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(module re mzscheme
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(require (lib "match.ss")
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(lib "list.ss")
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"util.ss")
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(provide ->re build-epsilon build-zero build-char-set build-concat
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build-repeat build-or build-and build-neg
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epsilonR? zeroR? char-setR? concatR? repeatR? orR? andR? negR?
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char-setR-chars concatR-re1 concatR-re2 repeatR-re orR-res
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andR-res negR-re
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re-nullable? re-index)
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;; get-index : -> nat
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(define get-index (make-counter))
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;; An re is either
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;; - (make-epsilonR bool nat)
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;; - (make-zeroR bool nat)
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;; - (make-char-setR bool nat (list-of char)) The list must be sorted
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;; - (make-concatR bool nat re re)
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;; - (make-repeatR bool nat re)
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;; - (make-orR bool nat (list-of re)) Must not directly contain any orRs
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;; - (make-andR bool nat (list-of re)) Must not directly contain any andRs
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;; - (make-negR bool nat re)
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;;
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;; Every re must have an index field globally different from all
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;; other re index fields.
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(define-struct re (nullable? index) (make-inspector))
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(define-struct (epsilonR re) () (make-inspector))
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(define-struct (zeroR re) () (make-inspector))
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(define-struct (char-setR re) (chars) (make-inspector))
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(define-struct (concatR re) (re1 re2) (make-inspector))
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(define-struct (repeatR re) (re))
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(define-struct (orR re) (res) (make-inspector))
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(define-struct (andR re) (res))
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(define-struct (negR re) (re))
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;; e : re
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;; The unique epsilon re
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(define e (make-epsilonR #t (get-index)))
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;; z : re
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;; The unique zero re
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(define z (make-zeroR #f (get-index)))
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;; s-re = char match the given character
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;; | string match its sequence of characters
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;; | re a precompiled re
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;; | (epsilon) match the empty string
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;; | (* s-re) match 0 or more
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;; | (+ s-re) match 1 or more
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;; | (? s-re) match 0 or 1
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;; | (: s-re ...) match one of the sub-expressions
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;; | (@ s-re ...) match each sub-expression in succession
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;; | (- char char) match any character between two (inclusive)
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;; | (^ char_or_range ...1) match any character not listed
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;; (the null concatenation `(@) means epsilon as does "".
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;; the null or `(:) means match nothing. The null carat `(^) means match
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;; any character.)
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;; ->re : s-re cache -> re
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(define (->re exp cache)
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(match exp
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((? char?) (build-char-set (list exp) cache))
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((? string?) (->re `(@ ,@(string->list exp)) cache))
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((? re?) exp)
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(`(epsilon) (build-epsilon))
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(`(* ,r)
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(build-repeat (->re r cache) cache))
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(`(+ ,r)
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(->re `(@ ,r (* ,r)) cache))
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(`(? ,r)
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(let ((c (->re r cache)))
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(if (re-nullable? c)
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c
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(build-or (list e c) cache))))
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(`(: ,rs ...)
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(build-or (flatten-res (map (lambda (r) (->re r cache)) rs) cache)
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cache))
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(`(@ ,rs ...)
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(foldr (lambda (x y)
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(build-concat (->re x cache) y cache))
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e
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rs))
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(`(- ,c1 ,c2)
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(let ((i1 (char->integer (if (string? c1) (string-ref c1 0) c1)))
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(i2 (char->integer (if (string? c2) (string-ref c2 0) c2))))
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(if (<= i1 i2)
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(build-char-set (make-range i1 i2) cache)
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z)))
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(`(^ ,crs ...)
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(let ((cs (->re `(: ,@crs) cache)))
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(cond
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((zeroR? cs) (build-char-set (make-range 0 255) cache))
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((char-setR? cs)
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(build-char-set
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(let loop ((bad-chars (map char->integer
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(char-setR-chars cs)))
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(i 0))
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(cond
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((> i 255) null)
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((and (not (null? bad-chars))
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(= i (car bad-chars)))
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(loop (cdr bad-chars) (add1 i)))
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(else
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(cons (integer->char i) (loop bad-chars (add1 i))))))
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cache))
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(else z))))))
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;; flatten-res: (list-of re) cache -> (list-of re)
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;; Takes all the char-sets in l and combines them into one element.
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;; Removes orRs too,
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(define (flatten-res l cache)
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(let loop ((res l)
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(chars null)
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(no-chars null))
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(cond
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((null? res)
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(if (null? chars)
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no-chars
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(cons (build-char-set (mergesort chars char<?) cache) no-chars)))
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((char-setR? (car res))
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(loop (cdr res) (merge (char-setR-chars (car res)) chars) no-chars))
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((orR? (car res))
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(loop (append (orR-res (car res)) (cdr res)) chars no-chars))
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(else (loop (cdr res) chars (cons (car res) no-chars))))))
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;; build-epsilon : -> re
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(define (build-epsilon) e)
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(define (build-zero) z)
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;; build-char-set : (list-of char) cache -> re
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;; cs must be sorted
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#;(define (build-char-set cs cache)
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(cond
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((null? cs) z)
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(else
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(make-char-setR #f (get-index) cs))))
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(define (build-char-set cs cache)
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(cond
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((null? cs) z)
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(else
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(cache cs
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(lambda ()
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(make-char-setR #f (get-index) cs))))))
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;; build-concat : re re cache -> re
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(define (build-concat r1 r2 cache)
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(cond
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((eq? e r1) r2)
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((eq? e r2) r1)
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((or (eq? z r1) (eq? z r2)) z)
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(else
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(cache (cons 'concat (cons (re-index r1) (re-index r2)))
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(lambda ()
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(make-concatR (and (re-nullable? r1) (re-nullable? r2))
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(get-index)
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r1 r2))))))
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;; build-repeat : re cache -> re
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(define (build-repeat r cache)
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(cache (cons 'repeat (re-index r))
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(lambda ()
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(make-repeatR #t (get-index) r))))
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;; build-or : (list-of re) cache -> re
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(define (build-or rs cache)
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(let ((rs
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(filter
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(lambda (x) (not (eq? x z)))
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(do-simple-equiv (replace rs orR? orR-res null) re-index))))
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(cond
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((null? rs) z)
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((null? (cdr rs)) (car rs))
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(else
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(cache (cons 'or (map re-index rs))
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(lambda ()
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(make-orR (ormap re-nullable? rs) (get-index) rs)))))))
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;; build-and : (list-of re) cache -> re
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(define (build-and rs cache)
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(let ((rs (do-simple-equiv (replace rs andR? andR-res null) rs)))
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(cond
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((ormap (lambda (x) (eq? x z)) rs) z)
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(else
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(cache (cons 'and (map re-index rs))
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(lambda ()
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(make-andR (andmap re-nullable? rs) (get-index) rs)))))))
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;; build-neg : re cache -> re
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(define (build-neg r cache)
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(cache (cons 'neg (re-index r))
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(lambda ()
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(make-negR (not (re-nullable? r)) (get-index) 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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(r3 (->re #\3 c))
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(rc (->re `(@ ,r1 ,r2) c))
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(rc2 (->re `(@ ,r2 ,r1) c))
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(rc3 (->re `(@ ,r1 ,r2 ,r3) c))
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(rr (->re `(* ,rc) c))
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(ro (->re `(: ,rr ,rc ,rr) c))
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(ro2 (->re `(: ,rc ,rr ,z) c))
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(ro3 (->re `(: ,rr ,rc) c))
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(real1 (->re `(+ (: (@ "|" (* (^ "|")) "|")
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(@ "|" (* (^ "|"))))) c)))
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((char-setR-chars r1) `(#\1))
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((char-setR-chars r2) `(#\2))
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((char-setR-chars r3) `(#\3))
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(ro ro2)
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(ro ro3)
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((->re `(* ,rc) c) rr)
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((build-char-set null c) z)
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((->re `(@) c) e)
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((->re `(:) c) z)
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((->re `(@ ,r1 (epsilon)) c) r1)
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((->re `(@ (epsilon) ,r1) c) r1)
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((->re `(@ ,r1 ,z) c) z)
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((->re `(@ ,z ,r1) c) z)
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((->re `(@ ,z (epsilon)) c) z)
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((->re `(@ (epsilon) ,z) c) z)
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((->re `(:) c) z)
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((->re `(: ,rr) c) rr)
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((build-or `(,z ,r1 ,z) c) r1)
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((build-or (list
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(build-or (list r1 r2) c)
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(build-or (list rc rr) c))
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c)
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(build-or (list r1 r2 rc rr) c))
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((concatR-re1 rc3) r1)
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((concatR-re1 (concatR-re2 rc3)) r2)
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((concatR-re2 (concatR-re2 rc3)) r3)
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((orR-res ro) (list rc rr))
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((repeatR-re rr) rc)
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((re-nullable? r1) #f)
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((re-nullable? rc) #f)
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((re-nullable? (->re `(@ ,rr ,rr) c)) #t)
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((re-nullable? rr) #t)
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((re-nullable? ro) #t)
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((re-nullable? (->re `(: ,r1 ,r2) c)) #f))
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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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(r3-5 (->re '(- #\3 #\5) c))
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(r4 (build-or `(,r1 ,r2) c))
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(r5 (->re `(: ,r3-5 #\7) c))
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(r6 (->re #\6 c)))
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((flatten-res null c) null)
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((char-setR-chars (car (flatten-res `(,r1) c))) '(#\1))
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((char-setR-chars (car (flatten-res `(,r4) c))) '(#\1 #\2))
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((char-setR-chars (car (flatten-res `(,r6 ,r5 ,r4 ,r3-5 ,r2 ,r1) c)))
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(string->list "1234567")))
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(test-block ((c (make-cache))
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(r (->re #\a c))
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(rr (->re `(@ ,r ,r) c))
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(rrr (->re `(@ ,r ,rr) c))
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(rrr* (->re `(* ,rrr) c)))
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((char-setR-chars r) '(#\a))
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((->re "" c) e)
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((->re "asdf" c) (->re `(@ #\a #\s #\d #\f) c))
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((->re r c) r)
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((->re `(epsilon) c) e)
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((->re `(* ,r) c) (build-repeat r c))
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((->re `(+ ,r) c) (build-concat r (build-repeat r c) c))
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((->re `(? ,r) c) (build-or (list e r) c))
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((->re `(? ,rrr*) c) rrr*)
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((->re `(: (: (- #\a #\c) (^ (- #\000 #\110) (- #\112 #\377)))
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(: (* #\2))) c)
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(build-or (list (build-char-set (list #\111 #\a #\b #\c) c)
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(build-repeat (build-char-set '(#\2) c) c))
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c))
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((->re `(: ,rr ,rrr) c) (build-or (list rr rrr) c))
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((->re `(: ,r) c) r)
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((->re `(:) c) z)
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((->re `(@) c) e)
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((->re `(@ ,rrr*) c) rrr*)
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(rr (build-concat r r c))
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((->re `(@ ,r ,rr ,rrr) c)
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(build-concat r (build-concat rr rrr c) c))
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((char-setR-chars (->re `(- #\1 #\1) c)) '(#\1))
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((char-setR-chars (->re `(- #\1 #\9) c)) (string->list "123456789"))
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((char-setR-chars (->re `(- "1" "1") c)) '(#\1))
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|
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((char-setR-chars (->re `(- "1" "9") c)) (string->list "123456789"))
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((->re `(- "9" "1") c) z)
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((char-setR-chars (->re `(^) c))
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(char-setR-chars (->re `(- #\000 #\377) c)))
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((char-setR-chars (->re `(^ #\001 (- #\002 #\377)) c)) `(#\000))
|
|
|
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)
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|
|
|
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)
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