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