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

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(module lr0 mzscheme
;; Handle the LR0 automaton
(require "grammar.rkt"
"graph.rkt"
mzlib/list
mzlib/class)
(provide build-lr0-automaton lr0%
(struct trans-key (st gs)) trans-key-list-remove-dups
kernel-items kernel-index)
;; 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
;; Each kernel is assigned a unique index, 0 <= index < number of states
;; trans-key = (make-trans-key kernel gram-sym)
(define-struct kernel (items index) (make-inspector))
(define-struct trans-key (st gs) (make-inspector))
(define (trans-key<? a b)
(let ((kia (kernel-index (trans-key-st a)))
(kib (kernel-index (trans-key-st b))))
(or (< kia kib)
(and (= kia kib)
(< (non-term-index (trans-key-gs a))
(non-term-index (trans-key-gs b)))))))
(define (trans-key-list-remove-dups tkl)
(let loop ((sorted (sort tkl trans-key<?)))
(cond
((null? sorted) null)
((null? (cdr sorted)) sorted)
(else
(if (and (= (non-term-index (trans-key-gs (car sorted)))
(non-term-index (trans-key-gs (cadr sorted))))
(= (kernel-index (trans-key-st (car sorted)))
(kernel-index (trans-key-st (cadr sorted)))))
(loop (cdr sorted))
(cons (car sorted) (loop (cdr sorted))))))))
;; build-transition-table : int (listof (cons/c trans-key X) ->
;; (vectorof (symbol X hashtable))
(define (build-transition-table num-states assoc)
(let ((transitions (make-vector num-states #f)))
(let loop ((i (sub1 (vector-length transitions))))
(when (>= i 0)
(vector-set! transitions i (make-hash-table))
(loop (sub1 i))))
(for-each
(lambda (trans-key/kernel)
(let ((tk (car trans-key/kernel)))
(hash-table-put! (vector-ref transitions (kernel-index (trans-key-st tk)))
(gram-sym-symbol (trans-key-gs tk))
(cdr trans-key/kernel))))
assoc)
transitions))
;; reverse-assoc : (listof (cons/c trans-key? kernel?)) ->
;; (listof (cons/c trans-key? (listof kernel?)))
(define (reverse-assoc assoc)
(let ((reverse-hash (make-hash-table 'equal))
(hash-table-add!
(lambda (ht k v)
(hash-table-put! ht k (cons v (hash-table-get ht k (lambda () null)))))))
(for-each
(lambda (trans-key/kernel)
(let ((tk (car trans-key/kernel)))
(hash-table-add! reverse-hash
(make-trans-key (cdr trans-key/kernel)
(trans-key-gs tk))
(trans-key-st tk))))
assoc)
(hash-table-map reverse-hash cons)))
;; kernel-list-remove-duplicates
;; LR0-automaton = object of class lr0%
(define lr0%
(class object%
(super-instantiate ())
;; term-assoc : (listof (cons/c trans-key? kernel?))
;; non-term-assoc : (listof (cons/c trans-key? kernel?))
;; states : (vectorof kernel?)
;; epsilons : ???
(init-field term-assoc non-term-assoc states epsilons)
(define transitions (build-transition-table (vector-length states)
(append term-assoc non-term-assoc)))
(define reverse-term-assoc (reverse-assoc term-assoc))
(define reverse-non-term-assoc (reverse-assoc non-term-assoc))
(define reverse-transitions
(build-transition-table (vector-length states)
(append reverse-term-assoc reverse-non-term-assoc)))
(define mapped-non-terms (map car non-term-assoc))
(define/public (get-mapped-non-term-keys)
mapped-non-terms)
(define/public (get-num-states)
(vector-length states))
(define/public (get-epsilon-trans)
epsilons)
(define/public (get-transitions)
(append term-assoc non-term-assoc))
;; for-each-state : (state ->) ->
;; Iteration over the states in an automaton
(define/public (for-each-state f)
(let ((num-states (vector-length states)))
(let loop ((i 0))
(if (< i num-states)
(begin
(f (vector-ref states i))
(loop (add1 i)))))))
;; run-automaton: kernel? gram-sym? -> (union kernel #f)
;; returns the state reached from state k on input s, or #f when k
;; has no transition on s
(define/public (run-automaton k s)
(hash-table-get (vector-ref transitions (kernel-index k))
(gram-sym-symbol s)
(lambda () #f)))
;; run-automaton-back : (listof kernel?) gram-sym? -> (listof kernel)
;; returns the list of states that can reach k by transitioning on s.
(define/public (run-automaton-back k s)
(apply append
(map
(lambda (k)
(hash-table-get (vector-ref reverse-transitions (kernel-index k))
(gram-sym-symbol s)
(lambda () null)))
k)))))
(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))
;; 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))
"}")))
;; 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 (
(epsilons (make-hash-table 'equal))
(grammar-symbols (append (send grammar get-non-terms)
(send grammar get-terms)))
;; 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 reduced to a string
;; of terms.
(first-non-term
(digraph (send grammar get-non-terms)
(lambda (nt)
(filter non-term?
(map (lambda (prod)
(sym-at-dot (make-item prod 0)))
(send grammar get-prods-for-non-term nt))))
(lambda (nt) (list nt))
(union non-term<?)
(lambda () 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))
(send grammar
get-prods-for-non-term
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-term null)
(automaton-non-term null)
;; keeps the kernels we have seen, so we can have a unique
;; list for each kernel
(kernels (make-hash-table 'equal))
(counter 0)
;; 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 a gram-syms to a list of items
(table (make-hash-table))
;; add-item!:
;; (symbol (listof item) hashtable) 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 ((already
(hash-table-get table
(gram-sym-symbol gs)
(lambda () null))))
(unless (member i already)
(hash-table-put! table
(gram-sym-symbol 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 (sort
(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)))))
(cond
((term? gs)
(set! automaton-term (cons (cons (make-trans-key kernel gs)
unique-kernel)
automaton-term)))
(else
(set! automaton-non-term (cons (cons (make-trans-key kernel gs)
unique-kernel)
automaton-non-term))))
#;(printf "~a -> ~a on ~a\n"
(kernel->string kernel)
(kernel->string unique-kernel)
(gram-sym-symbol gs))
(if new
unique-kernel
#f)))
(let loop ((gsyms grammar-symbols))
(cond
((null? gsyms) null)
(else
(let ((items (hash-table-get table
(gram-sym-symbol (car gsyms))
(lambda () null))))
(cond
((null? items) (loop (cdr gsyms)))
(else
(cons (list (car gsyms) items)
(loop (cdr gsyms))))))))))))))
(starts
(map (lambda (init-prod) (list (make-item init-prod 0)))
(send grammar get-init-prods)))
(startk
(map (lambda (start)
(let ((k (make-kernel start counter)))
(hash-table-put! kernels start k)
(set! counter (add1 counter))
k))
starts))
(new-kernels (make-queue)))
(let loop ((old-kernels startk)
(seen-kernels null))
(cond
((and (empty-queue? new-kernels) (null? old-kernels))
(make-object lr0%
automaton-term
automaton-non-term
(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 (mcons i null)))
(set-q-l! q i)
(set-q-f! q i))
(begin
(set-mcdr! (q-l q) (mcons i null))
(set-q-l! q (mcdr (q-l q))))))
(define (deq! q)
(begin0
(mcar (q-f q))
(set-q-f! q (mcdr (q-f q)))))
)