#cs
(module lalr mzscheme
  
  ;; Compute LALR lookaheads from DeRemer and Pennello 1982
  
  (require "lr0.ss"
	   "grammar.ss"
	   "array2d.ss"
	   (lib "list.ss")
	   (lib "class.ss"))

  (provide compute-LA)
  
  ;; compute-DR: LR0-automaton * grammar -> (trans-key -> term set)
  ;; computes for each state, non-term transition pair, the terminals
  ;; which can transition out of the resulting state
  ;; output term set is represented in bit-vector form
  (define (compute-DR a g)
    (lambda (tk)
      (let ((r (send a run-automaton (trans-key-st tk) (trans-key-gs tk))))
        (term-list->bit-vector
         (filter
          (lambda (term)
            (send a run-automaton r term))
          (send g get-terms))))))
  
  ;; compute-reads: 
  ;;   LR0-automaton * grammar -> (trans-key -> trans-key list)
  (define (compute-reads a g)
    (let ((nullable-non-terms 
           (filter (lambda (nt) (send g nullable-non-term? nt))
                   (send g get-non-terms))))
      (lambda (tk)
        (let ((r (send a run-automaton (trans-key-st tk) (trans-key-gs tk))))
          (map (lambda (x) (make-trans-key r x))
               (filter (lambda (non-term) (send a run-automaton r non-term))
                       nullable-non-terms))))))

  ;; compute-read: LR0-automaton * grammar -> (trans-key -> term set)
  ;; output term set is represented in bit-vector form
  (define (compute-read a g)
    (let* ((dr (compute-DR a g))
	   (reads (compute-reads a g)))
      (time
       (digraph-tk->terml (send a get-mapped-non-term-keys)
                          reads
                          dr
                          (send a get-num-states)
                          (send g get-num-terms)
                          (send g get-num-non-terms))))
  )
;  ;; run-lr0-backward: lr0-automaton * gram-sym list * kernel * int -> kernel list
;  ;; returns the list of all k such that state k transitions to state start on the
;  ;; transitions in rhs (in order)
;  (define (run-lr0-backward a rhs start num-states)
;    (let loop ((states (list start))
;               (rhs (reverse rhs)))
;      (cond
;        ((null? rhs) states)
;        (else (loop (send a run-automaton-back states (car rhs))
;		    (cdr rhs))))))
  
  ;; gram-sym list * kernel * int -> kernel list
  ;; returns the list of all k such that state k transitions to state start on the
  ;; transitions in rhs (in order)
  (define (run-lr0-backward a rhs dot-pos start num-states)
    (let loop ((states (list start))
               (i (sub1 dot-pos)))
      (cond
        ((< i 0) states)
        (else (loop (send a run-automaton-back states (vector-ref rhs i))
                    (sub1 i))))))

  ;; prod->items-for-include: grammar * prod * non-term -> lr0-item list
  ;; returns the list of all (B -> beta . nt gamma) such that prod = (B -> beta nt gamma)
  ;; and gamma =>* epsilon
  (define (prod->items-for-include g prod nt)
    (let* ((rhs (prod-rhs prod))
           (rhs-l (vector-length rhs)))
      (append (if (and (> rhs-l 0) (eq? nt (vector-ref rhs (sub1 rhs-l))))
                  (list (make-item prod (sub1 rhs-l)))
                  null)
              (let loop ((i (sub1 rhs-l)))
                (cond
                  ((and (> i 0) 
                        (non-term? (vector-ref rhs i)) 
                        (send g nullable-non-term? (vector-ref rhs i)))
                   (if (eq? nt (vector-ref rhs (sub1 i)))
                       (cons (make-item prod (sub1 i))
                             (loop (sub1 i)))
                       (loop (sub1 i))))
                  (else null))))))

  ;; prod-list->items-for-include: grammar * prod list * non-term -> lr0-item list
  ;; return the list of all (B -> beta . nt gamma) such that  (B -> beta nt gamma) in prod-list
  ;; and gamma =>* epsilon
  (define (prod-list->items-for-include g prod-list nt)
    (apply append (map (lambda (prod) (prod->items-for-include g prod nt)) prod-list)))

  ;; comput-includes: lr0-automaton * grammar -> (trans-key -> trans-key list)
  (define (compute-includes a g)
    (let ((num-states (send a get-num-states))
          (items-for-input-nt (make-vector (send g get-num-non-terms) null)))
      (for-each
       (lambda (input-nt)
         (vector-set! items-for-input-nt (non-term-index input-nt)
                      (prod-list->items-for-include g (send g get-prods) input-nt)))
       (send g get-non-terms))
      (lambda (tk)
        (let* ((goal-state (trans-key-st tk))
               (non-term (trans-key-gs tk))
               (items (vector-ref items-for-input-nt (non-term-index non-term))))
          (trans-key-list-remove-dups
           (apply append
                  (map (lambda (item)
                         (let* ((prod (item-prod item))
                                (rhs (prod-rhs prod))
                                (lhs (prod-lhs prod)))
                           (map (lambda (state)
                                  (make-trans-key state lhs))
                                (run-lr0-backward a 
                                                  rhs
                                                  (item-dot-pos item)
                                                  goal-state 
                                                  num-states))))
                       items)))))))
           
;   ;; compute-includes: lr0-automaton * grammar -> (trans-key -> trans-key list)
;   (define (compute-includes a g)
;     (let* ((non-terms (send g get-non-terms))
; 	   (num-states (vector-length (send a get-states)))
; 	   (num-non-terms (length non-terms))
; 	   (includes (make-array2d num-states num-non-terms null)))
;       (send a for-each-state
; 	    (lambda (state)
; 	      (for-each
; 	       (lambda (non-term)
; 		 (for-each
; 		  (lambda (prod)
; 		    (let loop ((i (make-item prod 0))
; 			       (p state))
; 		      (if (and p i)
; 			  (let* ((next-sym (sym-at-dot i))
; 				 (new-i (move-dot-right i)))
; 			    (if (and (non-term? next-sym)
; 				     (send g nullable-after-dot? new-i))
; 				(array2d-add! includes
; 					      (kernel-index p)
; 					      (gram-sym-index next-sym)
; 					      (make-trans-key state non-term)))
; 			    (if next-sym
; 				(loop new-i
; 				      (send a run-automaton p next-sym)))))))
; 		  (send g get-prods-for-non-term non-term)))
; 	       non-terms)))
;      
;       (lambda (tk)
; 	(array2d-ref includes 
; 		     (kernel-index (trans-key-st tk))
; 		     (gram-sym-index (trans-key-gs tk))))))
  
  ;; compute-lookback: lr0-automaton * grammar -> (kernel * proc -> trans-key list)
  (define (compute-lookback a g)
    (let ((num-states (send a get-num-states)))
      (lambda (state prod)
        (map (lambda (k) (make-trans-key k (prod-lhs prod)))
             (run-lr0-backward a (prod-rhs prod) (vector-length (prod-rhs prod)) state num-states)))))
  
  ;; compute-follow:  LR0-automaton * grammar -> (trans-key -> term set)
  ;; output term set is represented in bit-vector form
  (define (compute-follow a g includes)
    (let ((read (compute-read a g)))
      (digraph-tk->terml (send a get-mapped-non-term-keys)
                         includes
                         read
                         (send a get-num-states)
                         (send g get-num-terms)
                         (send g get-num-non-terms))))
  
  ;; compute-LA: LR0-automaton * grammar -> (kernel * prod -> term set)
  ;; output term set is represented in bit-vector form
  (define (compute-LA a g)
    (let* ((includes (compute-includes a g))
	   (lookback (compute-lookback a g))
	   (follow  (compute-follow a g includes)))
      (lambda (k p)
	(let* ((l (lookback k p))
	       (f (map follow l)))
	  (apply bitwise-ior (cons 0 f))))))


  (define (print-DR dr a g)
    (print-input-st-sym dr "DR" a g print-output-terms))
  (define (print-Read Read a g)
    (print-input-st-sym Read "Read" a g print-output-terms))
  (define (print-includes i a g)
    (print-input-st-sym i "includes" a g print-output-st-nt))
  (define (print-lookback l a g)
    (print-input-st-prod l "lookback" a g print-output-st-nt))
  (define (print-follow f a g)
    (print-input-st-sym f "follow" a g print-output-terms))
  (define (print-LA l a g)
    (print-input-st-prod l "LA" a g print-output-terms))

  (define (print-input-st-sym f name a g print-output)
    (printf "~a:~n" name)
    (send a for-each-state
     (lambda (state)
       (for-each
        (lambda (non-term)
          (let ((res (f (make-trans-key state non-term))))
            (if (not (null? res))
                (printf "~a(~a, ~a) = ~a~n"
                        name
                        state
                        (gram-sym-symbol non-term)
                        (print-output res)))))
        (send g get-non-terms))))
    (newline))

  (define (print-input-st-prod f name a g print-output)
    (printf "~a:~n" name)
    (send a for-each-state
     (lambda (state)
       (for-each
        (lambda (non-term)
          (for-each
           (lambda (prod)
             (let ((res (f state prod)))
               (if (not (null? res))
                   (printf "~a(~a, ~a) = ~a~n"
                           name
                           (kernel-index state)
                           (prod-index prod)
                           (print-output res)))))
           (send g get-prods-for-non-term non-term)))
        (send g get-non-terms)))))
  
  (define (print-output-terms r)
    (map 
     (lambda (p)
       (gram-sym-symbol p))
     r))
  
  (define (print-output-st-nt r)
    (map
     (lambda (p)
       (list
	(kernel-index (trans-key-st p))
	(gram-sym-symbol (trans-key-gs p))))
     r))

  ;; digraph-tk->terml: 
  ;;   (trans-key list) * (trans-key -> trans-key list) * (trans-key -> term list) * int * int * int
  ;;     -> (trans-key -> term list)
  ;; DeRemer and Pennello 1982
  ;; Computes (f x) = (f- x) union Union{(f y) | y in (edges x)}
  ;; A specialization of digraph in the file graph.ss
  (define (digraph-tk->terml nodes edges f- num-states num-terms num-non-terms)
    (letrec (
	     ;; Will map elements of trans-key to term sets represented as bit vectors
	     (results-terms (make-array2d num-states num-terms 0))
	     (results-non-terms (make-array2d num-states num-non-terms 0))

	     ;; Maps elements of trans-keys to integers.
	     (N-terms (make-array2d num-states num-terms 0))
	     (N-non-terms (make-array2d num-states num-non-terms 0))

	     (lookup-tk-map
	      (lambda (map-term map-non-term)
		(lambda (tk) 
		  (let ((st (trans-key-st tk))
			(gs (trans-key-gs tk)))
		    (if (term? gs)
			(array2d-ref map-term (kernel-index st) (term-index gs))
			(array2d-ref map-non-term (kernel-index st) (non-term-index gs)))))))
	     (add-tk-map
	      (lambda (map-term map-non-term)
		(lambda (tk v)
		  (let ((st (trans-key-st tk))
			(gs (trans-key-gs tk)))
		    (if (term? gs)
			(array2d-set! map-term (kernel-index st) (term-index gs) v)
			(array2d-set! map-non-term (kernel-index st) (non-term-index gs) v))))))
		      
	     (get-N (lookup-tk-map N-terms N-non-terms))
	     (set-N (add-tk-map N-terms N-non-terms))
	     (get-f (lookup-tk-map results-terms results-non-terms))
	     (set-f (add-tk-map results-terms results-non-terms))
	     
	     (stack null)
	     (push (lambda (x)
		     (set! stack (cons x stack))))
	     (pop (lambda () 
                    (begin0 
		     (car stack)
		     (set! stack (cdr stack)))))
       	     (depth (lambda () (length stack)))

	     ;; traverse: 'a -> 
	     (traverse
	      (lambda (x)
		(push x)
		(let ((d (depth)))
		  (set-N x d)
		  (set-f x (f- x))
		  (for-each (lambda (y)
			      (if (= 0 (get-N y))
				  (traverse y))
			      (set-f x (bitwise-ior (get-f x) (get-f y)))
			      (set-N x (min (get-N x) (get-N y))))
			    (edges x))
		  (if (= d (get-N x))
		      (let loop ((p (pop)))
			(set-N p +inf.0)
			(set-f p (get-f x))
			(if (not (equal? x p))
			    (loop (pop)))))))))
      (for-each (lambda (x)
		  (if (= 0 (get-N x))
		      (traverse x)))
		nodes)
      get-f))
)