1 | include "RTL/RTLTailcall.ma". |
---|
2 | include "utilities/RegisterSet.ma". |
---|
3 | include "common/Identifiers.ma". |
---|
4 | include "ERTL/ERTL.ma". |
---|
5 | |
---|
6 | definition fresh_label ≝ |
---|
7 | λglobals.λdef: joint_internal_function … (ertl_params globals). |
---|
8 | fresh LabelTag (joint_if_luniverse … def). |
---|
9 | |
---|
10 | definition change_label ≝ |
---|
11 | λglobals.λe: joint_statement ertl_params_ globals.λl. |
---|
12 | match e with |
---|
13 | [ joint_st_goto _ ⇒ joint_st_goto … l |
---|
14 | | joint_st_return ⇒ joint_st_return ?? |
---|
15 | | joint_st_sequential instr _ ⇒ joint_st_sequential … instr l]. |
---|
16 | |
---|
17 | (*CSC: bad programming habit: the code below puts everywhere a fake |
---|
18 | label and then adds_graph fixes them *) |
---|
19 | (*CSC: the code is artificially fixed to work on ertl_statements, but |
---|
20 | it works on every graph_params *) |
---|
21 | (*CSC: this is just an instance of add_translates below! *) |
---|
22 | let rec adds_graph |
---|
23 | (globals: list ident) |
---|
24 | (stmt_list: list (ertl_statement globals)) (start_lbl: label) |
---|
25 | (dest_lbl: label) (def: ertl_internal_function globals) |
---|
26 | on stmt_list ≝ |
---|
27 | match stmt_list with |
---|
28 | [ nil ⇒ add_graph … start_lbl (joint_st_goto … dest_lbl) def |
---|
29 | | cons stmt stmt_list ⇒ |
---|
30 | match stmt_list with |
---|
31 | [ nil ⇒ add_graph … start_lbl (change_label … stmt dest_lbl) def |
---|
32 | | _ ⇒ |
---|
33 | let 〈tmp_lbl, nuniv〉 ≝ fresh_label … def in |
---|
34 | let stmt ≝ change_label … stmt tmp_lbl in |
---|
35 | let def ≝ add_graph … start_lbl stmt def in |
---|
36 | adds_graph globals stmt_list tmp_lbl dest_lbl def]]. |
---|
37 | |
---|
38 | (*CSC: bad programming habit: the code below puts everywhere a fake |
---|
39 | label and then adds_graph fixes them *) |
---|
40 | (*CSC: the code is artificially fixed to work on ertl_statements, but |
---|
41 | it works on every graph_params *) |
---|
42 | let rec add_translates |
---|
43 | (globals: list ident) (translate_list: list ?) (start_lbl: label) (dest_lbl: label) |
---|
44 | (def: ertl_internal_function globals) |
---|
45 | on translate_list ≝ |
---|
46 | match translate_list with |
---|
47 | [ nil ⇒ add_graph … start_lbl (joint_st_goto … dest_lbl) def |
---|
48 | | cons trans translate_list ⇒ |
---|
49 | match translate_list with |
---|
50 | [ nil ⇒ trans start_lbl dest_lbl def |
---|
51 | | _ ⇒ |
---|
52 | let 〈tmp_lbl, nuniv〉 ≝ fresh_label … def in |
---|
53 | let def ≝ trans start_lbl tmp_lbl def in |
---|
54 | add_translates globals translate_list tmp_lbl dest_lbl def]]. |
---|
55 | |
---|
56 | definition fresh_reg: |
---|
57 | ∀globals. ertl_internal_function globals → (ertl_internal_function globals) × register ≝ |
---|
58 | λglobals,def. |
---|
59 | let 〈r,runiverse〉 ≝ fresh … (joint_if_runiverse … def) in |
---|
60 | 〈set_locals … (set_runiverse … def runiverse) (r::joint_if_locals … def), r〉. |
---|
61 | |
---|
62 | let rec fresh_regs (globals: list ident) (def: ertl_internal_function globals) (n: nat) on n ≝ |
---|
63 | match n with |
---|
64 | [ O ⇒ 〈def, [ ]〉 |
---|
65 | | S n' ⇒ |
---|
66 | let 〈def', regs'〉 ≝ fresh_regs globals def n' in |
---|
67 | let 〈def', reg〉 ≝ fresh_reg … def' in |
---|
68 | 〈def', reg :: regs'〉 |
---|
69 | ]. |
---|
70 | |
---|
71 | lemma fresh_regs_length: |
---|
72 | ∀globals.∀def: ertl_internal_function globals. ∀n: nat. |
---|
73 | |(\snd (fresh_regs … def n))| = n. |
---|
74 | #globals #def #n elim n |
---|
75 | [ % |
---|
76 | | #m whd in ⊢ (? → ??(??%)?) whd in ⊢ (? → ??(??match % with [ _ ⇒ ?])?) |
---|
77 | cases (fresh_regs globals def m) normalize nodelta |
---|
78 | #def' #regs #EQ change in EQ with (|regs| = m) <EQ |
---|
79 | change with |
---|
80 | (|let 〈a,b〉 ≝ let 〈x,y〉 ≝ let 〈r,runiverse〉 ≝ ? in ? in ? in ?| = ?) |
---|
81 | cases (fresh … (joint_if_runiverse … def')) normalize // ] |
---|
82 | qed. |
---|
83 | |
---|
84 | definition fresh_regs_strong: |
---|
85 | ∀globals. ertl_internal_function globals → |
---|
86 | ∀n: nat. Σregs: (ertl_internal_function globals) × (list register). |\snd regs| = n ≝ |
---|
87 | λdef,n.fresh_regs def n. // |
---|
88 | qed. |
---|
89 | |
---|
90 | definition save_hdws ≝ |
---|
91 | λglobals,l. |
---|
92 | let save_hdws_internal ≝ |
---|
93 | λdestr_srcr.λstart_lbl. |
---|
94 | let 〈destr, srcr〉 ≝ destr_srcr in |
---|
95 | adds_graph globals [ joint_st_sequential … (joint_instr_move … 〈pseudo destr,hardware srcr〉) start_lbl ] start_lbl |
---|
96 | in |
---|
97 | map ? ? save_hdws_internal l. |
---|
98 | |
---|
99 | definition restore_hdws ≝ |
---|
100 | λglobals,l. |
---|
101 | let restore_hdws_internal ≝ |
---|
102 | λsrcr_destr: register × Register. |
---|
103 | λstart_lbl: label. |
---|
104 | let 〈srcr, destr〉 ≝ srcr_destr in |
---|
105 | adds_graph globals [ joint_st_sequential … (joint_instr_move … 〈hardware destr, pseudo srcr〉) start_lbl ] start_lbl |
---|
106 | in |
---|
107 | map ? ? restore_hdws_internal l. |
---|
108 | |
---|
109 | definition get_params_hdw ≝ |
---|
110 | λglobals. |
---|
111 | λparams: list register. |
---|
112 | match params with |
---|
113 | [ nil ⇒ [λstart_lbl: label. adds_graph globals [ joint_st_goto … start_lbl ] start_lbl] |
---|
114 | | _ ⇒ |
---|
115 | let l ≝ zip_pottier ? ? params RegisterParams in |
---|
116 | save_hdws globals l ]. |
---|
117 | |
---|
118 | definition get_param_stack ≝ |
---|
119 | λglobals. |
---|
120 | λoff: nat. |
---|
121 | λdestr. |
---|
122 | λstart_lbl, dest_lbl: label. |
---|
123 | λdef. |
---|
124 | let 〈def, addr1〉 ≝ fresh_reg … def in |
---|
125 | let 〈def, addr2〉 ≝ fresh_reg … def in |
---|
126 | let 〈def, tmpr〉 ≝ fresh_reg … def in |
---|
127 | let 〈carry, int_offset〉 ≝ half_add ? (bitvector_of_nat ? off) int_size in |
---|
128 | adds_graph globals [ |
---|
129 | joint_st_sequential … (joint_instr_extension … (ertl_st_ext_frame_size addr1)) start_lbl; |
---|
130 | joint_st_sequential … (joint_instr_int … tmpr int_offset) start_lbl; |
---|
131 | joint_st_sequential … (joint_instr_op2 … Sub addr1 addr1 tmpr) start_lbl; |
---|
132 | joint_st_sequential … (joint_instr_move … 〈pseudo tmpr, hardware RegisterSPL〉) start_lbl; |
---|
133 | joint_st_sequential … (joint_instr_op2 … Add addr1 addr1 tmpr) start_lbl; |
---|
134 | joint_st_sequential … (joint_instr_int … addr2 (bitvector_of_nat 8 0)) start_lbl; |
---|
135 | joint_st_sequential … (joint_instr_move … 〈pseudo tmpr, hardware RegisterSPH〉) start_lbl; |
---|
136 | joint_st_sequential … (joint_instr_op2 … Addc addr2 addr2 tmpr) start_lbl; |
---|
137 | joint_st_sequential … (joint_instr_load … destr addr1 addr2) start_lbl |
---|
138 | ] start_lbl dest_lbl def. |
---|
139 | |
---|
140 | definition get_params_stack ≝ |
---|
141 | λglobals,params. |
---|
142 | match params with |
---|
143 | [ nil ⇒ [ λstart_lbl. adds_graph … [joint_st_goto … start_lbl] start_lbl ] |
---|
144 | | _ ⇒ mapi ? ? (get_param_stack globals) params ]. |
---|
145 | |
---|
146 | definition get_params ≝ |
---|
147 | λglobals,params. |
---|
148 | let n ≝ min (length … params) (length … RegisterParams) in |
---|
149 | let 〈hdw_params, stack_params〉 ≝ list_split … n params in |
---|
150 | let hdw_params ≝ get_params_hdw globals hdw_params in |
---|
151 | hdw_params @ (get_params_stack … stack_params). |
---|
152 | |
---|
153 | definition add_prologue ≝ |
---|
154 | λglobals. |
---|
155 | λparams: list register. |
---|
156 | λsral. |
---|
157 | λsrah. |
---|
158 | λsregs. |
---|
159 | λdef. |
---|
160 | let start_lbl ≝ joint_if_entry … (ertl_params globals) def in |
---|
161 | let 〈tmp_lbl, nuniv〉 ≝ fresh_label … def in |
---|
162 | match lookup … (joint_if_code … (ertl_params globals) def) start_lbl |
---|
163 | return λx. x ≠ None ? → ertl_internal_function globals with |
---|
164 | [ None ⇒ λnone_absrd. ⊥ |
---|
165 | | Some last_stmt ⇒ λsome_prf. |
---|
166 | let def ≝ |
---|
167 | add_translates … |
---|
168 | ((adds_graph … [ |
---|
169 | joint_st_sequential … (joint_instr_extension ertl_params_ globals ertl_st_ext_new_frame) start_lbl |
---|
170 | ]) :: |
---|
171 | (adds_graph … [ |
---|
172 | joint_st_sequential … (joint_instr_pop … sral) start_lbl; |
---|
173 | joint_st_sequential … (joint_instr_pop … srah) start_lbl |
---|
174 | ]) :: |
---|
175 | (save_hdws … sregs) @ |
---|
176 | (get_params … params)) |
---|
177 | start_lbl tmp_lbl def |
---|
178 | in |
---|
179 | add_graph … tmp_lbl last_stmt def |
---|
180 | ] ?. |
---|
181 | [ cases start_lbl #x #H @H |
---|
182 | | cases (none_absrd) /2/ ] |
---|
183 | qed. |
---|
184 | |
---|
185 | definition save_return ≝ |
---|
186 | λglobals. |
---|
187 | λret_regs. |
---|
188 | λstart_lbl: label. |
---|
189 | λdest_lbl: label. |
---|
190 | λdef: ertl_internal_function globals. |
---|
191 | let 〈def, tmpr〉 ≝ fresh_reg … def in |
---|
192 | match reduce_strong ? ? RegisterSTS ret_regs with |
---|
193 | [ dp crl crl_proof ⇒ |
---|
194 | let commonl ≝ \fst (\fst crl) in |
---|
195 | let commonr ≝ \fst (\snd crl) in |
---|
196 | let restl ≝ \snd (\fst crl) in |
---|
197 | let restr ≝ \snd (\snd crl) in |
---|
198 | let init_tmpr ≝ joint_st_sequential ertl_params_ … (joint_instr_int … tmpr (zero ?)) start_lbl in |
---|
199 | let f_save ≝ λst. λr. joint_st_sequential ertl_params_ … (joint_instr_move … 〈hardware st, pseudo r〉) start_lbl in |
---|
200 | let saves ≝ map2 ? ? ? f_save commonl commonr crl_proof in |
---|
201 | let f_default ≝ λst. joint_st_sequential ertl_params_ … (joint_instr_move … 〈hardware st, pseudo tmpr〉) start_lbl in |
---|
202 | let defaults ≝ map ? ? f_default restl in |
---|
203 | adds_graph … (init_tmpr :: saves @ defaults) start_lbl dest_lbl def |
---|
204 | ]. |
---|
205 | |
---|
206 | definition assign_result ≝ |
---|
207 | λglobals.λstart_lbl: label. |
---|
208 | match reduce_strong ? ? RegisterRets RegisterSTS with |
---|
209 | [ dp crl crl_proof ⇒ |
---|
210 | let commonl ≝ \fst (\fst crl) in |
---|
211 | let commonr ≝ \fst (\snd crl) in |
---|
212 | let f ≝ λret. λst. joint_st_sequential ertl_params_ globals (joint_instr_move … 〈hardware ret, hardware st〉) start_lbl in |
---|
213 | let insts ≝ map2 ? ? ? f commonl commonr crl_proof in |
---|
214 | adds_graph … insts start_lbl |
---|
215 | ]. |
---|
216 | |
---|
217 | definition add_epilogue ≝ |
---|
218 | λglobals. |
---|
219 | λret_regs. |
---|
220 | λsral. |
---|
221 | λsrah. |
---|
222 | λsregs. |
---|
223 | λdef. |
---|
224 | let start_lbl ≝ joint_if_exit … (ertl_params globals) def in |
---|
225 | let 〈tmp_lbl, nuniv〉 ≝ fresh_label … def in |
---|
226 | match lookup … (joint_if_code … (ertl_params globals) def) start_lbl |
---|
227 | return λx. x ≠ None ? → ertl_internal_function globals with |
---|
228 | [ None ⇒ λnone_absrd. ⊥ |
---|
229 | | Some last_stmt ⇒ λsome_prf. |
---|
230 | let def ≝ |
---|
231 | add_translates … ( |
---|
232 | [save_return globals ret_regs] @ |
---|
233 | restore_hdws … sregs @ |
---|
234 | [adds_graph … [ |
---|
235 | joint_st_sequential … (joint_instr_push … srah) start_lbl; |
---|
236 | joint_st_sequential … (joint_instr_push … sral) start_lbl |
---|
237 | ]] @ |
---|
238 | [adds_graph … [ |
---|
239 | joint_st_sequential … (joint_instr_extension … ertl_st_ext_del_frame) start_lbl |
---|
240 | ]] @ |
---|
241 | [assign_result globals] |
---|
242 | ) start_lbl tmp_lbl def |
---|
243 | in |
---|
244 | let def' ≝ add_graph … tmp_lbl last_stmt def in |
---|
245 | set_joint_if_exit … tmp_lbl def' ? |
---|
246 | ] ?. |
---|
247 | [ cases start_lbl #x #H @H |
---|
248 | | cases (none_absrd) /2/ |
---|
249 | | cases daemon (* CSC: XXXXX *) |
---|
250 | ] |
---|
251 | qed. |
---|
252 | |
---|
253 | |
---|
254 | definition allocate_regs ≝ |
---|
255 | λglobals. |
---|
256 | λrs. |
---|
257 | λsaved: rs_set rs. |
---|
258 | λdef. |
---|
259 | let allocate_regs_internal ≝ |
---|
260 | λr: Register. |
---|
261 | λdef_sregs. |
---|
262 | let 〈def, sregs〉 ≝ def_sregs in |
---|
263 | let 〈def, r'〉 ≝ fresh_reg globals def in |
---|
264 | 〈def, 〈r', r〉 :: sregs〉 |
---|
265 | in |
---|
266 | rs_fold ? ? allocate_regs_internal saved 〈def, [ ]〉. |
---|
267 | |
---|
268 | definition add_pro_and_epilogue ≝ |
---|
269 | λglobals. |
---|
270 | λparams. |
---|
271 | λret_regs. |
---|
272 | λdef. |
---|
273 | match fresh_regs_strong globals def 2 with |
---|
274 | [ dp def_sra def_sra_proof ⇒ |
---|
275 | let def ≝ \fst def_sra in |
---|
276 | let sra ≝ \snd def_sra in |
---|
277 | let sral ≝ nth_safe ? 0 sra ? in |
---|
278 | let srah ≝ nth_safe ? 1 sra ? in |
---|
279 | let 〈def, sregs〉 ≝ allocate_regs … register_list_set RegisterCalleeSaved def in |
---|
280 | let def ≝ add_prologue … params sral srah sregs def in |
---|
281 | let def ≝ add_epilogue … ret_regs sral srah sregs def in |
---|
282 | def |
---|
283 | ]. |
---|
284 | >def_sra_proof // |
---|
285 | qed. |
---|
286 | |
---|
287 | definition set_params_hdw ≝ |
---|
288 | λglobals,params. |
---|
289 | match params with |
---|
290 | [ nil ⇒ [ λstart_lbl. adds_graph … [joint_st_goto … start_lbl] start_lbl] |
---|
291 | | _ ⇒ |
---|
292 | let l ≝ zip_pottier ? ? params RegisterParams in |
---|
293 | restore_hdws globals l |
---|
294 | ]. |
---|
295 | |
---|
296 | definition set_param_stack ≝ |
---|
297 | λoff. |
---|
298 | λsrcr. |
---|
299 | λstart_lbl: label. |
---|
300 | λdest_lbl: label. |
---|
301 | λdef: ertl_internal_function. |
---|
302 | let 〈def, addr1〉 ≝ fresh_reg def in |
---|
303 | let 〈def, addr2〉 ≝ fresh_reg def in |
---|
304 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
305 | let 〈ignore, int_off〉 ≝ half_add ? off int_size in |
---|
306 | adds_graph [ |
---|
307 | ertl_st_int addr1 int_off start_lbl; |
---|
308 | ertl_st_get_hdw tmpr RegisterSPL start_lbl; |
---|
309 | ertl_st_clear_carry start_lbl; |
---|
310 | ertl_st_op2 Sub addr1 tmpr addr1 start_lbl; |
---|
311 | ertl_st_get_hdw tmpr RegisterSPH start_lbl; |
---|
312 | ertl_st_int addr2 (zero ?) start_lbl; |
---|
313 | ertl_st_op2 Sub addr2 tmpr addr2 start_lbl; |
---|
314 | ertl_st_store addr1 addr2 srcr start_lbl |
---|
315 | ] start_lbl dest_lbl def. |
---|
316 | |
---|
317 | definition set_params_stack ≝ |
---|
318 | λparams. |
---|
319 | match params with |
---|
320 | [ nil ⇒ [ λstart_lbl. adds_graph [ertl_st_skip start_lbl] start_lbl] |
---|
321 | | _ ⇒ |
---|
322 | let f ≝ λi. λr. set_param_stack (bitvector_of_nat ? i) r in |
---|
323 | mapi ? ? f params |
---|
324 | ]. |
---|
325 | |
---|
326 | axiom min_fst: |
---|
327 | ∀m, n: nat. |
---|
328 | min m n ≤ m. |
---|
329 | |
---|
330 | definition set_params ≝ |
---|
331 | λparams. |
---|
332 | let n ≝ min (|params|) (|RegisterParams|) in |
---|
333 | let hdw_stack_params ≝ split ? params n ? in |
---|
334 | let hdw_params ≝ \fst hdw_stack_params in |
---|
335 | let stack_params ≝ \snd hdw_stack_params in |
---|
336 | set_params_hdw hdw_params @ set_params_stack stack_params. |
---|
337 | @min_fst |
---|
338 | qed. |
---|
339 | |
---|
340 | definition fetch_result ≝ |
---|
341 | λret_regs. |
---|
342 | λstart_lbl: label. |
---|
343 | match reduce_strong ? ? RegisterSTS RegisterRets with |
---|
344 | [ dp crl first_crl_proof ⇒ |
---|
345 | let commonl ≝ \fst (\fst crl) in |
---|
346 | let commonr ≝ \fst (\snd crl) in |
---|
347 | let f_save ≝ λst. λret. ertl_st_hdw_to_hdw st ret start_lbl in |
---|
348 | let saves ≝ map2 ? ? ? f_save commonl commonr ? in |
---|
349 | match reduce_strong ? ? ret_regs RegisterSTS with |
---|
350 | [ dp crl second_crl_proof ⇒ |
---|
351 | let commonl ≝ \fst (\fst crl) in |
---|
352 | let commonr ≝ \fst (\snd crl) in |
---|
353 | let f_restore ≝ λr. λst. ertl_st_get_hdw r st start_lbl in |
---|
354 | let restores ≝ map2 ? ? ? f_restore commonl commonr ? in |
---|
355 | adds_graph (saves @ restores) start_lbl |
---|
356 | ] |
---|
357 | ]. |
---|
358 | [ normalize nodelta; @second_crl_proof |
---|
359 | | @first_crl_proof |
---|
360 | ] |
---|
361 | qed. |
---|
362 | |
---|
363 | definition translate_call_id ≝ |
---|
364 | λf. |
---|
365 | λargs. |
---|
366 | λret_regs. |
---|
367 | λstart_lbl. |
---|
368 | λdest_lbl. |
---|
369 | λdef. |
---|
370 | let nb_args ≝ |args| in |
---|
371 | add_translates ( |
---|
372 | set_params args @ [ |
---|
373 | adds_graph [ ertl_st_call_id f nb_args start_lbl ]; |
---|
374 | fetch_result ret_regs |
---|
375 | ] |
---|
376 | ) start_lbl dest_lbl def. |
---|
377 | |
---|
378 | definition translate_stmt ≝ |
---|
379 | λlbl. |
---|
380 | λstmt. |
---|
381 | λdef. |
---|
382 | match stmt with |
---|
383 | [ rtl_st_skip lbl' ⇒ add_graph lbl (ertl_st_skip lbl') def |
---|
384 | | rtl_st_cost cost_lbl lbl' ⇒ add_graph lbl (ertl_st_cost cost_lbl lbl') def |
---|
385 | | rtl_st_addr r1 r2 x lbl' ⇒ add_graph lbl (ertl_st_addr r1 r2 x lbl') def |
---|
386 | | rtl_st_stack_addr r1 r2 lbl' ⇒ |
---|
387 | adds_graph [ |
---|
388 | ertl_st_get_hdw r1 RegisterSPL lbl; |
---|
389 | ertl_st_get_hdw r2 RegisterSPH lbl |
---|
390 | ] lbl lbl' def |
---|
391 | | rtl_st_int r i lbl' ⇒ add_graph lbl (ertl_st_int r i lbl') def |
---|
392 | | rtl_st_move r1 r2 lbl' ⇒ add_graph lbl (ertl_st_move r1 r2 lbl') def |
---|
393 | | rtl_st_opaccs op destr1 destr2 srcr1 srcr2 lbl' ⇒ |
---|
394 | add_graph lbl (ertl_st_opaccs op destr1 destr2 srcr1 srcr2 lbl) def |
---|
395 | (* XXX: change from o'caml |
---|
396 | adds_graph [ |
---|
397 | ertl_st_opaccs_a op destr1 srcr1 srcr2 lbl; |
---|
398 | ertl_st_opaccs_b op destr2 srcr1 srcr2 lbl |
---|
399 | ] lbl lbl' def |
---|
400 | *) |
---|
401 | | rtl_st_op1 op1 destr srcr lbl' ⇒ |
---|
402 | add_graph lbl (ertl_st_op1 op1 destr srcr lbl') def |
---|
403 | | rtl_st_op2 op2 destr srcr1 srcr2 lbl' ⇒ |
---|
404 | add_graph lbl (ertl_st_op2 op2 destr srcr1 srcr2 lbl') def |
---|
405 | | rtl_st_clear_carry lbl' ⇒ |
---|
406 | add_graph lbl (ertl_st_clear_carry lbl') def |
---|
407 | | rtl_st_set_carry lbl' ⇒ |
---|
408 | add_graph lbl (ertl_st_set_carry lbl') def |
---|
409 | | rtl_st_load destr addr1 addr2 lbl' ⇒ |
---|
410 | add_graph lbl (ertl_st_load destr addr1 addr2 lbl') def |
---|
411 | | rtl_st_store addr1 addr2 srcr lbl' ⇒ |
---|
412 | add_graph lbl (ertl_st_store addr1 addr2 srcr lbl') def |
---|
413 | | rtl_st_call_id f args ret_regs lbl' ⇒ |
---|
414 | translate_call_id f args ret_regs lbl lbl' def |
---|
415 | | rtl_st_cond srcr lbl_true lbl_false ⇒ |
---|
416 | add_graph lbl (ertl_st_cond srcr lbl_true lbl_false) def |
---|
417 | | rtl_st_return ⇒ |
---|
418 | add_graph lbl ertl_st_return def |
---|
419 | | _ ⇒ ? (* assert false: not implemented or should not happen *) |
---|
420 | ]. |
---|
421 | cases not_implemented |
---|
422 | qed. |
---|
423 | |
---|
424 | (* hack with empty graphs used here *) |
---|
425 | definition translate_funct_internal ≝ |
---|
426 | λdef. |
---|
427 | let nb_params ≝ |rtl_if_params def| in |
---|
428 | let added_stacksize ≝ max 0 (nb_params - |RegisterParams|) in |
---|
429 | let new_locals ≝ nub_by ? (eq_identifier ?) ((rtl_if_locals def) @ (rtl_if_params def)) in |
---|
430 | let entry' ≝ rtl_if_entry def in |
---|
431 | let exit' ≝ rtl_if_exit def in |
---|
432 | let graph' ≝ add ? ? (empty_map ? ?) entry' (ertl_st_skip entry') in |
---|
433 | let graph' ≝ add ? ? graph' exit' (ertl_st_skip exit') in |
---|
434 | let def' ≝ |
---|
435 | mk_ertl_internal_function |
---|
436 | (rtl_if_luniverse def) (rtl_if_runiverse def) |
---|
437 | nb_params new_locals ((rtl_if_stacksize def) + added_stacksize) |
---|
438 | graph' ? ? in |
---|
439 | let def' ≝ foldi ? ? ? translate_stmt (rtl_if_graph def) def' in |
---|
440 | let def' ≝ add_pro_and_epilogue (rtl_if_params def) (rtl_if_result def) def' in |
---|
441 | def'. |
---|
442 | [1: % |
---|
443 | [1: @entry' |
---|
444 | |2: normalize nodelta |
---|
445 | @graph_add_lookup |
---|
446 | @graph_add |
---|
447 | ] |
---|
448 | |2: % |
---|
449 | [1: @exit' |
---|
450 | |2: normalize nodelta |
---|
451 | @graph_add |
---|
452 | ] |
---|
453 | ] |
---|
454 | qed. |
---|
455 | |
---|
456 | definition translate_funct ≝ |
---|
457 | λid_def: ident × ?. |
---|
458 | let 〈id, def〉 ≝ id_def in |
---|
459 | let def' ≝ |
---|
460 | match def with |
---|
461 | [ Internal def ⇒ Internal ? (translate_funct_internal def) |
---|
462 | | External def ⇒ External ? def |
---|
463 | ] in |
---|
464 | 〈id, def'〉. |
---|
465 | |
---|
466 | definition generate ≝ |
---|
467 | λstmt. |
---|
468 | λdef. |
---|
469 | let 〈entry, nuniv〉 ≝ fresh_label def in |
---|
470 | let graph ≝ add ? ? (ertl_if_graph def) entry stmt in |
---|
471 | mk_ertl_internal_function |
---|
472 | nuniv (ertl_if_runiverse def) (ertl_if_params def) |
---|
473 | (ertl_if_locals def) (ertl_if_stacksize def) graph |
---|
474 | ? ?. |
---|
475 | [1: % |
---|
476 | [1: @entry |
---|
477 | |2: normalize nodelta; |
---|
478 | @graph_add |
---|
479 | ] |
---|
480 | |2: generalize in match (ertl_if_exit def) |
---|
481 | #HYP |
---|
482 | cases HYP |
---|
483 | #LBL #LBL_PRF |
---|
484 | % |
---|
485 | [1: @LBL |
---|
486 | |2: normalize nodelta; |
---|
487 | @graph_add_lookup |
---|
488 | @LBL_PRF |
---|
489 | ] |
---|
490 | ] |
---|
491 | qed. |
---|
492 | |
---|
493 | let rec find_and_remove_first_cost_label_internal |
---|
494 | (def: ertl_internal_function) (lbl: label) (num_nodes: nat) |
---|
495 | on num_nodes ≝ |
---|
496 | match num_nodes with |
---|
497 | [ O ⇒ 〈None ?, def〉 |
---|
498 | | S num_nodes' ⇒ |
---|
499 | match lookup ? ? (ertl_if_graph def) lbl with |
---|
500 | [ None ⇒ 〈None ?, def〉 |
---|
501 | | Some stmt ⇒ |
---|
502 | match stmt with |
---|
503 | [ ertl_st_cost cost_lbl next_lbl ⇒ |
---|
504 | 〈Some ? cost_lbl, add_graph lbl (ertl_st_skip next_lbl) def〉 |
---|
505 | | ertl_st_cond _ _ _ ⇒ 〈None ?, def〉 |
---|
506 | | ertl_st_return ⇒ 〈None ?, def〉 |
---|
507 | | ertl_st_skip lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
508 | | ertl_st_comment _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
509 | | ertl_st_get_hdw _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
510 | | ertl_st_set_hdw _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
511 | | ertl_st_hdw_to_hdw _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
512 | | ertl_st_pop _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
513 | | ertl_st_push _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
514 | | ertl_st_addr _ _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
515 | | ertl_st_int _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
516 | | ertl_st_move _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
517 | | ertl_st_opaccs _ _ _ _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
518 | | ertl_st_op1 _ _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
519 | | ertl_st_op2 _ _ _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
520 | | ertl_st_clear_carry lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
521 | | ertl_st_set_carry lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
522 | | ertl_st_load _ _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
523 | | ertl_st_store _ _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
524 | | ertl_st_call_id _ _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
525 | | ertl_st_new_frame lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
526 | | ertl_st_del_frame lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
527 | | ertl_st_frame_size _ lbl ⇒ find_and_remove_first_cost_label_internal def lbl num_nodes' |
---|
528 | ] |
---|
529 | ] |
---|
530 | ]. |
---|
531 | |
---|
532 | definition find_and_remove_first_cost_label ≝ |
---|
533 | λdef. |
---|
534 | find_and_remove_first_cost_label_internal def (ertl_if_entry def) (graph_num_nodes ? (ertl_if_graph def)). |
---|
535 | |
---|
536 | definition move_first_cost_label_up_internal ≝ |
---|
537 | λdef. |
---|
538 | let 〈cost_label, def〉 ≝ find_and_remove_first_cost_label def in |
---|
539 | match cost_label with |
---|
540 | [ None ⇒ def |
---|
541 | | Some cost_label ⇒ generate (ertl_st_cost cost_label (ertl_if_entry def)) def |
---|
542 | ]. |
---|
543 | |
---|
544 | definition move_first_cost_label_up ≝ |
---|
545 | λA: Type[0]. |
---|
546 | λid_def: A × ?. |
---|
547 | let 〈id, def〉 ≝ id_def in |
---|
548 | let def' ≝ |
---|
549 | match def with |
---|
550 | [ Internal int_fun ⇒ Internal ? (move_first_cost_label_up_internal int_fun) |
---|
551 | | External ext ⇒ def |
---|
552 | ] |
---|
553 | in |
---|
554 | 〈id, def'〉. |
---|
555 | |
---|
556 | definition translate ≝ |
---|
557 | λp. |
---|
558 | let p ≝ tailcall_simplify p in (* tailcall simplification here *) |
---|
559 | let f ≝ λfunct. move_first_cost_label_up ? (translate_funct funct) in |
---|
560 | let vars ≝ map ? ? f (rtl_pr_functs p) in |
---|
561 | mk_ertl_program (rtl_pr_vars p) vars (rtl_pr_main p). |
---|