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Status.ma @ 844

Last change on this file since 844 was 843, checked in by sacerdot, 10 years ago
Function moved from Interpret to Status.
File size: 36.1 KB

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1	(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
2	(* Interpret.ma: Operational semantics for the 8051/8052 processor. *)
3	(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
4
5	include "ASM/ASM.ma".
6	include "ASM/Arithmetic.ma".
7	include "ASM/BitVectorTrie.ma".
8
9	definition Time ≝ nat.
10
11	inductive SerialBufferType: Type[0] ≝
12	Eight: Byte → SerialBufferType
13	\| Nine: Bit → Byte → SerialBufferType.
14
15	inductive LineType: Type[0] ≝
16	P1: Byte → LineType
17	\| P3: Byte → LineType
18	\| SerialBuffer: SerialBufferType → LineType.
19
20	(* What is a continuation, now? *)
21
22	inductive SFR8051: Type[0] ≝
23	SFR_SP: SFR8051
24	\| SFR_DPL: SFR8051
25	\| SFR_DPH: SFR8051
26	\| SFR_PCON: SFR8051
27	\| SFR_TCON: SFR8051
28	\| SFR_TMOD: SFR8051
29	\| SFR_TL0: SFR8051
30	\| SFR_TL1: SFR8051
31	\| SFR_TH0: SFR8051
32	\| SFR_TH1: SFR8051
33	\| SFR_P1: SFR8051
34	\| SFR_SCON: SFR8051
35	\| SFR_SBUF: SFR8051
36	\| SFR_IE: SFR8051
37	\| SFR_P3: SFR8051
38	\| SFR_IP: SFR8051
39	\| SFR_PSW: SFR8051
40	\| SFR_ACC_A: SFR8051
41	\| SFR_ACC_B: SFR8051.
42
43	definition sfr_8051_index ≝
44	λs: SFR8051.
45	match s with
46	[ SFR_SP ⇒ O
47	\| SFR_DPL ⇒ 1
48	\| SFR_DPH ⇒ 2
49	\| SFR_PCON ⇒ 3
50	\| SFR_TCON ⇒ 4
51	\| SFR_TMOD ⇒ 5
52	\| SFR_TL0 ⇒ 6
53	\| SFR_TL1 ⇒ 7
54	\| SFR_TH0 ⇒ 8
55	\| SFR_TH1 ⇒ 9
56	\| SFR_P1 ⇒ 10
57	\| SFR_SCON ⇒ 11
58	\| SFR_SBUF ⇒ 12
59	\| SFR_IE ⇒ 13
60	\| SFR_P3 ⇒ 14
61	\| SFR_IP ⇒ 15
62	\| SFR_PSW ⇒ 16
63	\| SFR_ACC_A ⇒ 17
64	\| SFR_ACC_B ⇒ 18
65	].
66
67	inductive SFR8052: Type[0] ≝
68	SFR_T2CON: SFR8052
69	\| SFR_RCAP2L: SFR8052
70	\| SFR_RCAP2H: SFR8052
71	\| SFR_TL2: SFR8052
72	\| SFR_TH2: SFR8052.
73
74	definition sfr_8052_index ≝
75	λs: SFR8052.
76	match s with
77	[ SFR_T2CON ⇒ O
78	\| SFR_RCAP2L ⇒ 1
79	\| SFR_RCAP2H ⇒ 2
80	\| SFR_TL2 ⇒ 3
81	\| SFR_TH2 ⇒ 4
82	].
83
84	(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
85	(* Processor status. *)
86	(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
87	record PreStatus (M: Type[0]): Type[0] ≝
88	{
89	code_memory: M;
90	low_internal_ram: BitVectorTrie Byte 7;
91	high_internal_ram: BitVectorTrie Byte 7;
92	external_ram: BitVectorTrie Byte 16;
93
94	program_counter: Word;
95
96	special_function_registers_8051: Vector Byte 19;
97	special_function_registers_8052: Vector Byte 5;
98
99	p1_latch: Byte;
100	p3_latch: Byte;
101
102	clock: Time
103	}.
104
105	definition Status ≝ PreStatus (BitVectorTrie Byte 16).
106	definition PseudoStatus ≝ PreStatus (pseudo_assembly_program).
107
108	lemma sfr8051_index_19:
109	∀i: SFR8051.
110	sfr_8051_index i < 19.
111	# i
112	cases i
113	normalize
114	repeat (@ le_S_S)
115	@ le_O_n
116	qed.
117
118	lemma sfr8052_index_5:
119	∀i: SFR8052.
120	sfr_8052_index i < 5.
121	# i
122	cases i
123	normalize
124	repeat (@ le_S_S)
125	@ le_O_n
126	qed.
127
128	definition set_clock ≝
129	λM: Type[0].
130	λs: PreStatus M.
131	λt: Time.
132	let old_code_memory ≝ code_memory ? s in
133	let old_low_internal_ram ≝ low_internal_ram ? s in
134	let old_high_internal_ram ≝ high_internal_ram ? s in
135	let old_external_ram ≝ external_ram ? s in
136	let old_program_counter ≝ program_counter ? s in
137	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
138	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
139	let old_p1_latch ≝ p1_latch ? s in
140	let old_p3_latch ≝ p3_latch ? s in
141	mk_PreStatus M old_code_memory
142	old_low_internal_ram
143	old_high_internal_ram
144	old_external_ram
145	old_program_counter
146	old_special_function_registers_8051
147	old_special_function_registers_8052
148	old_p1_latch
149	old_p3_latch
150	t.
151
152	definition set_p1_latch ≝
153	λM: Type[0].
154	λs: PreStatus M.
155	λb: Byte.
156	let old_code_memory ≝ code_memory ? s in
157	let old_low_internal_ram ≝ low_internal_ram ? s in
158	let old_high_internal_ram ≝ high_internal_ram ? s in
159	let old_external_ram ≝ external_ram ? s in
160	let old_program_counter ≝ program_counter ? s in
161	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
162	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
163	let old_p3_latch ≝ p3_latch ? s in
164	let old_clock ≝ clock ? s in
165	mk_PreStatus M old_code_memory
166	old_low_internal_ram
167	old_high_internal_ram
168	old_external_ram
169	old_program_counter
170	old_special_function_registers_8051
171	old_special_function_registers_8052
172	b
173	old_p3_latch
174	old_clock.
175
176	definition set_p3_latch ≝
177	λM: Type[0].
178	λs: PreStatus M.
179	λb: Byte.
180	let old_code_memory ≝ code_memory ? s in
181	let old_low_internal_ram ≝ low_internal_ram ? s in
182	let old_high_internal_ram ≝ high_internal_ram ? s in
183	let old_external_ram ≝ external_ram ? s in
184	let old_program_counter ≝ program_counter ? s in
185	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
186	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
187	let old_p1_latch ≝ p1_latch ? s in
188	let old_clock ≝ clock ? s in
189	mk_PreStatus M old_code_memory
190	old_low_internal_ram
191	old_high_internal_ram
192	old_external_ram
193	old_program_counter
194	old_special_function_registers_8051
195	old_special_function_registers_8052
196	old_p1_latch
197	b
198	old_clock.
199
200	definition get_8051_sfr ≝
201	λM: Type[0].
202	λs: PreStatus M.
203	λi: SFR8051.
204	let sfr ≝ special_function_registers_8051 ? s in
205	let index ≝ sfr_8051_index i in
206	get_index_v … sfr index ?.
207	@ sfr8051_index_19
208	qed.
209
210	definition get_8052_sfr ≝
211	λM: Type[0].
212	λs: PreStatus M.
213	λi: SFR8052.
214	let sfr ≝ special_function_registers_8052 ? s in
215	let index ≝ sfr_8052_index i in
216	get_index_v … sfr index ?.
217	@ sfr8052_index_5
218	qed.
219
220	definition set_8051_sfr ≝
221	λM: Type[0].
222	λs: PreStatus M.
223	λi: SFR8051.
224	λb: Byte.
225	let index ≝ sfr_8051_index i in
226	let old_code_memory ≝ code_memory ? s in
227	let old_low_internal_ram ≝ low_internal_ram ? s in
228	let old_high_internal_ram ≝ high_internal_ram ? s in
229	let old_external_ram ≝ external_ram ? s in
230	let old_program_counter ≝ program_counter ? s in
231	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
232	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
233	let new_special_function_registers_8051 ≝
234	set_index Byte 19 old_special_function_registers_8051 index b ? in
235	let old_p1_latch ≝ p1_latch ? s in
236	let old_p3_latch ≝ p3_latch ? s in
237	let old_clock ≝ clock ? s in
238	mk_PreStatus M old_code_memory
239	old_low_internal_ram
240	old_high_internal_ram
241	old_external_ram
242	old_program_counter
243	new_special_function_registers_8051
244	old_special_function_registers_8052
245	old_p1_latch
246	old_p3_latch
247	old_clock.
248	@ (sfr8051_index_19 i)
249	qed.
250
251	definition set_8052_sfr ≝
252	λM: Type[0].
253	λs: PreStatus M.
254	λi: SFR8052.
255	λb: Byte.
256	let index ≝ sfr_8052_index i in
257	let old_code_memory ≝ code_memory ? s in
258	let old_low_internal_ram ≝ low_internal_ram ? s in
259	let old_high_internal_ram ≝ high_internal_ram ? s in
260	let old_external_ram ≝ external_ram ? s in
261	let old_program_counter ≝ program_counter ? s in
262	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
263	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
264	let new_special_function_registers_8052 ≝
265	set_index Byte 5 old_special_function_registers_8052 index b ? in
266	let old_p1_latch ≝ p1_latch ? s in
267	let old_p3_latch ≝ p3_latch ? s in
268	let old_clock ≝ clock ? s in
269	mk_PreStatus M old_code_memory
270	old_low_internal_ram
271	old_high_internal_ram
272	old_external_ram
273	old_program_counter
274	old_special_function_registers_8051
275	new_special_function_registers_8052
276	old_p1_latch
277	old_p3_latch
278	old_clock.
279	@ (sfr8052_index_5 i)
280	qed.
281
282	definition set_program_counter ≝
283	λM: Type[0].
284	λs: PreStatus M.
285	λw: Word.
286	let old_code_memory ≝ code_memory ? s in
287	let old_low_internal_ram ≝ low_internal_ram ? s in
288	let old_high_internal_ram ≝ high_internal_ram ? s in
289	let old_external_ram ≝ external_ram ? s in
290	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
291	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
292	let old_p1_latch ≝ p1_latch ? s in
293	let old_p3_latch ≝ p3_latch ? s in
294	let old_clock ≝ clock ? s in
295	mk_PreStatus M old_code_memory
296	old_low_internal_ram
297	old_high_internal_ram
298	old_external_ram
299	w
300	old_special_function_registers_8051
301	old_special_function_registers_8052
302	old_p1_latch
303	old_p3_latch
304	old_clock.
305
306	definition set_code_memory ≝
307	λM: Type[0].
308	λs: PreStatus M.
309	λr: M.
310	let old_low_internal_ram ≝ low_internal_ram ? s in
311	let old_high_internal_ram ≝ high_internal_ram ? s in
312	let old_external_ram ≝ external_ram ? s in
313	let old_program_counter ≝ program_counter ? s in
314	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
315	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
316	let old_p1_latch ≝ p1_latch ? s in
317	let old_p3_latch ≝ p3_latch ? s in
318	let old_clock ≝ clock ? s in
319	mk_PreStatus M r
320	old_low_internal_ram
321	old_high_internal_ram
322	old_external_ram
323	old_program_counter
324	old_special_function_registers_8051
325	old_special_function_registers_8052
326	old_p1_latch
327	old_p3_latch
328	old_clock.
329
330	definition set_low_internal_ram ≝
331	λM: Type[0].
332	λs: PreStatus M.
333	λr: BitVectorTrie Byte 7.
334	let old_code_memory ≝ code_memory ? s in
335	let old_high_internal_ram ≝ high_internal_ram ? s in
336	let old_external_ram ≝ external_ram ? s in
337	let old_program_counter ≝ program_counter ? s in
338	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
339	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
340	let old_p1_latch ≝ p1_latch ? s in
341	let old_p3_latch ≝ p3_latch ? s in
342	let old_clock ≝ clock ? s in
343	mk_PreStatus M old_code_memory
344	r
345	old_high_internal_ram
346	old_external_ram
347	old_program_counter
348	old_special_function_registers_8051
349	old_special_function_registers_8052
350	old_p1_latch
351	old_p3_latch
352	old_clock.
353
354	definition set_high_internal_ram ≝
355	λM: Type[0].
356	λs: PreStatus M.
357	λr: BitVectorTrie Byte 7.
358	let old_code_memory ≝ code_memory ? s in
359	let old_low_internal_ram ≝ low_internal_ram ? s in
360	let old_high_internal_ram ≝ high_internal_ram ? s in
361	let old_external_ram ≝ external_ram ? s in
362	let old_program_counter ≝ program_counter ? s in
363	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
364	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
365	let old_p1_latch ≝ p1_latch ? s in
366	let old_p3_latch ≝ p3_latch ? s in
367	let old_clock ≝ clock ? s in
368	mk_PreStatus M old_code_memory
369	old_low_internal_ram
370	r
371	old_external_ram
372	old_program_counter
373	old_special_function_registers_8051
374	old_special_function_registers_8052
375	old_p1_latch
376	old_p3_latch
377	old_clock.
378
379	definition set_external_ram ≝
380	λM: Type[0].
381	λs: PreStatus M.
382	λr: BitVectorTrie Byte 16.
383	let old_code_memory ≝ code_memory ? s in
384	let old_low_internal_ram ≝ low_internal_ram ? s in
385	let old_high_internal_ram ≝ high_internal_ram ? s in
386	let old_program_counter ≝ program_counter ? s in
387	let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in
388	let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in
389	let old_p1_latch ≝ p1_latch ? s in
390	let old_p3_latch ≝ p3_latch ? s in
391	let old_clock ≝ clock ? s in
392	mk_PreStatus M old_code_memory
393	old_low_internal_ram
394	old_high_internal_ram
395	r
396	old_program_counter
397	old_special_function_registers_8051
398	old_special_function_registers_8052
399	old_p1_latch
400	old_p3_latch
401	old_clock.
402
403	definition get_cy_flag ≝
404	λM: Type[0].
405	λs: PreStatus M.
406	let sfr ≝ special_function_registers_8051 ? s in
407	let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in
408	get_index_v bool 8 psw O ?.
409	normalize
410	@ (le_S_S ? ?)
411	[ @ le_O_n
412	\| repeat (@ (le_S_S));
413	//
414	]
415	qed.
416
417	definition get_ac_flag ≝
418	λM: Type[0].
419	λs: PreStatus M.
420	let sfr ≝ special_function_registers_8051 ? s in
421	let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in
422	get_index_v bool 8 psw (S O) ?.
423	normalize
424	repeat (@ (le_S_S ? ?))
425	@ le_O_n
426	qed.
427
428	definition get_fo_flag ≝
429	λM: Type[0].
430	λs: PreStatus M.
431	let sfr ≝ special_function_registers_8051 ? s in
432	let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in
433	get_index_v bool 8 psw 2 ?.
434	normalize
435	repeat (@ (le_S_S ? ?))
436	@ le_O_n
437	qed.
438
439	definition get_rs1_flag ≝
440	λM: Type[0].
441	λs: PreStatus M.
442	let sfr ≝ special_function_registers_8051 ? s in
443	let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in
444	get_index_v bool 8 psw 3 ?.
445	normalize
446	repeat (@ (le_S_S ? ?))
447	@ le_O_n
448	qed.
449
450	definition get_rs0_flag ≝
451	λM: Type[0].
452	λs: PreStatus M.
453	let sfr ≝ special_function_registers_8051 ? s in
454	let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in
455	get_index_v bool 8 psw 4 ?.
456	normalize
457	repeat (@ (le_S_S ? ?))
458	@ le_O_n
459	qed.
460
461	definition get_ov_flag ≝
462	λM: Type[0].
463	λs: PreStatus M.
464	let sfr ≝ special_function_registers_8051 ? s in
465	let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in
466	get_index_v bool 8 psw 5 ?.
467	normalize
468	repeat (@ (le_S_S ? ?))
469	@ le_O_n
470	qed.
471
472	definition get_ud_flag ≝
473	λM: Type[0].
474	λs: PreStatus M.
475	let sfr ≝ special_function_registers_8051 ? s in
476	let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in
477	get_index_v bool 8 psw 6 ?.
478	normalize
479	repeat (@ (le_S_S ? ?))
480	@ le_O_n
481	qed.
482
483	definition get_p_flag ≝
484	λM: Type[0].
485	λs: PreStatus M.
486	let sfr ≝ special_function_registers_8051 ? s in
487	let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in
488	get_index_v bool 8 psw 7 ?.
489	normalize
490	repeat (@ (le_S_S ? ?))
491	@ le_O_n
492	qed.
493
494	definition set_flags ≝
495	λM: Type[0].
496	λs: PreStatus M.
497	λcy: Bit.
498	λac: option Bit.
499	λov: Bit.
500	let 〈 nu, nl 〉 ≝ split … 4 4 (get_8051_sfr ? s SFR_PSW) in
501	let old_cy ≝ get_index_v… nu O ? in
502	let old_ac ≝ get_index_v… nu 1 ? in
503	let old_fo ≝ get_index_v… nu 2 ? in
504	let old_rs1 ≝ get_index_v… nu 3 ? in
505	let old_rs0 ≝ get_index_v… nl O ? in
506	let old_ov ≝ get_index_v… nl 1 ? in
507	let old_ud ≝ get_index_v… nl 2 ? in
508	let old_p ≝ get_index_v… nl 3 ? in
509	let new_ac ≝ match ac with [ None ⇒ old_ac \| Some j ⇒ j ] in
510	let new_psw ≝ [[ old_cy ; new_ac ; old_fo ; old_rs1 ;
511	old_rs0 ; old_ov ; old_ud ; old_p ]] in
512	set_8051_sfr ? s SFR_PSW new_psw.
513	[1,2,3,4,5,6,7,8:
514	normalize
515	repeat (@ le_S_S)
516	@ le_O_n
517	]
518	qed.
519
520	definition initialise_status ≝
521	λM: Type[0].
522	λcode_mem: M.
523	let status ≝ mk_PreStatus M code_mem (* Code mem. *)
524	(Stub Byte 7) (* Low mem. *)
525	(Stub Byte 7) (* High mem. *)
526	(Stub Byte 16) (* Ext mem. *)
527	(zero 16) (* PC. *)
528	(replicate Byte 19 (zero 8)) (* 8051 SFR. *)
529	(replicate Byte 5 (zero 8)) (* 8052 SFR. *)
530	(zero 8) (* P1 latch. *)
531	(zero 8) (* P3 latch. *)
532	O (* Clock. *)
533	in
534	set_8051_sfr ? status SFR_SP (bitvector_of_nat 8 7).
535
536	axiom not_implemented: False.
537
538	definition get_bit_addressable_sfr ≝
539	λM: Type[0].
540	λs: PreStatus M.
541	λn: nat.
542	λb: BitVector n.
543	λl: bool.
544	let address ≝ nat_of_bitvector … b in
545	if (eqb address 128) then
546	?
547	else if (eqb address 144) then
548	if l then
549	(p1_latch ? s)
550	else
551	(get_8051_sfr ? s SFR_P1)
552	else if (eqb address 160) then
553	?
554	else if (eqb address 176) then
555	if l then
556	(p3_latch ? s)
557	else
558	(get_8051_sfr ? s SFR_P3)
559	else if (eqb address 153) then
560	get_8051_sfr ? s SFR_SBUF
561	else if (eqb address 138) then
562	get_8051_sfr ? s SFR_TL0
563	else if (eqb address 139) then
564	get_8051_sfr ? s SFR_TL1
565	else if (eqb address 140) then
566	get_8051_sfr ? s SFR_TH0
567	else if (eqb address 141) then
568	get_8051_sfr ? s SFR_TH1
569	else if (eqb address 200) then
570	get_8052_sfr ? s SFR_T2CON
571	else if (eqb address 202) then
572	get_8052_sfr ? s SFR_RCAP2L
573	else if (eqb address 203) then
574	get_8052_sfr ? s SFR_RCAP2H
575	else if (eqb address 204) then
576	get_8052_sfr ? s SFR_TL2
577	else if (eqb address 205) then
578	get_8052_sfr ? s SFR_TH2
579	else if (eqb address 135) then
580	get_8051_sfr ? s SFR_PCON
581	else if (eqb address 136) then
582	get_8051_sfr ? s SFR_TCON
583	else if (eqb address 137) then
584	get_8051_sfr ? s SFR_TMOD
585	else if (eqb address 152) then
586	get_8051_sfr ? s SFR_SCON
587	else if (eqb address 168) then
588	get_8051_sfr ? s SFR_IE
589	else if (eqb address 184) then
590	get_8051_sfr ? s SFR_IP
591	else if (eqb address 129) then
592	get_8051_sfr ? s SFR_SP
593	else if (eqb address 130) then
594	get_8051_sfr ? s SFR_DPL
595	else if (eqb address 131) then
596	get_8051_sfr ? s SFR_DPH
597	else if (eqb address 208) then
598	get_8051_sfr ? s SFR_PSW
599	else if (eqb address 224) then
600	get_8051_sfr ? s SFR_ACC_A
601	else if (eqb address 240) then
602	get_8051_sfr ? s SFR_ACC_B
603	else
604	?.
605	cases not_implemented
606	qed.
607
608	definition set_bit_addressable_sfr ≝
609	λM: Type[0].
610	λs: PreStatus M.
611	λb: Byte.
612	λv: Byte.
613	let address ≝ nat_of_bitvector … b in
614	if (eqb address 128) then
615	?
616	else if (eqb address 144) then
617	let status_1 ≝ set_8051_sfr ? s SFR_P1 v in
618	let status_2 ≝ set_p1_latch ? s v in
619	status_2
620	else if (eqb address 160) then
621	?
622	else if (eqb address 176) then
623	let status_1 ≝ set_8051_sfr ? s SFR_P3 v in
624	let status_2 ≝ set_p3_latch ? s v in
625	status_2
626	else if (eqb address 153) then
627	set_8051_sfr ? s SFR_SBUF v
628	else if (eqb address 138) then
629	set_8051_sfr ? s SFR_TL0 v
630	else if (eqb address 139) then
631	set_8051_sfr ? s SFR_TL1 v
632	else if (eqb address 140) then
633	set_8051_sfr ? s SFR_TH0 v
634	else if (eqb address 141) then
635	set_8051_sfr ? s SFR_TH1 v
636	else if (eqb address 200) then
637	set_8052_sfr ? s SFR_T2CON v
638	else if (eqb address 202) then
639	set_8052_sfr ? s SFR_RCAP2L v
640	else if (eqb address 203) then
641	set_8052_sfr ? s SFR_RCAP2H v
642	else if (eqb address 204) then
643	set_8052_sfr ? s SFR_TL2 v
644	else if (eqb address 205) then
645	set_8052_sfr ? s SFR_TH2 v
646	else if (eqb address 135) then
647	set_8051_sfr ? s SFR_PCON v
648	else if (eqb address 136) then
649	set_8051_sfr ? s SFR_TCON v
650	else if (eqb address 137) then
651	set_8051_sfr ? s SFR_TMOD v
652	else if (eqb address 152) then
653	set_8051_sfr ? s SFR_SCON v
654	else if (eqb address 168) then
655	set_8051_sfr ? s SFR_IE v
656	else if (eqb address 184) then
657	set_8051_sfr ? s SFR_IP v
658	else if (eqb address 129) then
659	set_8051_sfr ? s SFR_SP v
660	else if (eqb address 130) then
661	set_8051_sfr ? s SFR_DPL v
662	else if (eqb address 131) then
663	set_8051_sfr ? s SFR_DPH v
664	else if (eqb address 208) then
665	set_8051_sfr ? s SFR_PSW v
666	else if (eqb address 224) then
667	set_8051_sfr ? s SFR_ACC_A v
668	else if (eqb address 240) then
669	set_8051_sfr ? s SFR_ACC_B v
670	else
671	?.
672	cases not_implemented
673	qed.
674
675	definition bit_address_of_register ≝
676	λM: Type[0].
677	λs: PreStatus M.
678	λr: BitVector 3.
679	let b ≝ get_index_v … r O ? in
680	let c ≝ get_index_v … r 1 ? in
681	let d ≝ get_index_v … r 2 ? in
682	let 〈 un, ln 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_PSW) in
683	let 〈 r1, r0 〉 ≝ 〈 get_index_v … 4 un 2 ?, get_index_v … 4 un 3 ? 〉 in
684	let offset ≝
685	if ¬r1 ∧ ¬r0 then
686	O
687	else if ¬r1 ∧ r0 then
688	8
689	else if r1 ∧ r0 then
690	24
691	else
692	16
693	in
694	bitvector_of_nat 7 (offset + (nat_of_bitvector ? [[ false ; b ; c ; d ]])).
695	[1,2,3,4,5:
696	normalize
697	repeat (@ le_S_S)
698	@ le_O_n;
699	]
700	qed.
701
702	definition get_register ≝
703	λM: Type[0].
704	λs: PreStatus M.
705	λr: BitVector 3.
706	let address ≝ bit_address_of_register ? s r in
707	lookup … address (low_internal_ram ? s) (zero 8).
708
709	definition set_register ≝
710	λM: Type[0].
711	λs: PreStatus M.
712	λr: BitVector 3.
713	λv: Byte.
714	let address ≝ bit_address_of_register ? s r in
715	let old_low_internal_ram ≝ low_internal_ram ? s in
716	let new_low_internal_ram ≝ insert … address v old_low_internal_ram in
717	set_low_internal_ram ? s new_low_internal_ram.
718
719	definition read_at_stack_pointer ≝
720	λM: Type[0].
721	λs: PreStatus M.
722	let 〈 nu, nl 〉 ≝ split … 4 4 (get_8051_sfr ? s SFR_SP) in
723	let m ≝ get_index_v … nu O ? in
724	let r1 ≝ get_index_v … nu 1 ? in
725	let r2 ≝ get_index_v … nu 2 ? in
726	let r3 ≝ get_index_v … nu 3 ? in
727	let address ≝ [[ r1 ; r2 ; r3 ]] @@ nl in
728	let memory ≝
729	if m then
730	(low_internal_ram ? s)
731	else
732	(high_internal_ram ? s)
733	in
734	lookup … address memory (zero 8).
735	[1,2,3,4:
736	normalize
737	repeat (@ le_S_S)
738	@ le_O_n
739	]
740	qed.
741
742	definition write_at_stack_pointer ≝
743	λM: Type[0].
744	λs: PreStatus M.
745	λv: Byte.
746	let 〈 nu, nl 〉 ≝ split … 4 4 (get_8051_sfr ? s SFR_SP) in
747	let bit_zero ≝ get_index_v… nu O ? in
748	let bit_1 ≝ get_index_v… nu 1 ? in
749	let bit_2 ≝ get_index_v… nu 2 ? in
750	let bit_3 ≝ get_index_v… nu 3 ? in
751	if bit_zero then
752	let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl)
753	v (low_internal_ram ? s) in
754	set_low_internal_ram ? s memory
755	else
756	let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl)
757	v (high_internal_ram ? s) in
758	set_high_internal_ram ? s memory.
759	[1,2,3,4:
760	normalize
761	repeat (@ le_S_S)
762	@ le_O_n
763	]
764	qed.
765
766	definition set_arg_16: ∀M: Type[0]. PreStatus M → Word → [[ dptr ]] → PreStatus M ≝
767	λM.
768	λs.
769	λv.
770	λa.
771	match a return λx. bool_to_Prop (is_in ? [[ dptr ]] x) → ? with
772	[ DPTR ⇒ λ_:True.
773	let 〈 bu, bl 〉 ≝ split … 8 8 v in
774	let status ≝ set_8051_sfr ? s SFR_DPH bu in
775	let status ≝ set_8051_sfr ? status SFR_DPL bl in
776	status
777	\| _ ⇒ λK.
778	match K in False with
779	[
780	]
781	] (subaddressing_modein … a).
782
783	definition get_arg_16: ∀M: Type[0]. PreStatus M → [[ data16 ]] → Word ≝
784	λm, s, a.
785	match a return λx. bool_to_Prop (is_in ? [[ data16 ]] x) → ? with
786	[ DATA16 d ⇒ λ_:True. d
787	\| _ ⇒ λK.
788	match K in False with
789	[
790	]
791	] (subaddressing_modein … a).
792
793	definition get_arg_8: ∀M: Type[0]. PreStatus M → bool → [[ direct ; indirect ; registr ;
794	acc_a ; acc_b ; data ; acc_dptr ;
795	acc_pc ; ext_indirect ;
796	ext_indirect_dptr ]] → Byte ≝
797	λm, s, l, a.
798	match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; registr ;
799	acc_a ; acc_b ; data ; acc_dptr ;
800	acc_pc ; ext_indirect ;
801	ext_indirect_dptr ]] x) → ? with
802	[ ACC_A ⇒ λacc_a: True. get_8051_sfr ? s SFR_ACC_A
803	\| ACC_B ⇒ λacc_b: True. get_8051_sfr ? s SFR_ACC_B
804	\| DATA d ⇒ λdata: True. d
805	\| REGISTER r ⇒ λregister: True. get_register ? s r
806	\| EXT_INDIRECT_DPTR ⇒
807	λext_indirect_dptr: True.
808	let address ≝ (get_8051_sfr ? s SFR_DPH) @@ (get_8051_sfr ? s SFR_DPL) in
809	lookup … 16 address (external_ram ? s) (zero 8)
810	\| EXT_INDIRECT e ⇒
811	λext_indirect: True.
812	let address ≝ get_register ? s [[ false; false; e ]] in
813	let padded_address ≝ pad 8 8 address in
814	lookup … 16 padded_address (external_ram ? s) (zero 8)
815	\| ACC_DPTR ⇒
816	λacc_dptr: True.
817	let dptr ≝ (get_8051_sfr ? s SFR_DPH) @@ (get_8051_sfr ? s SFR_DPL) in
818	let padded_acc ≝ pad 8 8 (get_8051_sfr ? s SFR_ACC_A) in
819	let 〈 carry, address 〉 ≝ half_add 16 dptr padded_acc in
820	lookup … 16 address (external_ram ? s) (zero 8)
821	\| ACC_PC ⇒
822	λacc_pc: True.
823	let padded_acc ≝ pad 8 8 (get_8051_sfr ? s SFR_ACC_A) in
824	let 〈 carry, address 〉 ≝ half_add 16 (program_counter ? s) padded_acc in
825	lookup … 16 address (external_ram ? s) (zero 8)
826	\| DIRECT d ⇒
827	λdirect: True.
828	let 〈 nu, nl 〉 ≝ split … 4 4 d in
829	let bit_1 ≝ get_index_v … nu 1 ? in
830	match bit_1 with
831	[ true ⇒
832	let 〈 bit_one, three_bits 〉 ≝ split ? 1 3 nu in
833	let address ≝ three_bits @@ nl in
834	lookup ? 7 address (low_internal_ram ? s) (zero 8)
835	\| false ⇒ get_bit_addressable_sfr ? s 8 d l
836	]
837	\| INDIRECT i ⇒
838	λindirect: True.
839	let 〈 nu, nl 〉 ≝ split ? 4 4 (get_register ? s [[ false; false; i]]) in
840	let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in
841	let bit_1 ≝ get_index_v … bit_one_v O ? in
842	match bit_1 with
843	[ true ⇒
844	lookup ? 7 (three_bits @@ nl) (low_internal_ram ? s) (zero 8)
845	\| false ⇒
846	lookup ? 7 (three_bits @@ nl) (high_internal_ram ? s) (zero 8)
847	]
848	\| _ ⇒ λother.
849	match other in False with [ ]
850	] (subaddressing_modein … a).
851	[1,2:
852	normalize
853	repeat (@ le_S_S)
854	@ le_O_n
855	]
856	qed.
857
858	definition set_arg_8: ∀M: Type[0]. PreStatus M → [[ direct ; indirect ; registr ;
859	acc_a ; acc_b ; ext_indirect ;
860	ext_indirect_dptr ]] → Byte → PreStatus M ≝
861	λm, s, a, v.
862	match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; registr ;
863	acc_a ; acc_b ; ext_indirect ;
864	ext_indirect_dptr ]] x) → ? with
865	[ DIRECT d ⇒
866	λdirect: True.
867	let 〈 nu, nl 〉 ≝ split … 4 4 d in
868	let bit_1 ≝ get_index_v … nu 1 ? in
869	let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in
870	match bit_1 with
871	[ true ⇒ set_bit_addressable_sfr ? s d v
872	\| false ⇒
873	let memory ≝ insert ? 7 (three_bits @@ nl) v (low_internal_ram ? s) in
874	set_low_internal_ram ? s memory
875	]
876	\| INDIRECT i ⇒
877	λindirect: True.
878	let register ≝ get_register ? s [[ false; false; i ]] in
879	let 〈nu, nl〉 ≝ split ? 4 4 register in
880	let bit_1 ≝ get_index_v … nu 1 ? in
881	let 〈ignore, three_bits〉 ≝ split ? 1 3 nu in
882	match bit_1 with
883	[ true ⇒
884	let memory ≝ insert … (three_bits @@ nl) v (low_internal_ram ? s) in
885	set_low_internal_ram ? s memory
886	\| false ⇒
887	let memory ≝ insert … (three_bits @@ nl) v (high_internal_ram ? s) in
888	set_high_internal_ram ? s memory
889	]
890	\| REGISTER r ⇒ λregister: True. set_register ? s r v
891	\| ACC_A ⇒ λacc_a: True. set_8051_sfr ? s SFR_ACC_A v
892	\| ACC_B ⇒ λacc_b: True. set_8051_sfr ? s SFR_ACC_B v
893	\| EXT_INDIRECT e ⇒
894	λext_indirect: True.
895	let address ≝ get_register ? s [[ false; false; e ]] in
896	let padded_address ≝ pad 8 8 address in
897	let memory ≝ insert ? 16 padded_address v (external_ram ? s) in
898	set_external_ram ? s memory
899	\| EXT_INDIRECT_DPTR ⇒
900	λext_indirect_dptr: True.
901	let address ≝ (get_8051_sfr ? s SFR_DPH) @@ (get_8051_sfr ? s SFR_DPL) in
902	let memory ≝ insert ? 16 address v (external_ram ? s) in
903	set_external_ram ? s memory
904	\| _ ⇒
905	λother: False.
906	match other in False with [ ]
907	] (subaddressing_modein … a).
908	[1,2,3,4:
909	normalize
910	repeat (@ le_S_S)
911	@ le_O_n
912	]
913	qed.
914
915	theorem modulus_less_than:
916	∀m,n: nat. (m mod (S n)) < S n.
917	#n #m
918	normalize
919	@ le_S_S
920	lapply (le_n n)
921	generalize in ⊢ (?%? → ?(??%?)?)
922	elim n in ⊢ (∀_:?. ??% → ?(?%??)?)
923	[ normalize
924	#n
925	@ (less_than_or_equal_b_elim n m)
926	normalize
927	[ //
928	\| #H #K
929	inversion K
930	[ # H1
931	< H1
932	//
933	\| #x #H1 #H2 #H3
934	destruct
935	]
936	]
937	\| normalize
938	# y # H1 # n # H2
939	@ (less_than_or_equal_b_elim n m)
940	normalize
941	[ //
942	\| # K
943	@ H1
944	cut (n ≤ S y → n - S m ≤ y)
945	/2/
946	cases n
947	normalize
948	//
949	# x # K1
950	lapply (le_S_S_to_le … K1)
951	generalize in match m
952	elim x
953	normalize
954	//
955	# w1 # H # m
956	cases m
957	normalize
958	//
959	# q # K2
960	apply H
961	/3/
962	]
963	]
964	qed.
965
966	definition get_arg_1: ∀M: Type[0]. PreStatus M → [[ bit_addr ; n_bit_addr ; carry ]] →
967	bool → bool ≝
968	λm, s, a, l.
969	match a return λx. bool_to_Prop (is_in ? [[ bit_addr ;
970	n_bit_addr ;
971	carry ]] x) → ? with
972	[ BIT_ADDR b ⇒
973	λbit_addr: True.
974	let 〈 nu, nl 〉 ≝ split … 4 4 b in
975	let bit_1 ≝ get_index_v … nu 1 ? in
976	let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in
977	match bit_1 with
978	[ true ⇒
979	let address ≝ nat_of_bitvector … (three_bits @@ nl) in
980	let d ≝ address ÷ 8 in
981	let m ≝ address mod 8 in
982	let trans ≝ bitvector_of_nat 8 ((d * 8) + 128) in
983	let sfr ≝ get_bit_addressable_sfr ? s ? trans l in
984	get_index_v … sfr m ?
985	\| false ⇒
986	let address ≝ nat_of_bitvector … (three_bits @@ nl) in
987	let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in
988	let t ≝ lookup … 7 address' (low_internal_ram ? s) (zero 8) in
989	get_index_v … t (modulus address 8) ?
990	]
991	\| N_BIT_ADDR n ⇒
992	λn_bit_addr: True.
993	let 〈 nu, nl 〉 ≝ split … 4 4 n in
994	let bit_1 ≝ get_index_v … nu 1 ? in
995	let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in
996	match bit_1 with
997	[ true ⇒
998	let address ≝ nat_of_bitvector … (three_bits @@ nl) in
999	let d ≝ address ÷ 8 in
1000	let m ≝ address mod 8 in
1001	let trans ≝ bitvector_of_nat 8 ((d * 8) + 128) in
1002	let sfr ≝ get_bit_addressable_sfr ? s ? trans l in
1003	¬(get_index_v … sfr m ?)
1004	\| false ⇒
1005	let address ≝ nat_of_bitvector … (three_bits @@ nl) in
1006	let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in
1007	let trans ≝ lookup … 7 address' (low_internal_ram ? s) (zero 8) in
1008	¬(get_index_v … trans (modulus address 8) ?)
1009	]
1010	\| CARRY ⇒ λcarry: True. get_cy_flag ? s
1011	\| _ ⇒ λother.
1012	match other in False with [ ]
1013	] (subaddressing_modein … a).
1014	[3,6:
1015	normalize
1016	repeat (@ le_S_S)
1017	@ le_O_n
1018	\|1,2,4,5:
1019	apply modulus_less_than
1020	]
1021	qed.
1022
1023	definition set_arg_1: ∀M: Type[0]. PreStatus M → [[ bit_addr ; carry ]] →
1024	Bit → PreStatus M ≝
1025	λm, s, a, v.
1026	match a return λx. bool_to_Prop (is_in ? [[ bit_addr ; carry ]] x) → ? with
1027	[ BIT_ADDR b ⇒ λbit_addr: True.
1028	let 〈 nu, nl 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_PSW) in
1029	let bit_1 ≝ get_index_v … nu 1 ? in
1030	let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in
1031	match bit_1 with
1032	[ true ⇒
1033	let address ≝ nat_of_bitvector … (three_bits @@ nl) in
1034	let d ≝ address ÷ 8 in
1035	let m ≝ address mod 8 in
1036	let t ≝ bitvector_of_nat 8 ((d * 8) + 128) in
1037	let sfr ≝ get_bit_addressable_sfr ? s ? t true in
1038	let new_sfr ≝ set_index … sfr m v ? in
1039	set_bit_addressable_sfr ? s new_sfr t
1040	\| false ⇒
1041	let address ≝ nat_of_bitvector … (three_bits @@ nl) in
1042	let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in
1043	let t ≝ lookup … 7 address' (low_internal_ram ? s) (zero 8) in
1044	let n_bit ≝ set_index … t (modulus address 8) v ? in
1045	let memory ≝ insert ? 7 address' n_bit (low_internal_ram ? s) in
1046	set_low_internal_ram ? s memory
1047	]
1048	\| CARRY ⇒
1049	λcarry: True.
1050	let 〈 nu, nl 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_PSW) in
1051	let bit_1 ≝ get_index_v… nu 1 ? in
1052	let bit_2 ≝ get_index_v… nu 2 ? in
1053	let bit_3 ≝ get_index_v… nu 3 ? in
1054	let new_psw ≝ [[ v; bit_1 ; bit_2; bit_3 ]] @@ nl in
1055	set_8051_sfr ? s SFR_PSW new_psw
1056	\| _ ⇒
1057	λother: False.
1058	match other in False with
1059	[ ]
1060	] (subaddressing_modein … a).
1061	[1,2,3,6:
1062	normalize
1063	repeat (@ le_S_S)
1064	@ le_O_n
1065	\|4,5:
1066	@ modulus_less_than
1067	]
1068	qed.
1069
1070	definition load_code_memory ≝
1071	fold_left_i … (
1072	λi, mem, v.
1073	insert … (bitvector_of_nat … i) v mem) (Stub Byte 16).
1074
1075	definition load ≝
1076	λl.
1077	λstatus.
1078	set_code_memory ? status (load_code_memory l).
1079
1080	definition fetch_pseudo_instruction: list labelled_instruction → Word → (pseudo_instruction × Word) ≝
1081	λcode_mem.
1082	λpc: Word.
1083	let 〈lbl, instr〉 ≝ nth (nat_of_bitvector ? pc) … code_mem ? in
1084	let 〈flags, new_pc〉 ≝ half_add ? pc (bitvector_of_nat ? 1) in
1085	〈instr, new_pc〉.
1086	cases not_implemented.
1087	qed.

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