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(* ML-Yacc Parser Generator (c) 1989 Andrew W. Appel, David R. Tarditi * * $Log$ * Revision 1.1.1.2 1998/01/18 01:00:09 monnier * *** empty log message *** * * Revision 1.1.1.1 1997/01/14 01:38:05 george * Version 109.24 * * Revision 1.1.1.1 1996/01/31 16:01:46 george * Version 109 * *) functor mkLook (structure IntGrammar : INTGRAMMAR) : LOOK = struct open Array List infix 9 sub structure Grammar = IntGrammar.Grammar structure IntGrammar = IntGrammar open Grammar IntGrammar structure TermSet = ListOrdSet (struct type elem = term val eq = eqTerm val gt = gtTerm end) val union = TermSet.union val make_set = TermSet.make_set val prLook = fn (termToString,print) => let val printTerm = print o termToString fun f nil = print " " | f (a :: b) = (printTerm a; print " "; f b) in f end structure NontermSet = ListOrdSet (struct type elem = nonterm val eq = eqNonterm val gt = gtNonterm end) val mkFuncs = fn {rules : rule list, nonterms : int, produces : nonterm -> rule list} => let (* nullable: create a function which tells if a nonterminal is nullable or not. Method: Keep an array of booleans. The nth entry is true if NT i is nullable. If is false if we don't know whether NT i is nullable. Keep a list of rules whose remaining rhs we must prove to be null. First, scan the list of rules and remove those rules whose rhs contains a terminal. These rules are not nullable. Now iterate through the rules that were left: (1) if there is no remaining rhs we have proved that the rule is nullable, mark the nonterminal for the rule as nullable (2) if the first element of the remaining rhs is nullable, place the rule back on the list with the rest of the rhs (3) if we don't know whether the nonterminal is nullable, place it back on the list (4) repeat until the list does not change. We have found all the possible nullable rules. *) val nullable = let fun ok_rhs nil = true | ok_rhs ((TERM _)::_) = false | ok_rhs ((NONTERM i)::r) = ok_rhs r fun add_rule (RULE {lhs,rhs,...},r) = if ok_rhs rhs then (lhs,map (fn (NONTERM (NT i)) => i) rhs)::r else r val items = List.foldr add_rule [] rules val nullable = array(nonterms,false) val f = fn ((NT i,nil),(l,_)) => (update(nullable,i,true); (l,true)) | (a as (lhs,(h::t)),(l,change)) => case (nullable sub h) of false => (a::l,change) | true => ((lhs,t)::l,true) fun prove(l,true) = prove(List.foldr f (nil,false) l) | prove(_,false) = () in (prove(items,true); fn (NT i) => nullable sub i) end (* scanRhs : look at a list of symbols, scanning past nullable nonterminals, applying addSymbol to the symbols scanned *) fun scanRhs addSymbol = let fun f (nil,result) = result | f ((sym as NONTERM nt) :: rest,result) = if nullable nt then f (rest,addSymbol(sym,result)) else addSymbol(sym,result) | f ((sym as TERM _) :: _,result) = addSymbol(sym,result) in f end (* accumulate: look at the start of the right-hand-sides of rules, looking past nullable nonterminals, applying addObj to the visible symbols. *) fun accumulate(rules, empty, addObj) = List.foldr (fn (RULE {rhs,...},r) =>(scanRhs addObj) (rhs,r)) empty rules val nontermMemo = fn f => let val lookup = array(nonterms,nil) fun g i = if i=nonterms then () else (update(lookup,i,f (NT i)); g (i+1)) in (g 0; fn (NT j) => lookup sub j) end (* first1: the FIRST set of a nonterminal in the grammar. Only looks at other terminals, but it is clever enough to move past nullable nonterminals at the start of a production. *) fun first1 nt = accumulate(produces nt, TermSet.empty, fn (TERM t, set) => TermSet.insert (t,set) | (_, set) => set) val first1 = nontermMemo(first1) (* starters1: given a nonterminal "nt", return the set of nonterminals which can start its productions. Looks past nullables, but doesn't recurse *) fun starters1 nt = accumulate(produces nt, nil, fn (NONTERM nt, set) => NontermSet.insert(nt,set) | (_, set) => set) val starters1 = nontermMemo(starters1) (* first: maps a nonterminal to its first-set. Get all the starters of the nonterminal, get the first1 terminal set of each of these, union the whole lot together *) fun first nt = List.foldr (fn (a,r) => TermSet.union(r,first1 a)) [] (NontermSet.closure (NontermSet.singleton nt, starters1)) val first = nontermMemo(first) (* prefix: all possible terminals starting a symbol list *) fun prefix symbols = scanRhs (fn (TERM t,r) => TermSet.insert(t,r) | (NONTERM nt,r) => TermSet.union(first nt,r)) (symbols,nil) fun nullable_string ((TERM t) :: r) = false | nullable_string ((NONTERM nt) :: r) = (case (nullable nt) of true => nullable_string r | f => f) | nullable_string nil = true in {nullable = nullable, first = prefix} end end;

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