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