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br-parser-tools/collects/parser-tools/private-yacc/grammar.rkt

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Racket

;; Constructs to create and access grammars, the internal
;; representation of the input to the parser generator.
(module grammar mzscheme
(require mzlib/class
mzlib/list
"yacc-helper.rkt"
mzlib/contract)
;; Each production has a unique index 0 <= index <= number of productions
(define-struct prod (lhs rhs index prec action) (make-inspector))
;; The dot-pos field is the index of the element in the rhs
;; of prod that the dot immediately precedes.
;; Thus 0 <= dot-pos <= (vector-length rhs).
(define-struct item (prod dot-pos) (make-inspector))
;; gram-sym = (union term? non-term?)
;; Each term has a unique index 0 <= index < number of terms
;; Each non-term has a unique index 0 <= index < number of non-terms
(define-struct term (sym index prec) (make-inspector))
(define-struct non-term (sym index) (make-inspector))
;; a precedence declaration.
(define-struct prec (num assoc) (make-inspector))
(provide/contract
(make-item (prod? (union false/c natural-number/c) . -> . item?))
(make-term (symbol? (union false/c natural-number/c) (union prec? false/c) . -> . term?))
(make-non-term (symbol? (union false/c natural-number/c) . -> . non-term?))
(make-prec (natural-number/c (symbols 'left 'right 'nonassoc) . -> . prec?))
(make-prod (non-term? (vectorof (union non-term? term?))
(union false/c natural-number/c) (union false/c prec?) syntax? . -> . prod?)))
(provide
;; Things that work on items
start-item? item-prod item->string
sym-at-dot move-dot-right item<? item-dot-pos
;; Things that operate on grammar symbols
gram-sym-symbol gram-sym-index term-prec gram-sym->string
non-term? term? non-term<? term<?
term-list->bit-vector term-index non-term-index
;; Things that work on precs
prec-num prec-assoc
grammar%
;; Things that work on productions
prod-index prod-prec prod-rhs prod-lhs prod-action)
;;---------------------- LR items --------------------------
;; item<?: LR-item * LR-item -> bool
;; Lexicographic comparison on two items.
(define (item<? i1 i2)
(let ((p1 (prod-index (item-prod i1)))
(p2 (prod-index (item-prod i2))))
(or (< p1 p2)
(and (= p1 p2)
(let ((d1 (item-dot-pos i1))
(d2 (item-dot-pos i2)))
(< d1 d2))))))
;; start-item?: LR-item -> bool
;; The start production always has index 0
(define (start-item? i)
(= 0 (non-term-index (prod-lhs (item-prod i)))))
;; move-dot-right: LR-item -> LR-item | #f
;; moves the dot to the right in the item, unless it is at its
;; rightmost, then it returns false
(define (move-dot-right i)
(cond
((= (item-dot-pos i) (vector-length (prod-rhs (item-prod i)))) #f)
(else (make-item (item-prod i)
(add1 (item-dot-pos i))))))
;; sym-at-dot: LR-item -> gram-sym | #f
;; returns the symbol after the dot in the item or #f if there is none
(define (sym-at-dot i)
(let ((dp (item-dot-pos i))
(rhs (prod-rhs (item-prod i))))
(cond
((= dp (vector-length rhs)) #f)
(else (vector-ref rhs dp)))))
;; print-item: LR-item ->
(define (item->string it)
(let ((print-sym (lambda (i)
(let ((gs (vector-ref (prod-rhs (item-prod it)) i)))
(cond
((term? gs) (format "~a " (term-sym gs)))
(else (format "~a " (non-term-sym gs))))))))
(string-append
(format "~a -> " (non-term-sym (prod-lhs (item-prod it))))
(let loop ((i 0))
(cond
((= i (vector-length (prod-rhs (item-prod it))))
(if (= i (item-dot-pos it))
". "
""))
((= i (item-dot-pos it))
(string-append ". " (print-sym i) (loop (add1 i))))
(else (string-append (print-sym i) (loop (add1 i)))))))))
;; --------------------- Grammar Symbols --------------------------
(define (non-term<? nt1 nt2)
(< (non-term-index nt1) (non-term-index nt2)))
(define (term<? nt1 nt2)
(< (term-index nt1) (term-index nt2)))
(define (gram-sym-index gs)
(cond
((term? gs) (term-index gs))
(else (non-term-index gs))))
(define (gram-sym-symbol gs)
(cond
((term? gs) (term-sym gs))
(else (non-term-sym gs))))
(define (gram-sym->string gs)
(symbol->string (gram-sym-symbol gs)))
;; term-list->bit-vector: term list -> int
;; Creates a number where the nth bit is 1 if the term with index n is in
;; the list, and whose nth bit is 0 otherwise
(define (term-list->bit-vector terms)
(cond
((null? terms) 0)
(else
(bitwise-ior (arithmetic-shift 1 (term-index (car terms))) (term-list->bit-vector (cdr terms))))))
;; ------------------------- Grammar ------------------------------
(define grammar%
(class object%
(super-instantiate ())
;; prods: production list list
;; where there is one production list per non-term
(init prods)
;; init-prods: production list
;; The productions parsing can start from
;; nullable-non-terms is indexed by the non-term-index and is true iff non-term is nullable
(init-field init-prods terms non-terms end-terms)
;; list of all productions
(define all-prods (apply append prods))
(define num-prods (length all-prods))
(define num-terms (length terms))
(define num-non-terms (length non-terms))
(let ((count 0))
(for-each
(lambda (nt)
(set-non-term-index! nt count)
(set! count (add1 count)))
non-terms))
(let ((count 0))
(for-each
(lambda (t)
(set-term-index! t count)
(set! count (add1 count)))
terms))
(let ((count 0))
(for-each
(lambda (prod)
(set-prod-index! prod count)
(set! count (add1 count)))
all-prods))
;; indexed by the index of the non-term - contains the list of productions for that non-term
(define nt->prods
(let ((v (make-vector (length prods) #f)))
(for-each (lambda (prods)
(vector-set! v (non-term-index (prod-lhs (car prods))) prods))
prods)
v))
(define nullable-non-terms
(nullable all-prods num-non-terms))
(define/public (get-num-terms) num-terms)
(define/public (get-num-non-terms) num-non-terms)
(define/public (get-prods-for-non-term nt)
(vector-ref nt->prods (non-term-index nt)))
(define/public (get-prods) all-prods)
(define/public (get-init-prods) init-prods)
(define/public (get-terms) terms)
(define/public (get-non-terms) non-terms)
(define/public (get-num-prods) num-prods)
(define/public (get-end-terms) end-terms)
(define/public (nullable-non-term? nt)
(vector-ref nullable-non-terms (non-term-index nt)))
(define/public (nullable-after-dot? item)
(let* ((rhs (prod-rhs (item-prod item)))
(prod-length (vector-length rhs)))
(let loop ((i (item-dot-pos item)))
(cond
((< i prod-length)
(if (and (non-term? (vector-ref rhs i)) (nullable-non-term? (vector-ref rhs i)))
(loop (add1 i))
#f))
((= i prod-length) #t)))))
(define/public (nullable-non-term-thunk)
(lambda (nt)
(nullable-non-term? nt)))
(define/public (nullable-after-dot?-thunk)
(lambda (item)
(nullable-after-dot? item)))))
;; nullable: production list * int -> non-term set
;; determines which non-terminals can derive epsilon
(define (nullable prods num-nts)
(letrec ((nullable (make-vector num-nts #f))
(added #f)
;; possible-nullable: producion list -> production list
;; Removes all productions that have a terminal
(possible-nullable
(lambda (prods)
(filter (lambda (prod)
(vector-andmap non-term? (prod-rhs prod)))
prods)))
;; set-nullables: production list -> production list
;; makes one pass through the productions, adding the ones
;; known to be nullable now to nullable and returning a list
;; of productions that we don't know about yet.
(set-nullables
(lambda (prods)
(cond
((null? prods) null)
((vector-ref nullable
(gram-sym-index (prod-lhs (car prods))))
(set-nullables (cdr prods)))
((vector-andmap (lambda (nt)
(vector-ref nullable (gram-sym-index nt)))
(prod-rhs (car prods)))
(vector-set! nullable
(gram-sym-index (prod-lhs (car prods)))
#t)
(set! added #t)
(set-nullables (cdr prods)))
(else
(cons (car prods)
(set-nullables (cdr prods))))))))
(let loop ((P (possible-nullable prods)))
(cond
((null? P) nullable)
(else
(set! added #f)
(let ((new-P (set-nullables P)))
(if added
(loop new-P)
nullable)))))))
)