#lang racket/base
;; Constructs to create and access grammars, the internal
;; representation of the input to the parser generator.
  
(require yaragg/parser-tools/private-yacc/yacc-helper
         racket/contract)

(provide
 ;; Things that work on items
 start-item? item-prod item->string 
 sym-at-dot move-dot-right item<? item-dot-pos
   
 ;; Things that operate on grammar symbols
 gram-sym-symbol gram-sym-index term-prec gram-sym->string
 non-term? term? non-term<? term<?
 term-list->bit-vector term-index non-term-index
   
 ;; Things that work on precs
 prec-num prec-assoc

 grammar?
 make-grammar
 grammar-num-terms
 grammar-num-non-terms
 grammar-prods-for-non-term
 grammar-all-prods
 grammar-init-prods
 grammar-terms
 grammar-non-terms
 grammar-num-prods
 grammar-end-terms
 grammar-nullable-non-term?
   
 ;; Things that work on productions
 prod-index prod-prec prod-rhs prod-lhs prod-action

 (contract-out
  [item (prod? (or/c #f natural-number/c) . -> . item?)]
  [term (symbol? (or/c #f natural-number/c) (or/c prec? #f) . -> . term?)]
  [non-term (symbol? (or/c #f natural-number/c) . -> . non-term?)]
  [prec (natural-number/c (or/c 'left 'right 'nonassoc) . -> . prec?)]
  [prod (non-term? (vectorof (or/c non-term? term?))
                   (or/c #f natural-number/c) (or/c #f prec?) syntax? . -> . prod?)]))
  
;; Each production has a unique index 0 <= index <= number of productions
(struct prod (lhs rhs index prec action) #:mutable)

;; The dot-pos field is the index of the element in the rhs
;; of prod that the dot immediately precedes.
;; Thus 0 <= dot-pos <= (vector-length rhs).
(struct item (prod dot-pos) #:transparent)
  
;; gram-sym = (union term? non-term?)
;; Each term has a unique index 0 <= index < number of terms
;; Each non-term has a unique index 0 <= index < number of non-terms  
(struct term (sym index prec) #:mutable)
(struct non-term (sym index) #:mutable)

;; a precedence declaration.
(struct prec (num assoc) #:transparent)
  
;;---------------------- LR items --------------------------
  
;; item<?: LR-item * LR-item -> bool
;; Lexicographic comparison on two items.
(define (item<? i1 i2)
  (define p1 (prod-index (item-prod i1)))
  (define p2 (prod-index (item-prod i2)))
  (or (< p1 p2)
      (and (= p1 p2)
           (< (item-dot-pos i1) (item-dot-pos i2)))))

;; start-item?: LR-item -> bool
;; The start production always has index 0
(define (start-item? i)
  (zero? (non-term-index (prod-lhs (item-prod i)))))

  
;; move-dot-right: LR-item -> LR-item | #f
;; moves the dot to the right in the item, unless it is at its 
;; rightmost, then it returns false
(define (move-dot-right i)
  (cond
    [(= (item-dot-pos i) (vector-length (prod-rhs (item-prod i)))) #f]
    [else (item (item-prod i)
                (add1 (item-dot-pos i)))]))

;; sym-at-dot: LR-item -> gram-sym | #f
;; returns the symbol after the dot in the item or #f if there is none  
(define (sym-at-dot i)
  (define dp (item-dot-pos i))
  (define rhs (prod-rhs (item-prod i)))
  (cond
    [(= dp (vector-length rhs)) #f]
    [else (vector-ref rhs dp)]))
  
 
;; print-item: LR-item ->
(define (item->string it)
  (define (print-sym i)
    (define gs (vector-ref (prod-rhs (item-prod it)) i))
    (cond
      ((term? gs) (format "~a " (term-sym gs)))
      (else (format "~a " (non-term-sym gs)))))
  (string-append
   (format "~a -> " (non-term-sym (prod-lhs (item-prod it))))
   (let loop ((i 0))
     (cond
       [(= i (vector-length (prod-rhs (item-prod it)))) 
        (if (= i (item-dot-pos it))
            ". "
            "")]
       [(= i (item-dot-pos it)) 
        (string-append ". " (print-sym i) (loop (add1 i)))]
       [else (string-append (print-sym i) (loop (add1 i)))]))))

;; --------------------- Grammar Symbols --------------------------

(define (non-term<? nt1 nt2)
  (< (non-term-index nt1) (non-term-index nt2)))
  
(define (term<? nt1 nt2)
  (< (term-index nt1) (term-index nt2)))

(define (gram-sym-index gs)
  (if (term? gs)
      (term-index gs)
      (non-term-index gs)))

(define (gram-sym-symbol gs)
  (if (term? gs)
      (term-sym gs)
      (non-term-sym gs)))

(define (gram-sym->string gs)
  (symbol->string (gram-sym-symbol gs)))

;; term-list->bit-vector: term list -> int
;; Creates a number where the nth bit is 1 if the term with index n is in 
;; the list, and whose nth bit is 0 otherwise
(define (term-list->bit-vector terms)
  (if (null? terms)
      0
      (bitwise-ior (arithmetic-shift 1 (term-index (car terms)))
                   (term-list->bit-vector (cdr terms)))))
  

;; ------------------------- Grammar ------------------------------


;; prods: production list list
;; where there is one production list per non-term
;; init-prods: production list
;; The productions parsing can start from
;; nullable-non-terms is indexed by the non-term-index and is true iff non-term is nullable
(struct grammar (prods
                 init-prods
                 terms
                 non-terms
                 end-terms
                 all-prods
                 num-prods
                 num-terms
                 num-non-terms
                 nt->prods
                 nullable-non-terms))


(define (make-grammar #:prods prods
                      #:init-prods init-prods
                      #:terms terms
                      #:non-terms non-terms
                      #:end-terms end-terms)

  (define all-prods (apply append prods))
  (define num-prods (length all-prods))
  (define num-terms (length terms))
  (define num-non-terms (length non-terms))
  
  (for ([(nt count) (in-indexed non-terms)])
    (set-non-term-index! nt count))

  (for ([(t count) (in-indexed terms)])
    (set-term-index! t count))

  (for ([(prod count) (in-indexed all-prods)])
    (set-prod-index! prod count))

  ;; indexed by the index of the non-term - contains the list of productions for that non-term
  (define nt->prods (make-vector (length prods) #f))
  (for ([prods (in-list prods)])
    (vector-set! nt->prods (non-term-index (prod-lhs (car prods))) prods))
      
  (define nullable-non-terms
    (nullable all-prods num-non-terms))
  
  (grammar prods
           init-prods
           terms
           non-terms
           end-terms
           all-prods
           num-prods
           num-terms
           num-non-terms
           nt->prods
           nullable-non-terms))


(define (grammar-prods-for-non-term g nt)
  (vector-ref (grammar-nt->prods g) (non-term-index nt)))


(define (grammar-nullable-non-term? g nt)
  (vector-ref (grammar-nullable-non-terms g) (non-term-index nt)))

  
;; nullable: production list * int -> non-term set
;; determines which non-terminals can derive epsilon
(define (nullable prods num-nts)
  (define nullable (make-vector num-nts #f))
  (define added #f)
	     
  ;; possible-nullable: producion list -> production list
  ;; Removes all productions that have a terminal
  (define (possible-nullable prods)
    (for/list ([prod (in-list prods)]
               #:when (vector-andmap non-term? (prod-rhs prod)))
      prod))
	     
  ;; set-nullables: production list -> production list
  ;; makes one pass through the productions, adding the ones
  ;; known to be nullable now to nullable and returning a list
  ;; of productions that we don't know about yet. 
  (define (set-nullables prods)
    (cond
      [(null? prods) '()]
      [(vector-ref nullable (gram-sym-index (prod-lhs (car prods))))
       (set-nullables (cdr prods))]
      [(vector-andmap (λ (nt) (vector-ref nullable (gram-sym-index nt))) (prod-rhs (car prods)))
       (vector-set! nullable (gram-sym-index (prod-lhs (car prods))) #t)
       (set! added #t)
       (set-nullables (cdr prods))]
      [else (cons (car prods) (set-nullables (cdr prods)))]))
  (let loop ((P (possible-nullable prods)))
    (cond
      [(null? P) nullable]
      [else
       (set! added #f)
       (define new-P (set-nullables P))
       (if added
           (loop new-P)
           nullable)])))