ,r1) ,r2) c) #f)
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(list r1 r2))
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((get-char-groups (->re `(repetition 0 +inf.0 ,r1) c) #f)
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(list r1))
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((get-char-groups
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(->re `(union (repetition 0 +inf.0 ,r1)
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(concatenation (repetition 0 +inf.0 ,r2) "3") "4") c) #f)
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(list r1 r2 (->re "3" c) (->re "4" c)))
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((get-char-groups (->re `(complement ,r1) c) #f)
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(list all-chars r1))
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((get-char-groups
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(->re `(intersection (repetition 0 +inf.0 ,r1)
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(concatenation (repetition 0 +inf.0 ,r2) "3") "4") c) #f)
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(list r1 r2 (->re "3" c) (->re "4" c)))
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)
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(define loc:member? is:member?)
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;; deriveR : re char cache -> re
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(define (deriveR r c cache)
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(cond
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((or (eq? r e) (eq? r z)) z)
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((char-setR? r)
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(if (loc:member? c (char-setR-chars r)) e z))
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((concatR? r)
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(let* ((r1 (concatR-re1 r))
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(r2 (concatR-re2 r))
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(d (build-concat (deriveR r1 c cache) r2 cache)))
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(if (re-nullable? r1)
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(build-or (list d (deriveR r2 c cache)) cache)
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d)))
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((repeatR? r)
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(build-concat (deriveR (repeatR-re r) c cache)
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(build-repeat (sub1 (repeatR-low r))
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(sub1 (repeatR-high r))
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(repeatR-re r) cache)
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cache))
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((orR? r)
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(build-or (map (lambda (x) (deriveR x c cache))
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(orR-res r))
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cache))
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((andR? r)
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(build-and (map (lambda (x) (deriveR x c cache))
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(andR-res r))
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cache))
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((negR? r)
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(build-neg (deriveR (negR-re r) c cache) cache))))
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(test-block ((c (make-cache))
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(a (char->integer #\a))
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(b (char->integer #\b))
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(r1 (->re #\a c))
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(r2 (->re `(repetition 0 +inf.0 #\a) c))
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(r3 (->re `(repetition 0 +inf.0 ,r2) c))
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(r4 (->re `(concatenation #\a ,r2) c))
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(r5 (->re `(repetition 0 +inf.0 ,r4) c))
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(r6 (->re `(union ,r5 #\a) c))
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(r7 (->re `(concatenation ,r2 ,r2) c))
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(r8 (->re `(complement ,r4) c))
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(r9 (->re `(intersection ,r2 ,r4) c)))
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((deriveR e a c) z)
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((deriveR z a c) z)
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((deriveR r1 b c) z)
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((deriveR r1 a c) e)
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((deriveR r2 a c) r2)
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((deriveR r2 b c) z)
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((deriveR r3 a c) r2)
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((deriveR r3 b c) z)
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((deriveR r4 a c) r2)
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((deriveR r4 b c) z)
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((deriveR r5 a c) (->re `(concatenation ,r2 ,r5) c))
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((deriveR r5 b c) z)
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((deriveR r6 a c) (->re `(union (concatenation ,r2 ,r5) "") c))
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((deriveR r6 b c) z)
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((deriveR r7 a c) (->re `(union (concatenation ,r2 ,r2) ,r2) c))
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((deriveR r7 b c) z)
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((deriveR r8 a c) (->re `(complement, r2) c))
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((deriveR r8 b c) (->re `(complement ,z) c))
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((deriveR r9 a c) r2)
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((deriveR r9 b c) z)
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((deriveR (->re `(repetition 1 2 "ab") c) a c)
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(->re `(concatenation "b" (repetition 0 1 "ab")) c)))
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;; An re-action is (cons re action)
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;; derive : (list-of re-action) char cache -> (union (list-of re-action) #f)
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;; applies deriveR to all the re-actions's re parts.
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;; Returns #f if the derived state is equivalent to z.
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(define (derive r c cache)
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(let ((new-r (map (lambda (ra)
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(cons (deriveR (car ra) c cache) (cdr ra)))
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r)))
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(if (andmap (lambda (x) (eq? z (car x)))
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new-r)
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#f
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new-r)))
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(test-block ((c (make-cache))
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(r1 (->re #\1 c))
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(r2 (->re #\2 c)))
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((derive null (char->integer #\1) c) #f)
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((derive (list (cons r1 1) (cons r2 2)) (char->integer #\1) c)
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(list (cons e 1) (cons z 2)))
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((derive (list (cons r1 1) (cons r2 2)) (char->integer #\3) c) #f))
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;; get-final : (list-of re-action) -> (union #f syntax-object)
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;; An re that accepts e represents a final state. Return the
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;; action from the first final state or #f if there is none.
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(define (get-final res)
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(cond
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((null? res) #f)
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((re-nullable? (caar res)) (cdar res))
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(else (get-final (cdr res)))))
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(test-block ((c->i char->integer)
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(c (make-cache))
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(r1 (->re #\a c))
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(r2 (->re #\b c))
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(b (list (cons z 1) (cons z 2) (cons z 3) (cons e 4) (cons z 5)))
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(a (list (cons r1 1) (cons r2 2))))
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((derive null (c->i #\a) c) #f)
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((derive a (c->i #\a) c) (list (cons e 1) (cons z 2)))
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((derive a (c->i #\b) c) (list (cons z 1) (cons e 2)))
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((derive a (c->i #\c) c) #f)
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((derive (list (cons (->re `(union " " "\n" ",") c) 1)
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(cons (->re `(concatenation (repetition 0 1 "-")
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(repetition 1 +inf.0 (char-range "0" "9"))) c) 2)
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(cons (->re `(concatenation "-" (repetition 1 +inf.0 "-")) c) 3)
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(cons (->re "[" c) 4)
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(cons (->re "]" c) 5)) (c->i #\[) c)
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b)
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((get-final a) #f)
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((get-final (list (cons e 1) (cons e 2))) 1)
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((get-final b) 4))
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;; A state is (make-state (list-of re-action) nat)
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(define-struct state (spec index))
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;; get->key : re-action -> (list-of nat)
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;; states are indexed by the list of indexes of their res
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(define (get-key s)
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(map (lambda (x) (re-index (car x))) s))
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(define loc:partition is:partition)
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;; compute-chars : (list-of state) -> (list-of char-set)
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;; Computed the sets of equivalent characters for taking the
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;; derivative of the car of st. Only one derivative per set need to be taken.
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(define (compute-chars st)
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(cond
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((null? st) null)
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(else
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(loc:partition (map char-setR-chars
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(apply append (map (lambda (x) (get-char-groups (car x) #f))
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(state-spec (car st)))))))))
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(test-block ((c (make-cache))
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(c->i char->integer)
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(r1 (->re `(char-range #\1 #\4) c))
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(r2 (->re `(char-range #\2 #\3) c)))
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((compute-chars null) null)
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((compute-chars (list (make-state null 1))) null)
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((map is:integer-set-contents
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(compute-chars (list (make-state (list (cons r1 1) (cons r2 2)) 2))))
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(list (is:integer-set-contents (is:make-range (c->i #\2) (c->i #\3)))
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(is:integer-set-contents (is:union (is:make-range (c->i #\1))
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(is:make-range (c->i #\4)))))))
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;; A dfa is (make-dfa int int
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;; (list-of (cons int syntax-object))
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;; (list-of (cons int (list-of (cons char-set int)))))
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;; Each transitions is a state and a list of chars with the state to transition to.
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;; The finals and transitions are sorted by state number, and duplicate free.
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(define-struct dfa (num-states start-state final-states/actions transitions) (make-inspector))
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(define loc:get-integer is:get-integer)
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;; build-dfa : (list-of re-action) cache -> dfa
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(define (build-dfa rs cache)
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(let* ((transitions (make-hash-table))
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(get-state-number (make-counter))
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(start (make-state rs (get-state-number))))
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(cache (cons 'state (get-key rs)) (lambda () start))
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(let loop ((old-states (list start))
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(new-states null)
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(all-states (list start))
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(cs (compute-chars (list start))))
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(cond
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((and (null? old-states) (null? new-states))
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(make-dfa (get-state-number) (state-index start)
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(sort (filter (lambda (x) (cdr x))
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(map (lambda (state)
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(cons (state-index state) (get-final (state-spec state))))
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all-states))
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(lambda (a b) (< (car a) (car b))))
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(sort (hash-table-map transitions
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(lambda (state trans)
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(cons (state-index state)
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(map (lambda (t)
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(cons (car t)
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(state-index (cdr t))))
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trans))))
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(lambda (a b) (< (car a) (car b))))))
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((null? old-states)
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(loop new-states null all-states (compute-chars new-states)))
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((null? cs)
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(loop (cdr old-states) new-states all-states (compute-chars (cdr old-states))))
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(else
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(let* ((state (car old-states))
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(c (car cs))
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(new-re (derive (state-spec state) (loc:get-integer c) cache)))
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(cond
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(new-re
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(let* ((new-state? #f)
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(new-state (cache (cons 'state (get-key new-re))
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(lambda ()
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(set! new-state? #t)
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(make-state new-re (get-state-number)))))
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(new-all-states (if new-state? (cons new-state all-states) all-states)))
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(hash-table-put! transitions
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state
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(cons (cons c new-state)
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(hash-table-get transitions state
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(lambda () null))))
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(cond
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(new-state?
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(loop old-states (cons new-state new-states) new-all-states (cdr cs)))
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(else
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(loop old-states new-states new-all-states (cdr cs))))))
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(else (loop old-states new-states all-states (cdr cs))))))))))
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(define (print-dfa x)
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(printf "number of states: ~a\n" (dfa-num-states x))
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(printf "start state: ~a\n" (dfa-start-state x))
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(printf "final states: ~a\n" (map car (dfa-final-states/actions x)))
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(for-each (lambda (trans)
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(printf "state: ~a\n" (car trans))
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(for-each (lambda (rule)
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(printf " -~a-> ~a\n"
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(is:integer-set-contents (car rule))
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(cdr rule)))
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(cdr trans)))
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(dfa-transitions x)))
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(define (build-test-dfa rs)
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(let ((c (make-cache)))
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(build-dfa (map (lambda (x) (cons (->re x c) 'action))
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rs)
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c)))
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#|
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(define t1 (build-test-dfa null))
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(define t2 (build-test-dfa `(#\a)))
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(define t3 (build-test-dfa `(#\a #\b)))
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(define t4 (build-test-dfa `((repetition 0 +inf.0 #\a)
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(repetition 0 +inf.0 (concatenation #\a #\b)))))
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(define t5 (build-test-dfa `((concatenation (repetition 0 +inf.0 (union #\0 #\1)) #\1))))
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(define t6 (build-test-dfa `((repetition 0 +inf.0 (repetition 0 +inf.0 #\a))
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(repetition 0 +inf.0 (concatenation #\b (repetition 1 +inf.0 #\b))))))
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(define t7 (build-test-dfa `((concatenation (repetition 0 +inf.0 #\a) (repetition 0 +inf.0 #\b)
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(repetition 0 +inf.0 #\c) (repetition 0 +inf.0 #\d)
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(repetition 0 +inf.0 #\e)))))
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(define t8
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(build-test-dfa `((concatenation (repetition 0 +inf.0 (union #\a #\b)) #\a (union #\a #\b)
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(union #\a #\b) (union #\a #\b) (union #\a #\b)))))
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(define t9 (build-test-dfa `((concatenation "/*"
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(complement (concatenation (intersection) "*/" (intersection)))
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"*/"))))
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(define t11 (build-test-dfa `((complement "1"))))
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(define t12 (build-test-dfa `((concatenation (intersection (concatenation (repetition 0 +inf.0 "a") "b")
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(concatenation "a" (repetition 0 +inf.0 "b")))
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"ab"))))
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(define x (build-test-dfa `((union " " "\n" ",")
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(concatenation (repetition 0 1 "-") (repetition 1 +inf.0 (char-range "0" "9")))
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(concatenation "-" (repetition 1 +inf.0 "-"))
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"["
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"]")))
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(define y (build-test-dfa
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`((repetition 1 +inf.0
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(union (concatenation "|" (repetition 0 +inf.0 (char-complement "|")) "|")
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(concatenation "|" (repetition 0 +inf.0 (char-complement "|"))))))))
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(define t13 (build-test-dfa `((intersection (concatenation (intersection) "111" (intersection))
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(complement (union (concatenation (intersection) "01")
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(repetition 1 +inf.0 "1")))))))
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(define t14 (build-test-dfa `((complement "1"))))
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|#
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)
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