You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
267 lines
7.8 KiB
Scheme
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)))))
|
|
|
|
) |