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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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(prefix is: (lib "integer-set.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 char-set)
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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) (make-inspector))
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(define-struct (orR re) (res) (make-inspector))
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(define-struct (andR re) (res) (make-inspector))
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(define-struct (negR re) (re) (make-inspector))
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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 iff all sub-expressions match
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;; | (~ s-re) match iff s-re doesn't match
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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 ...) 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. The null intersection `(&) means match string.)
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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 (is:make-range (char->integer 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)
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orR? orR-res is:union cache)
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cache))
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(`(& ,rs ...)
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(build-and (flatten-res (map (lambda (r) (->re r cache)) rs)
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andR? andR-res (lambda (a b)
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(let-values (((i _ __) (is:split a b))) i))
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cache)
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cache))
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(`(~ ,r)
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(build-neg (->re r cache) 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 (is: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 (is:make-range 0 255) cache))
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((char-setR? cs)
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(build-char-set (is:complement (char-setR-chars cs) 0 255) cache))
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(else z))))))
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;; flatten-res: (list-of re) (re -> bool) (re -> (list-of re))
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;; (char-set char-set -> char-set) cache -> (list-of re)
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;; Takes all the char-sets in l and combines them into one char-set using the combine function.
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;; Flattens out the values of type?. get-res only needs to function on things type? returns
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;; true for.
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(define (flatten-res l type? get-res combine cache)
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(let loop ((res l)
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;; chars : (union #f char-set)
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(chars #f)
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(no-chars null))
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(cond
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((null? res)
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(if chars
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(cons (build-char-set chars cache) no-chars)
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no-chars))
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((char-setR? (car res))
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(if chars
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(loop (cdr res) (combine (char-setR-chars (car res)) chars) no-chars)
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(loop (cdr res) (char-setR-chars (car res)) no-chars)))
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((type? (car res))
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(loop (append (get-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 : char-set cache -> re
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(define (build-char-set cs cache)
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(let ((l (is:integer-set-contents cs)))
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(cond
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((null? l) z)
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(else
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(cache l
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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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(cond
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((eq? z r) e)
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((repeatR? r) r)
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(else
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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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((memq (build-neg z cache) rs) (build-neg z cache))
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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) re-index)))
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(cond
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((null? rs) (build-neg z cache))
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((null? (cdr rs)) (car rs))
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((memq 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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(cond
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((negR? r) (negR-re r))
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(else
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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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;; Tests for the build-functions
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(test-block ((c (make-cache))
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(isc is:integer-set-contents)
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(r1 (build-char-set (is:make-range (char->integer #\1)) c))
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(r2 (build-char-set (is:make-range (char->integer #\2)) c))
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(r3 (build-char-set (is:make-range (char->integer #\3)) c))
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(rc (build-concat r1 r2 c))
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(rc2 (build-concat r2 r1 c))
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(rr (build-repeat rc c))
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(ro (build-or `(,rr ,rc ,rr) c))
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(ro2 (build-or `(,rc ,rr ,z) c))
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(ro3 (build-or `(,rr ,rc) c))
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(ro4 (build-or `(,(build-or `(,r1 ,r2) c)
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,(build-or `(,r2 ,r3) c)) c))
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(ra (build-and `(,rr ,rc ,rr) c))
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(ra2 (build-and `(,rc ,rr) c))
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(ra3 (build-and `(,rr ,rc) c))
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(ra4 (build-and `(,(build-and `(,r3 ,r2) c)
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,(build-and `(,r2 ,r1) c)) c))
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(rn (build-neg z c))
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(rn2 (build-neg r1 c)))
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((isc (char-setR-chars r1)) (isc (is:make-range (char->integer #\1))))
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((isc (char-setR-chars r2)) (isc (is:make-range (char->integer #\2))))
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((isc (char-setR-chars r3)) (isc (is:make-range (char->integer #\3))))
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((build-char-set (is:make-range) c) z)
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((build-concat r1 e c) r1)
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((build-concat e r1 c) r1)
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((build-concat r1 z c) z)
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((build-concat z r1 c) z)
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((build-concat r1 r2 c) rc)
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((concatR-re1 rc) r1)
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((concatR-re2 rc) r2)
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((concatR-re1 rc2) r2)
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((concatR-re2 rc2) r1)
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(ro ro2)
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(ro ro3)
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(ro4 (build-or `(,r1 ,r2 ,r3) c))
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((orR-res ro) (list rc rr))
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((orR-res ro4) (list r1 r2 r3))
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((build-or null c) z)
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((build-or `(,r1 ,z) c) r1)
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((build-repeat rc c) rr)
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((build-repeat z c) e)
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((build-repeat (build-repeat rc c) c) (build-repeat rc c))
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((repeatR-re rr) rc)
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(ra ra2)
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(ra ra3)
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(ra4 (build-and `(,r1 ,r2 ,r3) c))
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((andR-res ra) (list rc rr))
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((andR-res ra4) (list r1 r2 r3))
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((build-and null c) (build-neg z c))
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((build-and `(,r1 ,z) c) z)
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((build-and `(,r1) c) r1)
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((build-neg r1 c) (build-neg r1 c))
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((build-neg (build-neg r1 c) c) r1)
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((negR-re (build-neg r2 c)) r2)
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((re-nullable? r1) #f)
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((re-nullable? rc) #f)
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((re-nullable? (build-concat 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? (build-or `(,r1 ,r2) c)) #f)
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((re-nullable? (build-and `(,r1 ,e) c)) #f)
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((re-nullable? (build-and `(,rr ,e) c)) #t)
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((re-nullable? (build-neg r1 c)) #t)
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((re-nullable? (build-neg rr c)) #f))
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(test-block ((c (make-cache))
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(isc is:integer-set-contents)
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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 orR? orR-res is:union c) null)
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((isc (char-setR-chars (car (flatten-res `(,r1) orR? orR-res is:union c))))
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(isc (is:make-range (char->integer #\1))))
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((isc (char-setR-chars (car (flatten-res `(,r4) orR? orR-res is:union c))))
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(isc (is:make-range (char->integer #\1) (char->integer #\2))))
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((isc (char-setR-chars (car (flatten-res `(,r6 ,r5 ,r4 ,r3-5 ,r2 ,r1) orR? orR-res is:union c))))
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(isc (is:make-range (char->integer #\1) (char->integer #\7))))
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((flatten-res `(,r1 ,r2) andR? andR-res (lambda (x y)
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(let-values (((i _ __)
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(is:split x y)))
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i))
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c)
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(list z)))
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;; ->re
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(test-block ((c (make-cache))
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(isc is:integer-set-contents)
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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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((isc (char-setR-chars r)) (isc (is:make-range (char->integer #\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 (is:union (is:make-range 73)
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(is:make-range 97 99))
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c)
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(build-repeat (build-char-set (is:make-range 50) 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 `(& (& #\111 (^ (- #\000 #\110) (- #\112 #\377)))
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(& (* #\2))) c)
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(build-and (list (build-char-set (is:make-range 73) c)
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(build-repeat (build-char-set (is:make-range 50) c) c))
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c))
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((->re `(& (& #\000 (^ (- #\000 #\110) (- #\112 #\377)))
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(& (* #\2))) c)
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z)
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((->re `(& ,rr ,rrr) c) (build-and (list rr rrr) c))
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((->re `(& ,r) c) r)
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((->re `(&) c) (build-neg z c))
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((->re `(~ ,r) c) (build-neg r c))
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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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((isc (char-setR-chars (->re `(- #\1 #\1) c))) (isc (is:make-range 49)))
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((isc (char-setR-chars (->re `(- #\1 #\9) c))) (isc (is:make-range 49 57)))
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((isc (char-setR-chars (->re `(- "1" "1") c))) (isc (is:make-range 49)))
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((isc (char-setR-chars (->re `(- "1" "9") c))) (isc (is:make-range 49 57)))
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((->re `(- "9" "1") c) z)
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((isc (char-setR-chars (->re `(^) c)))
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(isc (char-setR-chars (->re `(- #\000 #\377) c))))
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((isc (char-setR-chars (->re `(^ #\001 (- #\002 #\377)) c))) (isc (is:make-range 0)))
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)
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)
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