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br-parser-tools/collects/parser-tools/private-yacc/lr0.ss

267 lines
7.8 KiB
Scheme

#cs
(module lr0 mzscheme
;; Handle the LR0 automaton
(require "grammar.ss"
"graph.ss"
(lib "list.ss"))
(provide union build-lr0-automaton run-automaton (struct trans-key (st gs))
lr0-transitions lr0-states lr0-epsilon-trans
kernel-items kernel-index for-each-state)
(define (union comp<?)
(letrec ((union
(lambda (l1 l2)
(cond
((null? l1) l2)
((null? l2) l1)
(else (let ((c1 (car l1))
(c2 (car l2)))
(cond
((comp<? c1 c2)
(cons c1 (union (cdr l1) l2)))
((comp<? c2 c1)
(cons c2 (union l1 (cdr l2))))
(else (union (cdr l1) l2)))))))))
union))
;; kernel = (make-kernel (LR1-item list) index)
;; the list must be kept sorted according to item<? so that equal? can
;; be used to compare kernels
;; LR0-automaton = (make-lr0 (trans-key kernel hash-table) (kernel vector) (kernel item hashtable))
;; trans-key = (make-trans-key kernel gram-sym)
(define-struct kernel (items index) (make-inspector))
(define-struct trans-key (st gs) (make-inspector))
(define-struct lr0 (transitions states epsilon-trans) (make-inspector))
;; Iteration over the states in an automaton
(define (for-each-state f a)
(let* ((states (lr0-states a))
(num-states (vector-length states)))
(let loop ((i 0))
(if (< i num-states)
(begin
(f (vector-ref states i))
(loop (add1 i)))))))
;; The kernels in the automaton are represented cannonically.
;; That is (equal? a b) <=> (eq? a b)
(define (kernel->string k)
(apply string-append
`("{" ,@(map (lambda (i) (string-append (item->string i) ", "))
(kernel-items k))
"}")))
;; run-automaton: kernel * gram-sym * LR0-automaton -> kernel | #f
;; returns the state that the transition trans-key provides or #f
;; if there is no such state
(define (run-automaton k s a)
(hash-table-get (lr0-transitions a) (make-trans-key k s) (lambda () #f)))
;; build-LR0-automaton: grammar -> LR0-automaton
;; Constructs the kernels of the sets of LR(0) items of g
(define (build-lr0-automaton grammar)
; (printf "LR(0) automaton:~n")
(letrec (
(terms (list->vector (grammar-terms grammar)))
(non-terms (list->vector (grammar-non-terms grammar)))
(num-non-terms (vector-length non-terms))
(num-gram-syms (+ num-non-terms (vector-length terms)))
(epsilons (make-hash-table 'equal))
;; first-non-term: non-term -> non-term list
;; given a non-terminal symbol C, return those non-terminal
;; symbols A s.t. C -> An for some string of terminals and
;; non-terminals n where -> means a rightmost derivation in many
;; steps. Assumes that each non-term can be reduces to a string
;; of terms.
(first-non-term
(digraph (grammar-non-terms grammar)
(lambda (nt)
(filter non-term?
(map (lambda (prod)
(sym-at-dot (make-item prod 0)))
(get-nt-prods grammar nt))))
(lambda (nt) (list nt))
(union non-term<?)
null))
;; closure: LR1-item list -> LR1-item list
;; Creates a set of items containing i s.t. if A -> n.Xm is in it,
;; X -> .o is in it too.
(LR0-closure
(lambda (i)
(cond
((null? i) null)
(else
(let ((next-gsym (sym-at-dot (car i))))
(cond
((non-term? next-gsym)
(cons (car i)
(append
(apply append
(map (lambda (non-term)
(map (lambda (x)
(make-item x 0))
(get-nt-prods grammar
non-term)))
(first-non-term next-gsym)))
(LR0-closure (cdr i)))))
(else
(cons (car i) (LR0-closure (cdr i))))))))))
;; maps trans-keys to kernels
(automaton (make-hash-table 'equal))
;; keeps the kernels we have seen, so we can have a unique
;; list for each kernel
(kernels (make-hash-table 'equal))
(counter 1)
;; goto: LR1-item list -> LR1-item list list
;; creates new kernels by moving the dot in each item in the
;; LR0-closure of kernel to the right, and grouping them by
;; the term/non-term moved over. Returns the kernels not
;; yet seen, and places the trans-keys into automaton
(goto
(lambda (kernel)
(let (
;; maps each gram-syms to a list of items
(table (make-vector num-gram-syms null))
(epsilons (make-hash-table 'equal))
;; add-item!:
;; (item list) vector * item ->
;; adds i into the table grouped with the grammar
;; symbol following its dot
(add-item!
(lambda (table i)
(let ((gs (sym-at-dot i)))
(cond
(gs
(let* ((add (if (term? gs)
num-non-terms
0))
(already
(vector-ref table
(+ add
(gram-sym-index gs)))))
(if (not (member i already))
(vector-set! table
(+ add (gram-sym-index gs))
(cons i already)))))
((= 0 (vector-length (prod-rhs (item-prod i))))
(let ((current (hash-table-get epsilons
kernel
(lambda () null))))
(hash-table-put! epsilons
kernel
(cons i current)))))))))
;; Group the items of the LR0 closure of the kernel
;; by the character after the dot
(for-each (lambda (item)
(add-item! table item))
(LR0-closure (kernel-items kernel)))
;; each group is a new kernel, with the dot advanced.
;; sorts the items in a kernel so kernels can be compared
;; with equal? for using the table kernels to make sure
;; only one representitive of each kernel is created
(filter
(lambda (x) x)
(map
(lambda (i)
(let* ((gs (car i))
(items (cadr i))
(new #f)
(new-kernel (quicksort
(filter (lambda (x) x)
(map move-dot-right items))
item<?))
(unique-kernel (hash-table-get
kernels
new-kernel
(lambda ()
(let ((k (make-kernel
new-kernel
counter)))
(set! new #t)
(set! counter (add1 counter))
(hash-table-put! kernels
new-kernel
k)
k)))))
(hash-table-put! automaton
(make-trans-key kernel gs)
unique-kernel)
; (printf "~a -> ~a on ~a~n"
; (kernel->string kernel)
; (kernel->string unique-kernel)
; (gram-sym-symbol gs))
(if new
unique-kernel
#f)))
(let loop ((i 0))
(cond
((< i num-non-terms)
(let ((items (vector-ref table i)))
(cond
((null? items) (loop (add1 i)))
(else
(cons (list (vector-ref non-terms i) items)
(loop (add1 i)))))))
((< i num-gram-syms)
(let ((items (vector-ref table i)))
(cond
((null? items) (loop (add1 i)))
(else
(cons (list (vector-ref terms (- i num-non-terms))
items)
(loop (add1 i)))))))
(else null))))))))
(start (list (make-item (get-init-prod grammar) 0)))
(startk (make-kernel start 0))
(new-kernels (make-queue)))
(hash-table-put! kernels start startk)
(let loop ((old-kernels (list startk))
(seen-kernels null))
(cond
((and (empty-queue? new-kernels) (null? old-kernels))
(make-lr0 automaton (list->vector (reverse! seen-kernels)) epsilons))
((null? old-kernels)
(loop (deq! new-kernels) seen-kernels))
(else
(enq! new-kernels (goto (car old-kernels)))
(loop (cdr old-kernels) (cons (car old-kernels) seen-kernels)))))))
(define-struct q (f l) (make-inspector))
(define (empty-queue? q)
(null? (q-f q)))
(define (make-queue)
(make-q null null))
(define (enq! q i)
(if (empty-queue? q)
(let ((i (list i)))
(set-q-l! q i)
(set-q-f! q i))
(begin
(set-cdr! (q-l q) (list i))
(set-q-l! q (cdr (q-l q))))))
(define (deq! q)
(begin0
(car (q-f q))
(set-q-f! q (cdr (q-f q)))))
)