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1 | (* ML-Yacc Parser Generator (c) 1989 Andrew W. Appel, David R. Tarditi *) |
2 | ||
3 | functor mkLalr ( structure IntGrammar : INTGRAMMAR | |
4 | structure Core : CORE | |
5 | structure Graph : LRGRAPH | |
6 | structure Look: LOOK | |
7 | sharing Graph.Core = Core | |
8 | sharing Graph.IntGrammar = Core.IntGrammar = | |
9 | Look.IntGrammar = IntGrammar) : LALR_GRAPH = | |
10 | struct | |
11 | val sub = Array.sub | |
12 | infix 9 sub | |
13 | open IntGrammar.Grammar IntGrammar Core Graph Look | |
14 | structure Graph = Graph | |
15 | structure Core = Core | |
16 | structure Grammar = IntGrammar.Grammar | |
17 | structure IntGrammar = IntGrammar | |
18 | ||
19 | datatype tmpcore = TMPCORE of (item * term list ref) list * int | |
20 | datatype lcore = LCORE of (item * term list) list * int | |
21 | ||
22 | ||
23 | val prLcore = | |
24 | fn a as (SymbolToString,nontermToString,termToString,print) => | |
25 | let val printItem = prItem (SymbolToString,nontermToString,print) | |
26 | val printLookahead = prLook(termToString,print) | |
27 | in fn (LCORE (items,state)) => | |
28 | (print "\n"; | |
29 | print "state "; | |
30 | print (Int.toString state); | |
31 | print " :\n\n"; | |
32 | List.app (fn (item,lookahead) => | |
33 | (print "{"; | |
34 | printItem item; | |
35 | print ","; | |
36 | printLookahead lookahead; | |
37 | print "}\n")) items) | |
38 | end | |
39 | ||
40 | exception Lalr of int | |
41 | ||
42 | structure ItemList = ListOrdSet | |
43 | (struct | |
44 | type elem = item * term list ref | |
45 | val eq = fn ((a,_),(b,_)) => eqItem(a,b) | |
46 | val gt = fn ((a,_),(b,_)) => gtItem(a,b) | |
47 | end) | |
48 | ||
49 | structure NontermSet = ListOrdSet | |
50 | (struct | |
51 | type elem = nonterm | |
52 | val gt = gtNonterm | |
53 | val eq = eqNonterm | |
54 | end) | |
55 | ||
56 | (* NTL: nonterms with lookahead *) | |
57 | ||
58 | structure NTL = RbOrdSet | |
59 | (struct | |
60 | type elem = nonterm * term list | |
61 | val gt = fn ((i,_),(j,_)) => gtNonterm(i,j) | |
62 | val eq = fn ((i,_),(j,_)) => eqNonterm(i,j) | |
63 | end) | |
64 | ||
65 | val DEBUG = false | |
66 | ||
67 | val addLookahead = fn {graph,nullable,first,eop, | |
68 | rules,produces,nonterms,epsProds, | |
69 | print,termToString,nontermToString} => | |
70 | let | |
71 | ||
72 | val eop = Look.make_set eop | |
73 | ||
74 | val symbolToString = fn (TERM t) => termToString t | |
75 | | (NONTERM t) => nontermToString t | |
76 | ||
77 | val print = if DEBUG then print | |
78 | else fn _ => () | |
79 | ||
80 | val prLook = if DEBUG then prLook (termToString,print) | |
81 | else fn _ => () | |
82 | ||
83 | val prNonterm = print o nontermToString | |
84 | ||
85 | val prRule = if DEBUG | |
86 | then prRule(symbolToString,nontermToString,print) | |
87 | else fn _ => () | |
88 | ||
89 | val printInt = print o (Int.toString : int -> string) | |
90 | ||
91 | val printItem = prItem(symbolToString,nontermToString,print) | |
92 | ||
93 | (* look_pos: position in the rhs of a rule at which we should start placing | |
94 | lookahead ref cells, i.e. the minimum place at which A -> x .B y, where | |
95 | B is a nonterminal and y =*=> epsilon, or A -> x. is true. Positions are | |
96 | given by the number of symbols before the place. The place before the first | |
97 | symbol is 0, etc. *) | |
98 | ||
99 | val look_pos = | |
100 | let val positions = Array.array(length rules,0) | |
101 | ||
102 | (* rule_pos: calculate place in the rhs of a rule at which we should start | |
103 | placing lookahead ref cells *) | |
104 | ||
105 | fun rule_pos (RULE {rhs,...}) = | |
106 | case (rev rhs) of | |
107 | nil => 0 | |
108 | | (TERM t) :: r => length rhs | |
109 | | (NONTERM n :: r) => let | |
110 | (* f assumes that everything after n in the | |
111 | * rule has proven to be nullable so far. | |
112 | * Remember that the rhs has been reversed, | |
113 | * implying that this is true initially *) | |
114 | (* A -> .z t B y, where y is nullable *) | |
115 | fun f (b, (r as (TERM _ :: _))) = length r | |
116 | (* A -> .z B C y *) | |
117 | | f (c, (NONTERM b :: r)) = | |
118 | if nullable c then f (b, r) | |
119 | else length r + 1 | |
120 | (* A -> .B y, where y is nullable *) | |
121 | | f (_, []) = 0 | |
122 | in f (n, r) | |
123 | end | |
124 | ||
125 | val check_rule = fn (rule as RULE {num,...}) => | |
126 | let val pos = rule_pos rule | |
127 | in (print "look_pos: "; | |
128 | prRule rule; | |
129 | print " = "; | |
130 | printInt pos; | |
131 | print "\n"; | |
132 | Array.update(positions,num,rule_pos rule)) | |
133 | end | |
134 | in app check_rule rules; | |
135 | fn RULE{num,...} => (positions sub num) | |
136 | end | |
137 | ||
138 | (* rest_is_null: true for items of the form A -> x .B y, where y is nullable *) | |
139 | ||
140 | val rest_is_null = | |
141 | fn (ITEM{rule,dot, rhsAfter=NONTERM _ :: _}) => | |
142 | dot >= (look_pos rule) | |
143 | | _ => false | |
144 | ||
145 | (* map core to a new core including only items of the form A -> x. or | |
146 | A -> x. B y, where y =*=> epsilon. It also adds epsilon productions to the | |
147 | core. Each item is given a ref cell to hold the lookahead nonterminals for | |
148 | it.*) | |
149 | ||
150 | val map_core = | |
151 | let val f = fn (item as ITEM {rhsAfter=nil,...},r) => | |
152 | (item,ref nil) :: r | |
153 | | (item,r) => | |
154 | if (rest_is_null item) | |
155 | then (item,ref nil)::r | |
156 | else r | |
157 | in fn (c as CORE (items,state)) => | |
158 | let val epsItems = | |
159 | map (fn rule=>(ITEM{rule=rule,dot=0,rhsAfter=nil}, | |
160 | ref (nil : term list)) | |
161 | ) (epsProds c) | |
162 | in TMPCORE(ItemList.union(List.foldr f [] items,epsItems),state) | |
163 | end | |
164 | end | |
165 | ||
166 | val new_nodes = map map_core (nodes graph) | |
167 | ||
168 | exception Find | |
169 | ||
170 | (* findRef: state * item -> lookahead ref cell for item *) | |
171 | ||
172 | val findRef = | |
173 | let val states = Array.fromList new_nodes | |
174 | val dummy = ref nil | |
175 | in fn (state,item) => | |
176 | let val TMPCORE (l,_) = states sub state | |
177 | in case ItemList.find((item,dummy),l) | |
178 | of SOME (_,look_ref) => look_ref | |
179 | | NONE => (print "find failed: state "; | |
180 | printInt state; | |
181 | print "\nitem =\n"; | |
182 | printItem item; | |
183 | print "\nactual items =\n"; | |
184 | app (fn (i,_) => (printItem i; | |
185 | print "\n")) l; | |
186 | raise Find) | |
187 | end | |
188 | end | |
189 | ||
190 | ||
191 | (* findRuleRefs: state -> rule -> lookahead refs for rule. *) | |
192 | ||
193 | val findRuleRefs = | |
194 | let val shift = shift graph | |
195 | in fn state => | |
196 | (* handle epsilon productions *) | |
197 | fn (rule as RULE {rhs=nil,...}) => | |
198 | [findRef(state,ITEM{rule=rule,dot=0,rhsAfter=nil})] | |
199 | | (rule as RULE {rhs=sym::rest,...}) => | |
200 | let val pos = Int.max(look_pos rule,1) | |
201 | fun scan'(state,nil,pos,result) = | |
202 | findRef(state,ITEM{rule=rule, | |
203 | dot=pos, | |
204 | rhsAfter=nil}) :: result | |
205 | | scan'(state,rhs as sym::rest,pos,result) = | |
206 | scan'(shift(state,sym), rest, pos+1, | |
207 | findRef(state,ITEM{rule=rule, | |
208 | dot=pos, | |
209 | rhsAfter=rhs})::result) | |
210 | ||
211 | (* find first item of the form A -> x .B y, where y =*=> epsilon and | |
212 | x is not epsilon, or A -> x. use scan' to pick up all refs after this | |
213 | point *) | |
214 | ||
215 | fun scan(state,nil,_) = | |
216 | [findRef(state,ITEM{rule=rule,dot=pos,rhsAfter=nil})] | |
217 | | scan(state,rhs,0) = scan'(state,rhs,pos,nil) | |
218 | | scan(state,sym::rest,place) = | |
219 | scan(shift(state,sym),rest,place-1) | |
220 | ||
221 | in scan(shift(state,sym),rest,pos-1) | |
222 | end | |
223 | ||
224 | end | |
225 | ||
226 | (* function to compute for some nonterminal n the set of nonterminals A added | |
227 | through the closure of nonterminal n such that n =c*=> .A x, where x is | |
228 | nullable *) | |
229 | ||
230 | val nonterms_w_null = fn nt => | |
231 | let val collect_nonterms = fn n => | |
232 | List.foldr (fn (rule as RULE {rhs=rhs as NONTERM n :: _,...},r) => | |
233 | (case | |
234 | (rest_is_null(ITEM {dot=0,rhsAfter=rhs,rule=rule})) | |
235 | of true => n :: r | |
236 | | false => r) | |
237 | | (_,r) => r) [] (produces n) | |
238 | fun dfs(a as (n,r)) = | |
239 | if (NontermSet.exists a) then r | |
240 | else List.foldr dfs (NontermSet.insert(n,r)) | |
241 | (collect_nonterms n) | |
242 | in dfs(nt,NontermSet.empty) | |
243 | end | |
244 | ||
245 | val nonterms_w_null = | |
246 | let val data = Array.array(nonterms,NontermSet.empty) | |
247 | fun f n = if n=nonterms then () | |
248 | else (Array.update(data,n,nonterms_w_null (NT n)); | |
249 | f (n+1)) | |
250 | in (f 0; fn (NT nt) => data sub nt) | |
251 | end | |
252 | ||
253 | (* look_info: for some nonterminal n the set of nonterms A added | |
254 | through the closure of the nonterminal such that n =c+=> .Ax and the | |
255 | lookahead accumlated for each nonterm A *) | |
256 | ||
257 | val look_info = fn nt => | |
258 | let val collect_nonterms = fn n => | |
259 | List.foldr (fn (RULE {rhs=NONTERM n :: t,...},r) => | |
260 | (case NTL.find ((n,nil),r) | |
261 | of SOME (key,data) => | |
262 | NTL.insert((n,Look.union(data,first t)),r) | |
263 | | NONE => NTL.insert ((n,first t),r)) | |
264 | | (_,r) => r) | |
265 | NTL.empty (produces n) | |
266 | fun dfs(a as ((key1,data1),r)) = | |
267 | case (NTL.find a) | |
268 | of SOME (_,data2) => | |
269 | NTL.insert((key1,Look.union(data1,data2)),r) | |
270 | | NONE => NTL.fold dfs (collect_nonterms key1) | |
271 | (NTL.insert a) | |
272 | in dfs((nt,nil),NTL.empty) | |
273 | end | |
274 | ||
275 | val look_info = | |
276 | if not DEBUG then look_info | |
277 | else fn nt => | |
278 | (print "look_info of "; prNonterm nt; print "=\n"; | |
279 | let val info = look_info nt | |
280 | in (NTL.app (fn (nt,lookahead) => | |
281 | (prNonterm nt; print ": "; prLook lookahead; | |
282 | print "\n\n")) info; | |
283 | info) | |
284 | end) | |
285 | ||
286 | (* prop_look: propagate lookaheads for nonterms added in the closure of a | |
287 | nonterm. Lookaheads must be propagated from each nonterminal m to | |
288 | all nonterminals { n | m =c+=> nx, where x=*=>epsilon} *) | |
289 | ||
290 | val prop_look = fn ntl => | |
291 | let val upd_lookhd = fn new_look => fn (nt,r) => | |
292 | case NTL.find ((nt,new_look),r) | |
293 | of SOME (_,old_look) => | |
294 | NTL.insert((nt, Look.union(new_look,old_look)),r) | |
295 | | NONE => raise (Lalr 241) | |
296 | val upd_nonterm = fn ((nt,look),r) => | |
297 | NontermSet.fold (upd_lookhd look) | |
298 | (nonterms_w_null nt) r | |
299 | in NTL.fold upd_nonterm ntl ntl | |
300 | end | |
301 | ||
302 | val prop_look = | |
303 | if not DEBUG then prop_look | |
304 | else fn ntl => | |
305 | (print "prop_look =\n"; | |
306 | let val info = prop_look ntl | |
307 | in (NTL.app (fn (nt,lookahead) => | |
308 | (prNonterm nt; | |
309 | print ": "; | |
310 | prLook lookahead; | |
311 | print "\n\n")) info; info) | |
312 | end) | |
313 | ||
314 | (* now put the information from these functions together. Create a function | |
315 | which takes a nonterminal n and returns a list of triplets of | |
316 | (a nonterm added through closure, | |
317 | the lookahead for the nonterm, | |
318 | whether the nonterm should include the lookahead for the nonterminal | |
319 | whose closure is being taken (i.e. first(y) for an item j of the | |
320 | form A -> x .n y and lookahead(j) if y =*=> epsilon) | |
321 | *) | |
322 | ||
323 | val closure_nonterms = | |
324 | let val data = | |
325 | Array.array(nonterms,nil: (nonterm * term list * bool) list) | |
326 | val do_nonterm = fn i => | |
327 | let val nonterms_followed_by_null = | |
328 | nonterms_w_null i | |
329 | val nonterms_added_through_closure = | |
330 | NTL.make_list (prop_look (look_info i)) | |
331 | val result = | |
332 | map (fn (nt,l) => | |
333 | (nt,l,NontermSet.exists (nt,nonterms_followed_by_null)) | |
334 | ) nonterms_added_through_closure | |
335 | in if DEBUG then | |
336 | (print "closure_nonterms = "; | |
337 | prNonterm i; | |
338 | print "\n"; | |
339 | app (fn (nt,look,nullable) => | |
340 | (prNonterm nt; | |
341 | print ":"; | |
342 | prLook look; | |
343 | case nullable | |
344 | of false => print "(false)\n" | |
345 | | true => print "(true)\n")) result; | |
346 | print "\n") | |
347 | else (); | |
348 | result | |
349 | end | |
350 | fun f i = | |
351 | if i=nonterms then () | |
352 | else (Array.update(data,i,do_nonterm (NT i)); f (i+1)) | |
353 | val _ = f 0 | |
354 | in fn (NT i) => data sub i | |
355 | end | |
356 | ||
357 | (* add_nonterm_lookahead: Add lookahead to all completion items for rules added | |
358 | when the closure of a given nonterm in some state is taken. It returns | |
359 | a list of lookahead refs to which the given nonterm's lookahead should | |
360 | be propagated. For each rule, it must trace the shift/gotos in the LR(0) | |
361 | graph to find all items of the form A-> x .B y where y =*=> epsilon or | |
362 | A -> x. | |
363 | *) | |
364 | ||
365 | val add_nonterm_lookahead = fn (nt,state) => | |
366 | let val f = fn ((nt,lookahead,nullable),r) => | |
367 | let val refs = map (findRuleRefs state) (produces nt) | |
368 | val refs = List.concat refs | |
369 | val _ = app (fn r => | |
370 | r := (Look.union (!r,lookahead))) refs | |
371 | in if nullable then refs @ r else r | |
372 | end | |
373 | in List.foldr f [] (closure_nonterms nt) | |
374 | end | |
375 | ||
376 | (* scan_core: Scan a core for all items of the form A -> x .B y. Applies | |
377 | add_nonterm_lookahead to each such B, and then merges first(y) into | |
378 | the list of refs returned by add_nonterm_lookahead. It returns | |
379 | a list of ref * ref list for all the items where y =*=> epsilon *) | |
380 | ||
381 | val scan_core = fn (CORE (l,state)) => | |
382 | let fun f ((item as ITEM{rhsAfter= NONTERM b :: y, | |
383 | dot,rule})::t,r) = | |
384 | (case (add_nonterm_lookahead(b,state)) | |
385 | of nil => r | |
386 | | l => | |
387 | let val first_y = first y | |
388 | val newr = if dot >= (look_pos rule) | |
389 | then (findRef(state,item),l)::r | |
390 | else r | |
391 | in (app (fn r => | |
392 | r := Look.union(!r,first_y)) l; | |
393 | f (t,newr)) | |
394 | end) | |
395 | | f (_ :: t,r) = f (t,r) | |
396 | | f (nil,r) = r | |
397 | in f (l,nil) | |
398 | end | |
399 | ||
400 | (* add end-of-parse symbols to set of items consisting of all items | |
401 | immediately derived from the start symbol *) | |
402 | ||
403 | val add_eop = fn (c as CORE (l,state),eop) => | |
404 | let fun f (item as ITEM {rule,dot,...}) = | |
405 | let val refs = findRuleRefs state rule | |
406 | in | |
407 | ||
408 | (* first take care of kernal items. Add the end-of-parse symbols to | |
409 | the lookahead sets for these items. Epsilon productions of the | |
410 | start symbol do not need to be handled specially because they will | |
411 | be in the kernal also *) | |
412 | ||
413 | app (fn r => r := Look.union(!r,eop)) refs; | |
414 | ||
415 | (* now take care of closure items. These are all nonterminals C which | |
416 | have a derivation S =+=> .C x, where x is nullable *) | |
417 | ||
418 | if dot >= (look_pos rule) then | |
419 | case item | |
420 | of ITEM{rhsAfter=NONTERM b :: _,...} => | |
421 | (case add_nonterm_lookahead(b,state) | |
422 | of nil => () | |
423 | | l => app (fn r => r := Look.union(!r,eop)) l) | |
424 | | _ => () | |
425 | else () | |
426 | end | |
427 | in app f l | |
428 | end | |
429 | ||
430 | val iterate = fn l => | |
431 | let fun f lookahead (nil,done) = done | |
432 | | f lookahead (h::t,done) = | |
433 | let val old = !h | |
434 | in h := Look.union (old,lookahead); | |
435 | if (length (!h)) <> (length old) | |
436 | then f lookahead (t,false) | |
437 | else f lookahead(t,done) | |
438 | end | |
439 | fun g ((from,to)::rest,done) = | |
440 | let val new_done = f (!from) (to,done) | |
441 | in g (rest,new_done) | |
442 | end | |
443 | | g (nil,done) = done | |
444 | fun loop true = () | |
445 | | loop false = loop (g (l,true)) | |
446 | in loop false | |
447 | end | |
448 | ||
449 | val lookahead = List.concat (map scan_core (nodes graph)) | |
450 | ||
451 | (* used to scan the item list of a TMPCORE and remove the items not | |
452 | being reduced *) | |
453 | ||
454 | val create_lcore_list = | |
455 | fn ((item as ITEM {rhsAfter=nil,...},ref l),r) => | |
456 | (item,l) :: r | |
457 | | (_,r) => r | |
458 | ||
459 | in add_eop(Graph.core graph 0,eop); | |
460 | iterate lookahead; | |
461 | map (fn (TMPCORE (l,state)) => | |
462 | LCORE (List.foldr create_lcore_list [] l, state)) new_nodes | |
463 | end | |
464 | end; |