brag/grammar.rkt

#lang racket/base


(require racket/contract
         racket/match
         racket/set
         racket/stream
         racket/struct
         rebellion/collection/vector
         rebellion/private/guarded-block)


(module+ test
  (require (submod "..")
           rackunit))


;@----------------------------------------------------------------------------------------------------


;; Parsing takes a (Grammar T S L) and a sequence of (Token T V) and produces a set of
;; (Parser-Derivation V L) (also called a "parse forest"). A grammar contains an immutable
;; vector of (Context-Free-Production-Rule T S L) and a start symbol of type S.
;;   T: the terminals the grammar parses. Corresponds to the type field of the input tokens.
;;   S: the nonterminals the grammar rules are defined in terms of.
;;   L: the labels that grammar rules may have attached to them. These show up in parse tree
;;      branches, and can be used to determine which production rule produced a derivation.
(struct context-free-grammar (rules start-symbol) #:transparent)


(define (grammar-start-rules grammar)
  (define start (context-free-grammar-start-symbol grammar))
  (for/set ([rule (in-vector (context-free-grammar-rules grammar))]
            #:when (equal? (context-free-production-rule-nonterminal rule) start))
    rule))


;; A (Token T V) is a tagged value. The grammar rules are defined in terms of the type tag,
;; whereas the value is what appears in leaf nodes of the resulting parse trees.
(struct token (type value) #:transparent)


;; A (Context-Free-Production-Rule T S L) contains a nonterminal symbol of type S, a label of type L,
;; and a substitution sequence of (Grammar-Symbol T S) values, stored in an immutable vector.
(struct context-free-production-rule (nonterminal label substitution) #:transparent)


;; A (Grammar-Symbol T S) is either a (Terminal-Symbol T) or a (Nonterminal-Symbol S)
(struct grammar-symbol () #:transparent)
(struct terminal-symbol grammar-symbol (value) #:transparent)
(struct nonterminal-symbol grammar-symbol (value) #:transparent)


(define (make-grammar #:rules rules #:start-symbol start)
  (context-free-grammar (sequence->vector rules) start))


(define (make-rule #:symbol symbol #:substitution substitution #:label label)
  (context-free-production-rule symbol label (sequence->vector substitution)))


;; A (Parser-Derivation V L) is either a (Terminal-Derivation V) or a (Nonterminal-Derivation V L)
(struct parser-derivation () #:transparent)

;; A (Terminal-Derivation V) represents a terminal that was matched by the grammar. It contains the
;; value of the (Token T V) that was matched.
(struct terminal-derivation parser-derivation (value) #:transparent)

;; A (Nonterminal-Derivation V L) represents a nonterminal that was matched by the grammar. It
;; contains the label of type L of the production rule that matched, and an immutable vector of
;; subderivations 
(struct nonterminal-derivation parser-derivation (label children)
  #:transparent
  #:property prop:custom-print-quotable 'never
  #:methods gen:custom-write
  [(define write-proc
     (make-constructor-style-printer
      (λ (_) 'nonterminal-derivation)
      (λ (this)
        (cons (nonterminal-derivation-label this)
              (vector->list (nonterminal-derivation-children this))))))])


(define (make-nonterminal-derivation label [children '()])
  (nonterminal-derivation label (sequence->vector children)))


(define derivation
  (case-lambda
    [(value) (terminal-derivation value)]
    [(label first-child . children) (make-nonterminal-derivation label (cons first-child children))]))


;; Earley parser


;; The hash keys are sppf-labels and the values are a list of sppf-child-pairs
(struct sppf-forest (hash))


(define (make-sppf-forest)
  (sppf-forest (make-hash)))


(define (sppf-forest-add-node! forest label)
  (define h (sppf-forest-hash forest))
  (unless (hash-has-key? h label)
    (hash-set! h label '())))


(define (sppf-forest-add-child-pair! forest label #:left left-child #:right right-child)
  (define pair (sppf-child-pair left-child right-child))
  (hash-update! (sppf-forest-hash forest) label (λ (children) (cons pair children)) '()))


;; SPPF trees walk each rule down the left side, and each right child of the left spine corresponds to
;; the rule's components. See https://twitter.com/doitwithalambda/status/1510217894776348681 for a
;; diagram of the binarised parse tree.
(struct sppf-child-pair (left-child right-child) #:transparent)
(struct sppf-key () #:transparent)
(struct complete-sppf-key sppf-key (symbol input-start input-end) #:transparent)

(struct incomplete-sppf-key sppf-key (rule substitution-position input-start input-end)
  #:transparent)


(define (sppf-key-input-end key)
  (if (complete-sppf-key? key)
      (complete-sppf-key-input-end key)
      (incomplete-sppf-key-input-end key)))


(define (possible-children-lists forest key)
  (define hash (sppf-forest-hash forest))
  (let loop ([key key] [right-children '()])
    (guarded-block
     (guard key else
       (stream right-children))
     (match-define (list (sppf-child-pair left right) ...) (hash-ref hash key '()))
     (apply stream-append
            (for/list ([l (in-list left)]
                       [r (in-list right)])
              (loop l (cons r right-children)))))))


(define (cartesian-stream streams)

  (define (combine s1 s2)
    (for*/stream ([x (in-stream s1)]
                  [y (in-stream s2)])
      (cons x y)))

  (foldr combine (stream '()) streams))


(define (sppf-forest-derivations forest key tokens)
  (define hash (sppf-forest-hash forest))
  (let loop ([key key])
    (guarded-block
     (guard (complete-sppf-key? key) then
       (define tok (vector-ref tokens (complete-sppf-key-input-start key)))
       (stream (terminal-derivation (token-value tok))))
     (define label (context-free-production-rule-label (incomplete-sppf-key-rule key)))
     (define possible-children (possible-children-lists forest key))
     (for*/stream ([children (in-stream possible-children)]
                   [processed-children (in-stream (cartesian-stream (map loop children)))])
       (make-nonterminal-derivation label processed-children)))))


(struct earley-state (rule substitution-position input-position key)
  #:transparent
  #:property prop:custom-print-quotable 'never
  #:methods gen:custom-write
  [(define write-proc
     (make-constructor-style-printer
      (λ (_) 'earley-state)
      (λ (this)
        (define rule (earley-state-rule this))
        (define substitution (context-free-production-rule-substitution rule))
        (define pos (earley-state-substitution-position this))
        (append (list (context-free-production-rule-nonterminal rule) '->)
                (for/list ([sym (in-vector substitution 0 pos)])
                  (if (terminal-symbol? sym)
                      (terminal-symbol-value sym)
                      (nonterminal-symbol-value sym)))
                (list '•)
                (for/list ([sym (in-vector substitution pos)])
                  (if (terminal-symbol? sym)
                      (terminal-symbol-value sym)
                      (nonterminal-symbol-value sym)))
                (list (earley-state-input-position this) (earley-state-key this))))))])


(define (initial-earley-states grammar)
  (for/set ([rule (grammar-start-rules grammar)])
    (earley-state rule 0 0 #false)))


(define (earley-state-represents-successful-parse? state grammar)
  (and (zero? (earley-state-input-position state))
       (equal? (context-free-production-rule-nonterminal (earley-state-rule state))
               (context-free-grammar-start-symbol grammar))))


(define (earley-parse grammar token-sequence)
  (define tokens (sequence->vector token-sequence))
  (define token-count (vector-length tokens))
  (define position-count (add1 token-count))
  (define forest (make-sppf-forest))
  (define states (make-vector position-count (set)))
  (vector-set! states 0 (initial-earley-states grammar))
  (for ([k (in-range 0 position-count)])
    
    ;; Prediction and completion
    (define/guard (process-states unprocessed processed)
      (guard (set-empty? unprocessed) then
        processed)
      (define next (set-first unprocessed))
      
      (define added-states
        (guarded-block
         (guard (completed-state? next) then
           ;; find all states in S(j) of the form (X → α • Y β, j) and add (X → α Y • β, j)
           (define j (earley-state-input-position next))
           (define completed (context-free-production-rule-nonterminal (earley-state-rule next)))
           (define parent-states
             (if (equal? j k)
                 (set-union unprocessed processed)
                 (vector-ref states j)))
           (completer-states completed parent-states (earley-state-key next) #:forest forest))
         (define symbol (earley-state-next-symbol next))
         (guard (nonterminal-symbol? symbol) else
           (set))
         (predictor-states grammar (nonterminal-symbol-value symbol) k)))
      
      (define new-unprocessed (set-subtract (set-remove added-states next) processed))
      (process-states (set-union (set-rest unprocessed) new-unprocessed) (set-add processed next)))

    (define processed (process-states (vector-ref states k) (set)))
    (vector-set! states k processed)
    (unless (equal? k token-count)
      (define next-states (scanner-states processed k (vector-ref tokens k) #:forest forest))
      (vector-set! states (add1 k) next-states)))

  (define last-state-set (vector-ref states (sub1 position-count)))
  (apply stream-append
         (for/list ([s (in-set last-state-set)]
                    #:when (earley-state-represents-successful-parse? s grammar))
           (sppf-forest-derivations forest (earley-state-key s) tokens))))


(define (completed-state? state)
  (match-define (earley-state rule substitution-position _ _) state)
  (equal? substitution-position
          (vector-length (context-free-production-rule-substitution rule))))


(define/contract (earley-state-next-symbol state)
  (-> (and/c earley-state? (not/c completed-state?)) grammar-symbol?)
  (match-define (earley-state rule substitution-position _ _) state)
  (vector-ref (context-free-production-rule-substitution rule) substitution-position))


(define (earley-state-advance-substitution state #:key key)
  (match-define (earley-state rule substitution-position input-position _) state)
  (earley-state rule (add1 substitution-position) input-position key))


(define (completer-states completed-nonterminal states completed-key #:forest forest)
  (define expected (nonterminal-symbol completed-nonterminal))
  (for/set ([s (in-set states)]
            #:when (equal? (earley-state-next-symbol s) expected))
    (define rule (earley-state-rule s))
    (define start (earley-state-input-position s))
    (define end (sppf-key-input-end completed-key))
    (define old-key (earley-state-key s))
    (define new-key
      (incomplete-sppf-key rule (add1 (earley-state-substitution-position s)) start end))
    (sppf-forest-add-child-pair! forest new-key #:left old-key #:right completed-key)
    (earley-state-advance-substitution s #:key new-key)))


(define (predictor-states grammar nonterminal k)
  ;; add (Y → • γ, k) for every production in the grammar with Y on the left-hand side
  (for/set ([rule (in-vector (context-free-grammar-rules grammar))]
            #:when (equal? (context-free-production-rule-nonterminal rule) nonterminal))
    (earley-state rule 0 k #false)))


(define (scanner-states states k next-token #:forest forest)
  (define expected (terminal-symbol (token-type next-token)))
  (for/set ([s (in-set states)]
            #:when (not (completed-state? s))
            #:when (equal? (earley-state-next-symbol s) expected))
    (define rule (earley-state-rule s))
    (define start (earley-state-input-position s))
    (define end (add1 k))
    (define old-key (earley-state-key s))
    (define new-key
      (incomplete-sppf-key rule (add1 (earley-state-substitution-position s)) start end))
    (define scanned-key (complete-sppf-key expected k end))
    (sppf-forest-add-child-pair! forest new-key #:left old-key #:right scanned-key)
    (earley-state-advance-substitution s #:key new-key)))


(module+ test
  (test-case "earley-parse integration test"

    ;; Grammar, input, and states taken from https://en.wikipedia.org/wiki/Earley_parser#Example
    (define P-rule (make-rule #:symbol 'P #:label 'P #:substitution (list (nonterminal-symbol 'S))))
    (define S-rule0
      (make-rule
       #:symbol 'S
       #:label 'S0
       #:substitution (list (nonterminal-symbol 'S) (terminal-symbol '+) (nonterminal-symbol 'M))))
    (define S-rule1 (make-rule #:symbol 'S #:label 'S1 #:substitution (list (nonterminal-symbol 'M))))
    (define M-rule0
      (make-rule
       #:symbol 'M
       #:label 'M0
       #:substitution (list (nonterminal-symbol 'M) (terminal-symbol '*) (nonterminal-symbol 'T))))
    (define M-rule1 (make-rule #:symbol 'M #:label 'M1 #:substitution (list (nonterminal-symbol 'T))))
    (define T-rule (make-rule #:symbol 'T #:label 'T #:substitution (list (terminal-symbol 'number))))
    (define arithmetic-grammar
      (make-grammar #:rules (list P-rule S-rule0 S-rule1 M-rule0 M-rule1 T-rule) #:start-symbol 'P))
    (define input-tokens
      (list (token 'number 2) (token '+ 'plus) (token 'number 3) (token '* 'times) (token 'number 4)))

    (define arithmetic-parse-forest
      (earley-parse arithmetic-grammar input-tokens))

    (define expected-arithmetic-parse-tree
      (derivation
       'P
       (derivation 'S0
                   (derivation 'S1 (derivation 'M1 (derivation 'T (derivation 2))))
                   (derivation 'plus)
                   (derivation 'M0
                               (derivation 'M1 (derivation 'T (derivation 3)))
                               (derivation 'times)
                               (derivation 'T (derivation 4))))))
    
    (check-equal? (stream->list arithmetic-parse-forest) (list expected-arithmetic-parse-tree))))