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cf10678f AW |
1 | ;;; TREE-IL -> GLIL compiler |
2 | ||
3 | ;; Copyright (C) 2001,2008,2009 Free Software Foundation, Inc. | |
4 | ||
53befeb7 NJ |
5 | ;;;; This library is free software; you can redistribute it and/or |
6 | ;;;; modify it under the terms of the GNU Lesser General Public | |
7 | ;;;; License as published by the Free Software Foundation; either | |
8 | ;;;; version 3 of the License, or (at your option) any later version. | |
9 | ;;;; | |
10 | ;;;; This library is distributed in the hope that it will be useful, | |
11 | ;;;; but WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 | ;;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
13 | ;;;; Lesser General Public License for more details. | |
14 | ;;;; | |
15 | ;;;; You should have received a copy of the GNU Lesser General Public | |
16 | ;;;; License along with this library; if not, write to the Free Software | |
17 | ;;;; Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA | |
cf10678f AW |
18 | |
19 | ;;; Code: | |
20 | ||
21 | (define-module (language tree-il analyze) | |
66d3e9a3 | 22 | #:use-module (srfi srfi-1) |
4b856371 | 23 | #:use-module (srfi srfi-9) |
cf10678f | 24 | #:use-module (system base syntax) |
4b856371 | 25 | #:use-module (system base message) |
cf10678f | 26 | #:use-module (language tree-il) |
4b856371 LC |
27 | #:export (analyze-lexicals |
28 | report-unused-variables)) | |
cf10678f | 29 | |
66d3e9a3 AW |
30 | ;; Allocation is the process of assigning storage locations for lexical |
31 | ;; variables. A lexical variable has a distinct "address", or storage | |
32 | ;; location, for each procedure in which it is referenced. | |
33 | ;; | |
34 | ;; A variable is "local", i.e., allocated on the stack, if it is | |
35 | ;; referenced from within the procedure that defined it. Otherwise it is | |
36 | ;; a "closure" variable. For example: | |
37 | ;; | |
38 | ;; (lambda (a) a) ; a will be local | |
39 | ;; `a' is local to the procedure. | |
40 | ;; | |
41 | ;; (lambda (a) (lambda () a)) | |
42 | ;; `a' is local to the outer procedure, but a closure variable with | |
43 | ;; respect to the inner procedure. | |
44 | ;; | |
45 | ;; If a variable is ever assigned, it needs to be heap-allocated | |
46 | ;; ("boxed"). This is so that closures and continuations capture the | |
47 | ;; variable's identity, not just one of the values it may have over the | |
48 | ;; course of program execution. If the variable is never assigned, there | |
49 | ;; is no distinction between value and identity, so closing over its | |
50 | ;; identity (whether through closures or continuations) can make a copy | |
51 | ;; of its value instead. | |
52 | ;; | |
53 | ;; Local variables are stored on the stack within a procedure's call | |
54 | ;; frame. Their index into the stack is determined from their linear | |
55 | ;; postion within a procedure's binding path: | |
cf10678f AW |
56 | ;; (let (0 1) |
57 | ;; (let (2 3) ...) | |
58 | ;; (let (2) ...)) | |
59 | ;; (let (2 3 4) ...)) | |
60 | ;; etc. | |
61 | ;; | |
5af166bd AW |
62 | ;; This algorithm has the problem that variables are only allocated |
63 | ;; indices at the end of the binding path. If variables bound early in | |
64 | ;; the path are not used in later portions of the path, their indices | |
65 | ;; will not be recycled. This problem is particularly egregious in the | |
66 | ;; expansion of `or': | |
67 | ;; | |
68 | ;; (or x y z) | |
69 | ;; -> (let ((a x)) (if a a (let ((b y)) (if b b z)))) | |
70 | ;; | |
71 | ;; As you can see, the `a' binding is only used in the ephemeral `then' | |
72 | ;; clause of the first `if', but its index would be reserved for the | |
73 | ;; whole of the `or' expansion. So we have a hack for this specific | |
74 | ;; case. A proper solution would be some sort of liveness analysis, and | |
75 | ;; not our linear allocation algorithm. | |
76 | ;; | |
66d3e9a3 AW |
77 | ;; Closure variables are captured when a closure is created, and stored |
78 | ;; in a vector. Each closure variable has a unique index into that | |
79 | ;; vector. | |
80 | ;; | |
9059993f AW |
81 | ;; There is one more complication. Procedures bound by <fix> may, in |
82 | ;; some cases, be rendered inline to their parent procedure. That is to | |
83 | ;; say, | |
84 | ;; | |
85 | ;; (letrec ((lp (lambda () (lp)))) (lp)) | |
86 | ;; => (fix ((lp (lambda () (lp)))) (lp)) | |
87 | ;; => goto FIX-BODY; LP: goto LP; FIX-BODY: goto LP; | |
88 | ;; ^ jump over the loop ^ the fixpoint lp ^ starting off the loop | |
89 | ;; | |
90 | ;; The upshot is that we don't have to allocate any space for the `lp' | |
91 | ;; closure at all, as it can be rendered inline as a loop. So there is | |
92 | ;; another kind of allocation, "label allocation", in which the | |
93 | ;; procedure is simply a label, placed at the start of the lambda body. | |
94 | ;; The label is the gensym under which the lambda expression is bound. | |
95 | ;; | |
96 | ;; The analyzer checks to see that the label is called with the correct | |
97 | ;; number of arguments. Calls to labels compile to rename + goto. | |
98 | ;; Lambda, the ultimate goto! | |
99 | ;; | |
66d3e9a3 AW |
100 | ;; |
101 | ;; The return value of `analyze-lexicals' is a hash table, the | |
102 | ;; "allocation". | |
103 | ;; | |
104 | ;; The allocation maps gensyms -- recall that each lexically bound | |
105 | ;; variable has a unique gensym -- to storage locations ("addresses"). | |
106 | ;; Since one gensym may have many storage locations, if it is referenced | |
107 | ;; in many procedures, it is a two-level map. | |
108 | ;; | |
109 | ;; The allocation also stored information on how many local variables | |
9059993f AW |
110 | ;; need to be allocated for each procedure, lexicals that have been |
111 | ;; translated into labels, and information on what free variables to | |
112 | ;; capture from its lexical parent procedure. | |
66d3e9a3 AW |
113 | ;; |
114 | ;; That is: | |
115 | ;; | |
116 | ;; sym -> {lambda -> address} | |
9059993f | 117 | ;; lambda -> (nlocs labels . free-locs) |
66d3e9a3 | 118 | ;; |
9059993f AW |
119 | ;; address ::= (local? boxed? . index) |
120 | ;; labels ::= ((sym . lambda-vars) ...) | |
66d3e9a3 AW |
121 | ;; free-locs ::= ((sym0 . address0) (sym1 . address1) ...) |
122 | ;; free variable addresses are relative to parent proc. | |
123 | ||
124 | (define (make-hashq k v) | |
125 | (let ((res (make-hash-table))) | |
126 | (hashq-set! res k v) | |
127 | res)) | |
cf10678f AW |
128 | |
129 | (define (analyze-lexicals x) | |
66d3e9a3 AW |
130 | ;; bound-vars: lambda -> (sym ...) |
131 | ;; all identifiers bound within a lambda | |
9059993f | 132 | (define bound-vars (make-hash-table)) |
66d3e9a3 AW |
133 | ;; free-vars: lambda -> (sym ...) |
134 | ;; all identifiers referenced in a lambda, but not bound | |
135 | ;; NB, this includes identifiers referenced by contained lambdas | |
9059993f | 136 | (define free-vars (make-hash-table)) |
66d3e9a3 | 137 | ;; assigned: sym -> #t |
9059993f | 138 | (define assigned (make-hash-table)) |
66d3e9a3 | 139 | ;; variables that are assigned |
5af166bd | 140 | ;; refcounts: sym -> count |
66d3e9a3 | 141 | ;; allows us to detect the or-expansion in O(1) time |
9059993f AW |
142 | (define refcounts (make-hash-table)) |
143 | ;; labels: sym -> lambda-vars | |
144 | ;; for determining if fixed-point procedures can be rendered as | |
145 | ;; labels. lambda-vars may be an improper list. | |
146 | (define labels (make-hash-table)) | |
147 | ||
66d3e9a3 AW |
148 | ;; returns variables referenced in expr |
149 | (define (analyze! x proc) | |
150 | (define (step y) (analyze! y proc)) | |
151 | (define (recur x new-proc) (analyze! x new-proc)) | |
cf10678f AW |
152 | (record-case x |
153 | ((<application> proc args) | |
66d3e9a3 | 154 | (apply lset-union eq? (step proc) (map step args))) |
cf10678f AW |
155 | |
156 | ((<conditional> test then else) | |
66d3e9a3 | 157 | (lset-union eq? (step test) (step then) (step else))) |
cf10678f AW |
158 | |
159 | ((<lexical-ref> name gensym) | |
5af166bd | 160 | (hashq-set! refcounts gensym (1+ (hashq-ref refcounts gensym 0))) |
66d3e9a3 | 161 | (list gensym)) |
cf10678f AW |
162 | |
163 | ((<lexical-set> name gensym exp) | |
66d3e9a3 AW |
164 | (hashq-set! refcounts gensym (1+ (hashq-ref refcounts gensym 0))) |
165 | (hashq-set! assigned gensym #t) | |
166 | (lset-adjoin eq? (step exp) gensym)) | |
cf10678f AW |
167 | |
168 | ((<module-set> mod name public? exp) | |
169 | (step exp)) | |
170 | ||
171 | ((<toplevel-set> name exp) | |
172 | (step exp)) | |
173 | ||
174 | ((<toplevel-define> name exp) | |
175 | (step exp)) | |
176 | ||
177 | ((<sequence> exps) | |
66d3e9a3 | 178 | (apply lset-union eq? (map step exps))) |
cf10678f AW |
179 | |
180 | ((<lambda> vars meta body) | |
66d3e9a3 AW |
181 | (let ((locally-bound (let rev* ((vars vars) (out '())) |
182 | (cond ((null? vars) out) | |
183 | ((pair? vars) (rev* (cdr vars) | |
184 | (cons (car vars) out))) | |
185 | (else (cons vars out)))))) | |
186 | (hashq-set! bound-vars x locally-bound) | |
187 | (let* ((referenced (recur body x)) | |
188 | (free (lset-difference eq? referenced locally-bound)) | |
189 | (all-bound (reverse! (hashq-ref bound-vars x)))) | |
190 | (hashq-set! bound-vars x all-bound) | |
191 | (hashq-set! free-vars x free) | |
192 | free))) | |
193 | ||
f4aa8d53 | 194 | ((<let> vars vals body) |
66d3e9a3 AW |
195 | (hashq-set! bound-vars proc |
196 | (append (reverse vars) (hashq-ref bound-vars proc))) | |
197 | (lset-difference eq? | |
198 | (apply lset-union eq? (step body) (map step vals)) | |
199 | vars)) | |
cf10678f | 200 | |
f4aa8d53 | 201 | ((<letrec> vars vals body) |
66d3e9a3 AW |
202 | (hashq-set! bound-vars proc |
203 | (append (reverse vars) (hashq-ref bound-vars proc))) | |
204 | (for-each (lambda (sym) (hashq-set! assigned sym #t)) vars) | |
205 | (lset-difference eq? | |
206 | (apply lset-union eq? (step body) (map step vals)) | |
207 | vars)) | |
208 | ||
c21c89b1 AW |
209 | ((<fix> vars vals body) |
210 | (hashq-set! bound-vars proc | |
211 | (append (reverse vars) (hashq-ref bound-vars proc))) | |
212 | (lset-difference eq? | |
213 | (apply lset-union eq? (step body) (map step vals)) | |
214 | vars)) | |
215 | ||
f4aa8d53 | 216 | ((<let-values> vars exp body) |
bca488f1 AW |
217 | (let ((bound (let lp ((out (hashq-ref bound-vars proc)) (in vars)) |
218 | (if (pair? in) | |
219 | (lp (cons (car in) out) (cdr in)) | |
220 | (if (null? in) out (cons in out)))))) | |
221 | (hashq-set! bound-vars proc bound) | |
222 | (lset-difference eq? | |
223 | (lset-union eq? (step exp) (step body)) | |
224 | bound))) | |
66d3e9a3 AW |
225 | |
226 | (else '()))) | |
227 | ||
9059993f AW |
228 | ;; allocation: sym -> {lambda -> address} |
229 | ;; lambda -> (nlocs labels . free-locs) | |
230 | (define allocation (make-hash-table)) | |
231 | ||
66d3e9a3 AW |
232 | (define (allocate! x proc n) |
233 | (define (recur y) (allocate! y proc n)) | |
234 | (record-case x | |
235 | ((<application> proc args) | |
236 | (apply max (recur proc) (map recur args))) | |
cf10678f | 237 | |
66d3e9a3 AW |
238 | ((<conditional> test then else) |
239 | (max (recur test) (recur then) (recur else))) | |
cf10678f | 240 | |
66d3e9a3 AW |
241 | ((<lexical-set> name gensym exp) |
242 | (recur exp)) | |
243 | ||
244 | ((<module-set> mod name public? exp) | |
245 | (recur exp)) | |
246 | ||
247 | ((<toplevel-set> name exp) | |
248 | (recur exp)) | |
249 | ||
250 | ((<toplevel-define> name exp) | |
251 | (recur exp)) | |
252 | ||
253 | ((<sequence> exps) | |
254 | (apply max (map recur exps))) | |
255 | ||
256 | ((<lambda> vars meta body) | |
257 | ;; allocate closure vars in order | |
258 | (let lp ((c (hashq-ref free-vars x)) (n 0)) | |
259 | (if (pair? c) | |
260 | (begin | |
261 | (hashq-set! (hashq-ref allocation (car c)) | |
262 | x | |
263 | `(#f ,(hashq-ref assigned (car c)) . ,n)) | |
264 | (lp (cdr c) (1+ n))))) | |
265 | ||
266 | (let ((nlocs | |
267 | (let lp ((vars vars) (n 0)) | |
268 | (if (not (null? vars)) | |
269 | ;; allocate args | |
270 | (let ((v (if (pair? vars) (car vars) vars))) | |
271 | (hashq-set! allocation v | |
272 | (make-hashq | |
273 | x `(#t ,(hashq-ref assigned v) . ,n))) | |
274 | (lp (if (pair? vars) (cdr vars) '()) (1+ n))) | |
275 | ;; allocate body, return number of additional locals | |
276 | (- (allocate! body x n) n)))) | |
277 | (free-addresses | |
278 | (map (lambda (v) | |
279 | (hashq-ref (hashq-ref allocation v) proc)) | |
9059993f AW |
280 | (hashq-ref free-vars x))) |
281 | (labels (filter cdr | |
282 | (map (lambda (sym) | |
283 | (cons sym (hashq-ref labels sym))) | |
284 | (hashq-ref bound-vars x))))) | |
66d3e9a3 | 285 | ;; set procedure allocations |
9059993f | 286 | (hashq-set! allocation x (cons* nlocs labels free-addresses))) |
66d3e9a3 | 287 | n) |
cf10678f | 288 | |
66d3e9a3 AW |
289 | ((<let> vars vals body) |
290 | (let ((nmax (apply max (map recur vals)))) | |
291 | (cond | |
292 | ;; the `or' hack | |
293 | ((and (conditional? body) | |
294 | (= (length vars) 1) | |
295 | (let ((v (car vars))) | |
296 | (and (not (hashq-ref assigned v)) | |
297 | (= (hashq-ref refcounts v 0) 2) | |
298 | (lexical-ref? (conditional-test body)) | |
299 | (eq? (lexical-ref-gensym (conditional-test body)) v) | |
300 | (lexical-ref? (conditional-then body)) | |
301 | (eq? (lexical-ref-gensym (conditional-then body)) v)))) | |
302 | (hashq-set! allocation (car vars) | |
303 | (make-hashq proc `(#t #f . ,n))) | |
304 | ;; the 1+ for this var | |
305 | (max nmax (1+ n) (allocate! (conditional-else body) proc n))) | |
306 | (else | |
307 | (let lp ((vars vars) (n n)) | |
308 | (if (null? vars) | |
309 | (max nmax (allocate! body proc n)) | |
310 | (let ((v (car vars))) | |
cf10678f AW |
311 | (hashq-set! |
312 | allocation v | |
66d3e9a3 AW |
313 | (make-hashq proc |
314 | `(#t ,(hashq-ref assigned v) . ,n))) | |
315 | (lp (cdr vars) (1+ n))))))))) | |
316 | ||
317 | ((<letrec> vars vals body) | |
318 | (let lp ((vars vars) (n n)) | |
319 | (if (null? vars) | |
320 | (let ((nmax (apply max | |
321 | (map (lambda (x) | |
322 | (allocate! x proc n)) | |
323 | vals)))) | |
324 | (max nmax (allocate! body proc n))) | |
325 | (let ((v (car vars))) | |
326 | (hashq-set! | |
327 | allocation v | |
328 | (make-hashq proc | |
329 | `(#t ,(hashq-ref assigned v) . ,n))) | |
330 | (lp (cdr vars) (1+ n)))))) | |
cf10678f | 331 | |
c21c89b1 AW |
332 | ((<fix> vars vals body) |
333 | (let lp ((vars vars) (n n)) | |
334 | (if (null? vars) | |
335 | (let ((nmax (apply max | |
336 | (map (lambda (x) | |
337 | (allocate! x proc n)) | |
338 | vals)))) | |
339 | (max nmax (allocate! body proc n))) | |
340 | (let ((v (car vars))) | |
341 | (if (hashq-ref assigned v) | |
342 | (error "fixpoint procedures may not be assigned" x)) | |
343 | (hashq-set! allocation v (make-hashq proc `(#t #f . ,n))) | |
344 | (lp (cdr vars) (1+ n)))))) | |
345 | ||
66d3e9a3 AW |
346 | ((<let-values> vars exp body) |
347 | (let ((nmax (recur exp))) | |
cf10678f | 348 | (let lp ((vars vars) (n n)) |
bca488f1 AW |
349 | (cond |
350 | ((null? vars) | |
351 | (max nmax (allocate! body proc n))) | |
352 | ((not (pair? vars)) | |
353 | (hashq-set! allocation vars | |
354 | (make-hashq proc | |
355 | `(#t ,(hashq-ref assigned vars) . ,n))) | |
356 | ;; the 1+ for this var | |
357 | (max nmax (allocate! body proc (1+ n)))) | |
358 | (else | |
80af1168 AW |
359 | (let ((v (car vars))) |
360 | (hashq-set! | |
361 | allocation v | |
362 | (make-hashq proc | |
363 | `(#t ,(hashq-ref assigned v) . ,n))) | |
364 | (lp (cdr vars) (1+ n)))))))) | |
66d3e9a3 AW |
365 | |
366 | (else n))) | |
cf10678f | 367 | |
66d3e9a3 AW |
368 | (analyze! x #f) |
369 | (allocate! x #f 0) | |
cf10678f AW |
370 | |
371 | allocation) | |
4b856371 LC |
372 | |
373 | \f | |
374 | ;;; | |
375 | ;;; Unused variable analysis. | |
376 | ;;; | |
377 | ||
378 | ;; <binding-info> records are used during tree traversals in | |
379 | ;; `report-unused-variables'. They contain a list of the local vars | |
380 | ;; currently in scope, a list of locals vars that have been referenced, and a | |
381 | ;; "location stack" (the stack of `tree-il-src' values for each parent tree). | |
382 | (define-record-type <binding-info> | |
383 | (make-binding-info vars refs locs) | |
384 | binding-info? | |
385 | (vars binding-info-vars) ;; ((GENSYM NAME LOCATION) ...) | |
386 | (refs binding-info-refs) ;; (GENSYM ...) | |
387 | (locs binding-info-locs)) ;; (LOCATION ...) | |
388 | ||
389 | (define (report-unused-variables tree) | |
390 | "Report about unused variables in TREE. Return TREE." | |
391 | ||
392 | (define (dotless-list lst) | |
393 | ;; If LST is a dotted list, return a proper list equal to LST except that | |
394 | ;; the very last element is a pair; otherwise return LST. | |
395 | (let loop ((lst lst) | |
396 | (result '())) | |
397 | (cond ((null? lst) | |
398 | (reverse result)) | |
399 | ((pair? lst) | |
400 | (loop (cdr lst) (cons (car lst) result))) | |
401 | (else | |
402 | (loop '() (cons lst result)))))) | |
403 | ||
404 | (tree-il-fold (lambda (x info) | |
405 | ;; X is a leaf: extend INFO's refs accordingly. | |
406 | (let ((refs (binding-info-refs info)) | |
407 | (vars (binding-info-vars info)) | |
408 | (locs (binding-info-locs info))) | |
409 | (record-case x | |
410 | ((<lexical-ref> gensym) | |
411 | (make-binding-info vars (cons gensym refs) locs)) | |
412 | (else info)))) | |
413 | ||
414 | (lambda (x info) | |
415 | ;; Going down into X: extend INFO's variable list | |
416 | ;; accordingly. | |
417 | (let ((refs (binding-info-refs info)) | |
418 | (vars (binding-info-vars info)) | |
419 | (locs (binding-info-locs info)) | |
420 | (src (tree-il-src x))) | |
421 | (define (extend inner-vars inner-names) | |
422 | (append (map (lambda (var name) | |
423 | (list var name src)) | |
424 | inner-vars | |
425 | inner-names) | |
426 | vars)) | |
427 | (record-case x | |
428 | ((<lexical-set> gensym) | |
429 | (make-binding-info vars (cons gensym refs) | |
430 | (cons src locs))) | |
431 | ((<lambda> vars names) | |
432 | (let ((vars (dotless-list vars)) | |
433 | (names (dotless-list names))) | |
434 | (make-binding-info (extend vars names) refs | |
435 | (cons src locs)))) | |
436 | ((<let> vars names) | |
437 | (make-binding-info (extend vars names) refs | |
438 | (cons src locs))) | |
439 | ((<letrec> vars names) | |
440 | (make-binding-info (extend vars names) refs | |
441 | (cons src locs))) | |
c21c89b1 AW |
442 | ((<fix> vars names) |
443 | (make-binding-info (extend vars names) refs | |
444 | (cons src locs))) | |
4b856371 LC |
445 | ((<let-values> vars names) |
446 | (make-binding-info (extend vars names) refs | |
447 | (cons src locs))) | |
448 | (else info)))) | |
449 | ||
450 | (lambda (x info) | |
451 | ;; Leaving X's scope: shrink INFO's variable list | |
452 | ;; accordingly and reported unused nested variables. | |
453 | (let ((refs (binding-info-refs info)) | |
454 | (vars (binding-info-vars info)) | |
455 | (locs (binding-info-locs info))) | |
456 | (define (shrink inner-vars refs) | |
457 | (for-each (lambda (var) | |
458 | (let ((gensym (car var))) | |
459 | ;; Don't report lambda parameters as | |
460 | ;; unused. | |
461 | (if (and (not (memq gensym refs)) | |
462 | (not (and (lambda? x) | |
463 | (memq gensym | |
464 | inner-vars)))) | |
465 | (let ((name (cadr var)) | |
466 | ;; We can get approximate | |
467 | ;; source location by going up | |
468 | ;; the LOCS location stack. | |
469 | (loc (or (caddr var) | |
470 | (find pair? locs)))) | |
471 | (warning 'unused-variable loc name))))) | |
472 | (filter (lambda (var) | |
473 | (memq (car var) inner-vars)) | |
474 | vars)) | |
475 | (fold alist-delete vars inner-vars)) | |
476 | ||
477 | ;; For simplicity, we leave REFS untouched, i.e., with | |
478 | ;; names of variables that are now going out of scope. | |
479 | ;; It doesn't hurt as these are unique names, it just | |
480 | ;; makes REFS unnecessarily fat. | |
481 | (record-case x | |
482 | ((<lambda> vars) | |
483 | (let ((vars (dotless-list vars))) | |
484 | (make-binding-info (shrink vars refs) refs | |
485 | (cdr locs)))) | |
486 | ((<let> vars) | |
487 | (make-binding-info (shrink vars refs) refs | |
488 | (cdr locs))) | |
489 | ((<letrec> vars) | |
490 | (make-binding-info (shrink vars refs) refs | |
491 | (cdr locs))) | |
c21c89b1 AW |
492 | ((<fix> vars) |
493 | (make-binding-info (shrink vars refs) refs | |
494 | (cdr locs))) | |
4b856371 LC |
495 | ((<let-values> vars) |
496 | (make-binding-info (shrink vars refs) refs | |
497 | (cdr locs))) | |
498 | (else info)))) | |
499 | (make-binding-info '() '() '()) | |
500 | tree) | |
501 | tree) |