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

385 lines
16 KiB
Racket

#lang racket/base
(require racket/list
racket/match
(prefix-in is: data/integer-set)
"util.rkt")
(provide ->re build-epsilon build-zero build-char-set build-concat
build-repeat build-or build-and build-neg
epsilonR? zeroR? char-setR? concatR? repeatR? orR? andR? negR?
char-setR-chars concatR-re1 concatR-re2 repeatR-re repeatR-low repeatR-high
orR-res andR-res negR-re
re-nullable? re-index)
;; get-index : -> nat
(define get-index (make-counter))
;; An re is either
;; - (make-epsilonR bool nat)
;; - (make-zeroR bool nat)
;; - (make-char-setR bool nat char-set)
;; - (make-concatR bool nat re re)
;; - (make-repeatR bool nat nat nat-or-+inf.0 re)
;; - (make-orR bool nat (list-of re)) Must not directly contain any orRs
;; - (make-andR bool nat (list-of re)) Must not directly contain any andRs
;; - (make-negR bool nat re)
;;
;; Every re must have an index field globally different from all
;; other re index fields.
(define-struct re (nullable? index) #:inspector (make-inspector))
(define-struct (epsilonR re) () #:inspector (make-inspector))
(define-struct (zeroR re) () #:inspector (make-inspector))
(define-struct (char-setR re) (chars) #:inspector (make-inspector))
(define-struct (concatR re) (re1 re2) #:inspector (make-inspector))
(define-struct (repeatR re) (low high re) #:inspector (make-inspector))
(define-struct (orR re) (res) #:inspector (make-inspector))
(define-struct (andR re) (res) #:inspector (make-inspector))
(define-struct (negR re) (re) #:inspector (make-inspector))
;; e : re
;; The unique epsilon re
(define e (make-epsilonR #t (get-index)))
;; z : re
;; The unique zero re
(define z (make-zeroR #f (get-index)))
;; s-re = char constant
;; | string constant (sequence of characters)
;; | re a precompiled re
;; | (repetition low high s-re) repetition between low and high times (inclusive)
;; | (union s-re ...)
;; | (intersection s-re ...)
;; | (complement s-re)
;; | (concatenation s-re ...)
;; | (char-range rng rng) match any character between two (inclusive)
;; | (char-complement char-set) match any character not listed
;; low = natural-number
;; high = natural-number or +inf.0
;; rng = char or string with length 1
;; (concatenation) (repetition 0 0 x), and "" match the empty string.
;; (union) matches no strings.
;; (intersection) matches any string.
(define loc:make-range is:make-range)
(define loc:union is:union)
(define loc:split is:split)
(define loc:complement is:complement)
;; ->re : s-re cache -> re
(define (->re exp cache)
(match exp
[(? char?) (build-char-set (loc:make-range (char->integer exp)) cache)]
[(? string?) (->re `(concatenation ,@(string->list exp)) cache)]
[(? re?) exp]
[`(repetition ,low ,high ,r)
(build-repeat low high (->re r cache) cache)]
[`(union ,rs ...)
(build-or (flatten-res (map (λ (r) (->re r cache)) rs)
orR? orR-res loc:union cache)
cache)]
[`(intersection ,rs ...)
(build-and (flatten-res (map (λ (r) (->re r cache)) rs)
andR? andR-res (λ (a b)
(let-values (((i _ __) (loc:split a b))) i))
cache)
cache)]
[`(complement ,r) (build-neg (->re r cache) cache)]
[`(concatenation ,rs ...)
(foldr (λ (x y)
(build-concat (->re x cache) y cache))
e
rs)]
[`(char-range ,c1 ,c2)
(let ([i1 (char->integer (if (string? c1) (string-ref c1 0) c1))]
[i2 (char->integer (if (string? c2) (string-ref c2 0) c2))])
(if (<= i1 i2)
(build-char-set (loc:make-range i1 i2) cache)
z))]
[`(char-complement ,crs ...)
(let ([cs (->re `(union ,@crs) cache)])
(cond
[(zeroR? cs) (build-char-set (loc:make-range 0 max-char-num) cache)]
[(char-setR? cs)
(build-char-set (loc:complement (char-setR-chars cs) 0 max-char-num) cache)]
[else z]))]))
;; flatten-res: (list-of re) (re -> bool) (re -> (list-of re))
;; (char-set char-set -> char-set) cache -> (list-of re)
;; Takes all the char-sets in l and combines them into one char-set using the combine function.
;; Flattens out the values of type?. get-res only needs to function on things type? returns
;; true for.
(define (flatten-res l type? get-res combine cache)
(let loop ([res l]
;; chars : (union #f char-set)
[chars #f]
[no-chars null])
(cond
[(null? res)
(if chars
(cons (build-char-set chars cache) no-chars)
no-chars)]
[(char-setR? (car res))
(if chars
(loop (cdr res) (combine (char-setR-chars (car res)) chars) no-chars)
(loop (cdr res) (char-setR-chars (car res)) no-chars))]
[(type? (car res))
(loop (append (get-res (car res)) (cdr res)) chars no-chars)]
[else (loop (cdr res) chars (cons (car res) no-chars))])))
;; build-epsilon : -> re
(define (build-epsilon) e)
(define (build-zero) z)
(define loc:integer-set-contents is:integer-set-contents)
;; build-char-set : char-set cache -> re
(define (build-char-set cs cache)
(define l (loc:integer-set-contents cs))
(cond
[(null? l) z]
[else
(cache l
(λ ()
(make-char-setR #f (get-index) cs)))]))
;; build-concat : re re cache -> re
(define (build-concat r1 r2 cache)
(cond
[(eq? e r1) r2]
[(eq? e r2) r1]
[(or (eq? z r1) (eq? z r2)) z]
[else
(cache (cons 'concat (cons (re-index r1) (re-index r2)))
(λ ()
(make-concatR (and (re-nullable? r1) (re-nullable? r2))
(get-index)
r1 r2)))]))
;; build-repeat : nat nat-or-+inf.0 re cache -> re
(define (build-repeat low high r cache)
(let ([low (if (< low 0) 0 low)])
(cond
[(eq? r e) e]
[(and (= 0 low) (or (= 0 high) (eq? z r))) e]
[(and (= 1 low) (= 1 high)) r]
[(and (repeatR? r)
(eqv? (repeatR-high r) +inf.0)
(or (= 0 (repeatR-low r))
(= 1 (repeatR-low r))))
(build-repeat (* low (repeatR-low r))
+inf.0
(repeatR-re r)
cache)]
[else
(cache (cons 'repeat (cons low (cons high (re-index r))))
(λ ()
(make-repeatR (or (re-nullable? r) (= 0 low)) (get-index) low high r)))])))
;; build-or : (list-of re) cache -> re
(define (build-or rs cache)
(let ([rs
(filter
(λ (x) (not (eq? x z)))
(do-simple-equiv (replace rs orR? orR-res null) re-index))])
(cond
[(null? rs) z]
[(null? (cdr rs)) (car rs)]
[(memq (build-neg z cache) rs) (build-neg z cache)]
[else
(cache (cons 'or (map re-index rs))
(λ ()
(make-orR (ormap re-nullable? rs) (get-index) rs)))])))
;; build-and : (list-of re) cache -> re
(define (build-and rs cache)
(let ([rs (do-simple-equiv (replace rs andR? andR-res null) re-index)])
(cond
[(null? rs) (build-neg z cache)]
[(null? (cdr rs)) (car rs)]
[(memq z rs) z]
[else
(cache (cons 'and (map re-index rs))
(λ ()
(make-andR (andmap re-nullable? rs) (get-index) rs)))])))
;; build-neg : re cache -> re
(define (build-neg r cache)
(cond
[(negR? r) (negR-re r)]
[else
(cache (cons 'neg (re-index r))
(λ ()
(make-negR (not (re-nullable? r)) (get-index) r)))]))
;; Tests for the build-functions
(test-block ((c (make-cache))
(isc is:integer-set-contents)
(r1 (build-char-set (is:make-range (char->integer #\1)) c))
(r2 (build-char-set (is:make-range (char->integer #\2)) c))
(r3 (build-char-set (is:make-range (char->integer #\3)) c))
(rc (build-concat r1 r2 c))
(rc2 (build-concat r2 r1 c))
(rr (build-repeat 0 +inf.0 rc c))
(ro (build-or `(,rr ,rc ,rr) c))
(ro2 (build-or `(,rc ,rr ,z) c))
(ro3 (build-or `(,rr ,rc) c))
(ro4 (build-or `(,(build-or `(,r1 ,r2) c)
,(build-or `(,r2 ,r3) c)) c))
(ra (build-and `(,rr ,rc ,rr) c))
(ra2 (build-and `(,rc ,rr) c))
(ra3 (build-and `(,rr ,rc) c))
(ra4 (build-and `(,(build-and `(,r3 ,r2) c)
,(build-and `(,r2 ,r1) c)) c))
(rn (build-neg z c))
(rn2 (build-neg r1 c)))
((isc (char-setR-chars r1)) (isc (is:make-range (char->integer #\1))))
((isc (char-setR-chars r2)) (isc (is:make-range (char->integer #\2))))
((isc (char-setR-chars r3)) (isc (is:make-range (char->integer #\3))))
((build-char-set (is:make-range) c) z)
((build-concat r1 e c) r1)
((build-concat e r1 c) r1)
((build-concat r1 z c) z)
((build-concat z r1 c) z)
((build-concat r1 r2 c) rc)
((concatR-re1 rc) r1)
((concatR-re2 rc) r2)
((concatR-re1 rc2) r2)
((concatR-re2 rc2) r1)
(ro ro2)
(ro ro3)
(ro4 (build-or `(,r1 ,r2 ,r3) c))
((orR-res ro) (list rc rr))
((orR-res ro4) (list r1 r2 r3))
((build-or null c) z)
((build-or `(,r1 ,z) c) r1)
((build-repeat 0 +inf.0 rc c) rr)
((build-repeat 0 1 z c) e)
((build-repeat 0 0 rc c) e)
((build-repeat 0 +inf.0 z c) e)
((build-repeat -1 +inf.0 z c) e)
((build-repeat 0 +inf.0 (build-repeat 0 +inf.0 rc c) c)
(build-repeat 0 +inf.0 rc c))
((build-repeat 20 20 (build-repeat 0 +inf.0 rc c) c)
(build-repeat 0 +inf.0 rc c))
((build-repeat 20 20 (build-repeat 1 +inf.0 rc c) c)
(build-repeat 20 +inf.0 rc c))
((build-repeat 1 1 rc c) rc)
((repeatR-re rr) rc)
(ra ra2)
(ra ra3)
(ra4 (build-and `(,r1 ,r2 ,r3) c))
((andR-res ra) (list rc rr))
((andR-res ra4) (list r1 r2 r3))
((build-and null c) (build-neg z c))
((build-and `(,r1 ,z) c) z)
((build-and `(,r1) c) r1)
((build-neg r1 c) (build-neg r1 c))
((build-neg (build-neg r1 c) c) r1)
((negR-re (build-neg r2 c)) r2)
((re-nullable? r1) #f)
((re-nullable? rc) #f)
((re-nullable? (build-concat rr rr c)) #t)
((re-nullable? rr) #t)
((re-nullable? (build-repeat 0 1 rc c)) #t)
((re-nullable? (build-repeat 1 2 rc c)) #f)
((re-nullable? (build-repeat 1 2 (build-or (list e r1) c) c)) #t)
((re-nullable? ro) #t)
((re-nullable? (build-or `(,r1 ,r2) c)) #f)
((re-nullable? (build-and `(,r1 ,e) c)) #f)
((re-nullable? (build-and `(,rr ,e) c)) #t)
((re-nullable? (build-neg r1 c)) #t)
((re-nullable? (build-neg rr c)) #f))
(test-block ((c (make-cache))
(isc is:integer-set-contents)
(r1 (->re #\1 c))
(r2 (->re #\2 c))
(r3-5 (->re '(char-range #\3 #\5) c))
(r4 (build-or `(,r1 ,r2) c))
(r5 (->re `(union ,r3-5 #\7) c))
(r6 (->re #\6 c)))
((flatten-res null orR? orR-res is:union c) null)
((isc (char-setR-chars (car (flatten-res `(,r1) orR? orR-res is:union c))))
(isc (is:make-range (char->integer #\1))))
((isc (char-setR-chars (car (flatten-res `(,r4) orR? orR-res is:union c))))
(isc (is:make-range (char->integer #\1) (char->integer #\2))))
((isc (char-setR-chars (car (flatten-res `(,r6 ,r5 ,r4 ,r3-5 ,r2 ,r1)
orR? orR-res is:union c))))
(isc (is:make-range (char->integer #\1) (char->integer #\7))))
((flatten-res `(,r1 ,r2) andR? andR-res (λ (x y)
(let-values (((i _ __)
(is:split x y)))
i))
c)
(list z)))
;; ->re
(test-block ((c (make-cache))
(isc is:integer-set-contents)
(r (->re #\a c))
(rr (->re `(concatenation ,r ,r) c))
(rrr (->re `(concatenation ,r ,rr) c))
(rrr* (->re `(repetition 0 +inf.0 ,rrr) c)))
((isc (char-setR-chars r)) (isc (is:make-range (char->integer #\a))))
((->re "" c) e)
((->re "asdf" c) (->re `(concatenation #\a #\s #\d #\f) c))
((->re r c) r)
((->re `(repetition 0 +inf.0 ,r) c) (build-repeat 0 +inf.0 r c))
((->re `(repetition 1 +inf.0 ,r) c) (build-repeat 1 +inf.0 r c))
((->re `(repetition 0 1 ,r) c) (build-repeat 0 1 r c))
((->re `(repetition 0 1 ,rrr*) c) rrr*)
((->re `(union (union (char-range #\a #\c)
(char-complement (char-range #\000 #\110)
(char-range #\112 ,(integer->char max-char-num))))
(union (repetition 0 +inf.0 #\2))) c)
(build-or (list (build-char-set (is:union (is:make-range 73)
(is:make-range 97 99))
c)
(build-repeat 0 +inf.0 (build-char-set (is:make-range 50) c) c))
c))
((->re `(union ,rr ,rrr) c) (build-or (list rr rrr) c))
((->re `(union ,r) c) r)
((->re `(union) c) z)
((->re `(intersection (intersection #\111
(char-complement (char-range #\000 #\110)
(char-range #\112 ,(integer->char max-char-num))))
(intersection (repetition 0 +inf.0 #\2))) c)
(build-and (list (build-char-set (is:make-range 73) c)
(build-repeat 0 +inf.0 (build-char-set (is:make-range 50) c) c))
c))
((->re `(intersection (intersection #\000 (char-complement (char-range #\000 #\110)
(char-range #\112 ,(integer->char max-char-num))))
(intersection (repetition 0 +inf.0 #\2))) c)
z)
((->re `(intersection ,rr ,rrr) c) (build-and (list rr rrr) c))
((->re `(intersection ,r) c) r)
((->re `(intersection) c) (build-neg z c))
((->re `(complement ,r) c) (build-neg r c))
((->re `(concatenation) c) e)
((->re `(concatenation ,rrr*) c) rrr*)
(rr (build-concat r r c))
((->re `(concatenation ,r ,rr ,rrr) c)
(build-concat r (build-concat rr rrr c) c))
((isc (char-setR-chars (->re `(char-range #\1 #\1) c))) (isc (is:make-range 49)))
((isc (char-setR-chars (->re `(char-range #\1 #\9) c))) (isc (is:make-range 49 57)))
((isc (char-setR-chars (->re `(char-range "1" "1") c))) (isc (is:make-range 49)))
((isc (char-setR-chars (->re `(char-range "1" "9") c))) (isc (is:make-range 49 57)))
((->re `(char-range "9" "1") c) z)
((isc (char-setR-chars (->re `(char-complement) c)))
(isc (char-setR-chars (->re `(char-range #\000 ,(integer->char max-char-num)) c))))
((isc (char-setR-chars (->re `(char-complement #\001 (char-range #\002 ,(integer->char max-char-num))) c)))
(isc (is:make-range 0)))
)