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#lang racket/base
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(require "grammar.rkt"
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"graph.rkt"
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racket/list
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racket/class)
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;; Handle the LR0 automaton
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(provide build-lr0-automaton lr0%
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(struct-out trans-key) 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) #:inspector (make-inspector))
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(define-struct trans-key (st gs) #:inspector (make-inspector))
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(define (trans-key<? a b)
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(define kia (kernel-index (trans-key-st a)))
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(define 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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(define 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-hasheq))
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(loop (sub1 i))))
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(for ([trans-key/kernel (in-list assoc)])
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(define tk (car trans-key/kernel))
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(hash-set! (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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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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(define reverse-hash (make-hash))
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(define (hash-table-add! ht k v)
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(hash-set! ht k (cons v (hash-ref ht k (λ () null)))))
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(for ([trans-key/kernel (in-list assoc)])
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(define 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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(hash-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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(define num-states (vector-length states))
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(let loop ([i 0])
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(when (< i num-states)
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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-ref (vector-ref transitions (kernel-index k))
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(gram-sym-symbol s)
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(λ () #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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(for*/list ([k (in-list k)]
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[val (in-list (hash-ref (vector-ref reverse-transitions (kernel-index k))
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(gram-sym-symbol s)
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(λ () null)))])
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val))))
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(define ((union comp<?) l1 l2)
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(let loop ([l1 l1] [l2 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 (define c1 (car l1))
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(define c2 (car l2))
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(cond
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[(comp<? c1 c2) (cons c1 (loop (cdr l1) l2))]
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[(comp<? c2 c1) (cons c2 (loop l1 (cdr l2)))]
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[else (loop (cdr l1) l2)])])))
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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 (λ (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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(define epsilons (make-hash))
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(define 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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(define first-non-term
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(digraph (send grammar get-non-terms)
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(λ (nt)
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(filter non-term?
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(map (λ (prod) (sym-at-dot (make-item prod 0)))
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(send grammar get-prods-for-non-term nt))))
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(λ (nt) (list nt))
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(union non-term<?)
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(λ () 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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(define (LR0-closure i)
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(cond
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[(null? i) null]
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[else
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(define 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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(for*/list ([non-term (in-list (first-non-term next-gsym))]
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[x (in-list (send grammar
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get-prods-for-non-term
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non-term))])
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(make-item x 0))
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(LR0-closure (cdr i))))]
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[else (cons (car i) (LR0-closure (cdr i)))])]))
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;; maps trans-keys to kernels
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(define automaton-term null)
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(define 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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(define kernels (make-hash))
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(define 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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(define (goto kernel)
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;; maps a gram-syms to a list of items
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(define table (make-hasheq))
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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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(define (add-item! table i)
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(define gs (sym-at-dot i))
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(cond
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[gs (define already (hash-ref table (gram-sym-symbol gs) (λ () null)))
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(unless (member i already)
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(hash-set! table (gram-sym-symbol gs) (cons i already)))]
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((zero? (vector-length (prod-rhs (item-prod i))))
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(define current (hash-ref epsilons kernel (λ () null)))
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(hash-set! epsilons kernel (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 ([item (in-list (LR0-closure (kernel-items kernel)))])
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(add-item! table item))
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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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(define is
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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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(define items (hash-ref table (gram-sym-symbol (car gsyms)) (λ () null)))
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(cond
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[(null? items) (loop (cdr gsyms))]
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[else (cons (list (car gsyms) items)
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(loop (cdr gsyms)))])])))
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(filter
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values
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(for/list ([i (in-list is)])
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(define gs (car i))
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(define items (cadr i))
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(define new #f)
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(define new-kernel (sort (filter values (map move-dot-right items)) item<?))
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(define unique-kernel (hash-ref kernels new-kernel
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(λ ()
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(define k (make-kernel new-kernel counter))
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(set! new #t)
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(set! counter (add1 counter))
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(hash-set! kernels new-kernel k)
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k)))
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(if (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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(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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(and new unique-kernel))))
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(define starts (map (λ (init-prod) (list (make-item init-prod 0)))
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(send grammar get-init-prods)))
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(define startk (for/list ([start (in-list starts)])
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(define k (make-kernel start counter))
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(hash-set! kernels start k)
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(set! counter (add1 counter))
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k))
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(define 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% automaton-term automaton-non-term
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(list->vector (reverse seen-kernels)) epsilons)]
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[(null? old-kernels) (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) #:inspector (make-inspector) #:mutable)
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(define (empty-queue? q) (null? (q-f q)))
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(define (make-queue) (make-q null null))
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(define (enq! q i)
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(cond
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[(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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[else
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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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