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1(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
2(* Interpret.ma: Operational semantics for the 8051/8052 processor.           *)
3(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
4
5include "ASM.ma".
6include "Arithmetic.ma".
7include "BitVectorTrie.ma".
8
9ndefinition Time ≝ Nat.
10
11ninductive SerialBufferType: Type[0] ≝
12  Eight: Byte → SerialBufferType
13| Nine: Bit → Byte → SerialBufferType.
14
15ninductive LineType: Type[0] ≝
16  P1: Byte → LineType
17| P3: Byte → LineType
18| SerialBuffer: SerialBufferType → LineType.
19
20(* What is a continuation, now? *)
21
22ninductive 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
43ndefinition sfr_8051_index ≝
44  λs: SFR8051.
45    match s with
46      [ SFR_SP ⇒ Z
47      | SFR_DPL ⇒ S Z
48      | SFR_DPH ⇒ two
49      | SFR_PCON ⇒ three
50      | SFR_TCON ⇒ four
51      | SFR_TMOD ⇒ five
52      | SFR_TL0 ⇒ six
53      | SFR_TL1 ⇒ seven
54      | SFR_TH0 ⇒ eight
55      | SFR_TH1 ⇒ nine
56      | SFR_P1 ⇒ ten
57      | SFR_SCON ⇒ eleven
58      | SFR_SBUF ⇒ twelve
59      | SFR_IE ⇒ thirteen
60      | SFR_P3 ⇒ fourteen
61      | SFR_IP ⇒ fifteen
62      | SFR_PSW ⇒ sixteen
63      | SFR_ACC_A ⇒ seventeen
64      | SFR_ACC_B ⇒ eighteen
65      ].
66     
67ninductive SFR8052: Type[0] ≝
68   SFR_T2CON: SFR8052
69|  SFR_RCAP2L: SFR8052
70|  SFR_RCAP2H: SFR8052
71|  SFR_TL2: SFR8052
72|  SFR_TH2: SFR8052.
73
74ndefinition sfr_8052_index ≝
75  λs: SFR8052.
76    match s with
77      [ SFR_T2CON ⇒ Z
78      | SFR_RCAP2L ⇒ S Z
79      | SFR_RCAP2H ⇒ two
80      | SFR_TL2 ⇒ three
81      | SFR_TH2 ⇒ four
82      ].
83
84(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
85(* Processor status.                                                          *)
86(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
87nrecord Status: Type[0] ≝
88{
89  code_memory: BitVectorTrie Byte sixteen;
90  low_internal_ram: BitVectorTrie Byte seven;
91  high_internal_ram: BitVectorTrie Byte seven;
92  external_ram: BitVectorTrie Byte sixteen;
93 
94  program_counter: Word;
95 
96  special_function_registers_8051: Vector Byte nineteen;
97  special_function_registers_8052: Vector Byte five;
98 
99  p1_latch: Byte;
100  p3_latch: Byte;
101 
102  clock: Time
103}.
104
105naxiom sfr8051_index_nineteen:
106  ∀i: SFR8051.
107    sfr_8051_index i < nineteen.
108   
109naxiom sfr8052_index_five:
110  ∀i: SFR8052.
111    sfr_8052_index i < five.
112   
113ndefinition set_clock ≝
114  λs: Status.
115  λt: Time.
116    let old_code_memory ≝ code_memory s in
117    let old_low_internal_ram ≝ low_internal_ram s in
118    let old_high_internal_ram ≝ high_internal_ram s in
119    let old_external_ram ≝ external_ram s in
120    let old_program_counter ≝ program_counter s in
121    let old_special_function_registers_8051 ≝ special_function_registers_8051 s in
122    let old_special_function_registers_8052 ≝ special_function_registers_8052 s in
123    let old_p1_latch ≝ p1_latch s in   
124    let old_p3_latch ≝ p3_latch s in
125      mk_Status old_code_memory
126                old_low_internal_ram
127                old_high_internal_ram
128                old_external_ram
129                old_program_counter
130                old_special_function_registers_8051
131                old_special_function_registers_8052
132                old_p1_latch
133                old_p3_latch
134                t.
135   
136ndefinition set_p1_latch ≝
137  λs: Status.
138  λb: Byte.
139    let old_code_memory ≝ code_memory s in
140    let old_low_internal_ram ≝ low_internal_ram s in
141    let old_high_internal_ram ≝ high_internal_ram s in
142    let old_external_ram ≝ external_ram s in
143    let old_program_counter ≝ program_counter s in
144    let old_special_function_registers_8051 ≝ special_function_registers_8051 s in
145    let old_special_function_registers_8052 ≝ special_function_registers_8052 s in
146    let old_p3_latch ≝ p3_latch s in
147    let old_clock ≝ clock s in
148      mk_Status old_code_memory
149                old_low_internal_ram
150                old_high_internal_ram
151                old_external_ram
152                old_program_counter
153                old_special_function_registers_8051
154                old_special_function_registers_8052
155                b
156                old_p3_latch
157                old_clock.
158
159ndefinition set_p3_latch ≝
160  λs: Status.
161  λb: Byte.
162    let old_code_memory ≝ code_memory s in
163    let old_low_internal_ram ≝ low_internal_ram s in
164    let old_high_internal_ram ≝ high_internal_ram s in
165    let old_external_ram ≝ external_ram s in
166    let old_program_counter ≝ program_counter s in
167    let old_special_function_registers_8051 ≝ special_function_registers_8051 s in
168    let old_special_function_registers_8052 ≝ special_function_registers_8052 s in
169    let old_p1_latch ≝ p1_latch s in
170    let old_clock ≝ clock s in
171      mk_Status old_code_memory
172                old_low_internal_ram
173                old_high_internal_ram
174                old_external_ram
175                old_program_counter
176                old_special_function_registers_8051
177                old_special_function_registers_8052
178                old_p1_latch
179                b
180                old_clock.
181
182ndefinition get_8051_sfr ≝
183  λs: Status.
184  λi: SFR8051.
185    let sfr ≝ special_function_registers_8051 s in
186    let index ≝ sfr_8051_index i in
187      get_index … sfr index ?.
188    napply (sfr8051_index_nineteen i).
189nqed.
190
191ndefinition get_8052_sfr ≝
192  λs: Status.
193  λi: SFR8052.
194    let sfr ≝ special_function_registers_8052 s in
195    let index ≝ sfr_8052_index i in
196      get_index … sfr index ?.
197    napply (sfr8052_index_five i).
198nqed.
199
200ndefinition set_8051_sfr ≝
201  λs: Status.
202  λi: SFR8051.
203  λb: Byte.
204    let index ≝ sfr_8051_index i in
205    let old_code_memory ≝ code_memory s in
206    let old_low_internal_ram ≝ low_internal_ram s in
207    let old_high_internal_ram ≝ high_internal_ram s in
208    let old_external_ram ≝ external_ram s in
209    let old_program_counter ≝ program_counter s in
210    let old_special_function_registers_8051 ≝ special_function_registers_8051 s in
211    let old_special_function_registers_8052 ≝ special_function_registers_8052 s in
212    let new_special_function_registers_8051 ≝
213      cic:/matita/ng/Vector/set_index.fix(0,3,2) Byte nineteen old_special_function_registers_8051 index b ? in
214    let old_p1_latch ≝ p1_latch s in
215    let old_p3_latch ≝ p3_latch s in
216    let old_clock ≝ clock s in
217      mk_Status old_code_memory
218                old_low_internal_ram
219                old_high_internal_ram
220                old_external_ram
221                old_program_counter
222                new_special_function_registers_8051
223                old_special_function_registers_8052
224                old_p1_latch
225                old_p3_latch
226                old_clock.
227    napply (sfr8051_index_nineteen i).
228nqed.
229
230ndefinition set_8052_sfr ≝
231  λs: Status.
232  λi: SFR8052.
233  λb: Byte.
234    let index ≝ sfr_8052_index i in
235    let old_code_memory ≝ code_memory s in
236    let old_low_internal_ram ≝ low_internal_ram s in
237    let old_high_internal_ram ≝ high_internal_ram s in
238    let old_external_ram ≝ external_ram s in
239    let old_program_counter ≝ program_counter s in
240    let old_special_function_registers_8051 ≝ special_function_registers_8051 s in
241    let old_special_function_registers_8052 ≝ special_function_registers_8052 s in
242    let new_special_function_registers_8052 ≝
243      cic:/matita/ng/Vector/set_index.fix(0,3,2) Byte five old_special_function_registers_8052 index b ? in
244    let old_p1_latch ≝ p1_latch s in
245    let old_p3_latch ≝ p3_latch s in
246    let old_clock ≝ clock s in
247      mk_Status old_code_memory
248                old_low_internal_ram
249                old_high_internal_ram
250                old_external_ram
251                old_program_counter
252                old_special_function_registers_8051
253                new_special_function_registers_8052
254                old_p1_latch
255                old_p3_latch
256                old_clock.
257    napply (sfr8052_index_five i).
258nqed.
259
260ndefinition set_program_counter ≝
261  λs: Status.
262  λw: Word.
263    let old_code_memory ≝ code_memory s in
264    let old_low_internal_ram ≝ low_internal_ram s in
265    let old_high_internal_ram ≝ high_internal_ram s in
266    let old_external_ram ≝ external_ram s in
267    let old_special_function_registers_8051 ≝ special_function_registers_8051 s in
268    let old_special_function_registers_8052 ≝ special_function_registers_8052 s in
269    let old_p1_latch ≝ p1_latch s in
270    let old_p3_latch ≝ p3_latch s in
271    let old_clock ≝ clock s in
272      mk_Status old_code_memory
273                old_low_internal_ram
274                old_high_internal_ram
275                old_external_ram
276                w
277                old_special_function_registers_8051
278                old_special_function_registers_8052
279                old_p1_latch
280                old_p3_latch
281                old_clock.
282               
283ndefinition set_code_memory ≝
284  λs: Status.
285  λr: BitVectorTrie Byte sixteen.
286    let old_low_internal_ram ≝ low_internal_ram s in
287    let old_high_internal_ram ≝ high_internal_ram s in
288    let old_external_ram ≝ external_ram s in
289    let old_program_counter ≝ program_counter 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_Status r
296                old_low_internal_ram
297                old_high_internal_ram
298                old_external_ram
299                old_program_counter
300                old_special_function_registers_8051
301                old_special_function_registers_8052
302                old_p1_latch
303                old_p3_latch
304                old_clock.
305               
306ndefinition set_low_internal_ram ≝
307  λs: Status.
308  λr: BitVectorTrie Byte seven.
309    let old_code_memory ≝ code_memory s in
310    let old_high_internal_ram ≝ high_internal_ram s in
311    let old_external_ram ≝ external_ram s in
312    let old_program_counter ≝ program_counter s in
313    let old_special_function_registers_8051 ≝ special_function_registers_8051 s in
314    let old_special_function_registers_8052 ≝ special_function_registers_8052 s in
315    let old_p1_latch ≝ p1_latch s in
316    let old_p3_latch ≝ p3_latch s in
317    let old_clock ≝ clock s in
318      mk_Status old_code_memory
319                r
320                old_high_internal_ram
321                old_external_ram
322                old_program_counter
323                old_special_function_registers_8051
324                old_special_function_registers_8052
325                old_p1_latch
326                old_p3_latch
327                old_clock.
328               
329ndefinition set_high_internal_ram ≝
330  λs: Status.
331  λr: BitVectorTrie Byte seven.
332    let old_code_memory ≝ code_memory s in
333    let old_low_internal_ram ≝ low_internal_ram s in
334    let old_high_internal_ram ≝ high_internal_ram s in
335    let old_external_ram ≝ external_ram s in
336    let old_program_counter ≝ program_counter s in
337    let old_special_function_registers_8051 ≝ special_function_registers_8051 s in
338    let old_special_function_registers_8052 ≝ special_function_registers_8052 s in
339    let old_p1_latch ≝ p1_latch s in
340    let old_p3_latch ≝ p3_latch s in
341    let old_clock ≝ clock s in
342      mk_Status old_code_memory
343                old_low_internal_ram
344                r
345                old_external_ram
346                old_program_counter
347                old_special_function_registers_8051
348                old_special_function_registers_8052
349                old_p1_latch
350                old_p3_latch
351                old_clock.
352               
353ndefinition set_external_ram ≝
354  λs: Status.
355  λr: BitVectorTrie Byte sixteen.
356    let old_code_memory ≝ code_memory s in
357    let old_low_internal_ram ≝ low_internal_ram s in
358    let old_high_internal_ram ≝ high_internal_ram s in
359    let old_program_counter ≝ program_counter s in
360    let old_special_function_registers_8051 ≝ special_function_registers_8051 s in
361    let old_special_function_registers_8052 ≝ special_function_registers_8052 s in
362    let old_p1_latch ≝ p1_latch s in
363    let old_p3_latch ≝ p3_latch s in
364    let old_clock ≝ clock s in
365      mk_Status old_code_memory
366                old_low_internal_ram
367                old_high_internal_ram
368                r
369                old_program_counter
370                old_special_function_registers_8051
371                old_special_function_registers_8052
372                old_p1_latch
373                old_p3_latch
374                old_clock.
375               
376naxiom less_than_or_equal_monotone:
377  ∀m, n: Nat.
378    m ≤ n → S m ≤ S n.
379   
380alias id "get_index" = "cic:/matita/ng/Vector/get_index.fix(0,3,2)".
381               
382ndefinition get_cy_flag ≝
383  λs: Status.
384    let sfr ≝ special_function_registers_8051 s in
385    let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in
386      get_index Bool eight psw Z ?.
387    nnormalize.
388    napply (less_than_or_equal_monotone ? ?).
389    napply (less_than_or_equal_zero).
390    nrepeat (napply (less_than_or_equal_monotone ? ?)).
391    napply (less_than_or_equal_zero).
392nqed.
393
394ndefinition get_ac_flag ≝
395  λs: Status.
396    let sfr ≝ special_function_registers_8051 s in
397    let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in
398      get_index Bool eight psw (S Z) ?.
399    nnormalize.
400    nrepeat (napply (less_than_or_equal_monotone ? ?)).
401    napply (less_than_or_equal_zero).
402    nrepeat (napply (less_than_or_equal_monotone ? ?)).
403    napply (less_than_or_equal_zero).
404nqed.
405
406ndefinition get_fo_flag ≝
407  λs: Status.
408    let sfr ≝ special_function_registers_8051 s in
409    let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in
410      get_index Bool eight psw two ?.
411    nnormalize.
412    nrepeat (napply (less_than_or_equal_monotone ? ?)).
413    napply (less_than_or_equal_zero).
414    nrepeat (napply (less_than_or_equal_monotone ? ?)).
415    napply (less_than_or_equal_zero).
416nqed.
417
418ndefinition get_rs1_flag ≝
419  λs: Status.
420    let sfr ≝ special_function_registers_8051 s in
421    let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in
422      get_index Bool eight psw three ?.
423    nnormalize.
424    nrepeat (napply (less_than_or_equal_monotone ? ?)).
425    napply (less_than_or_equal_zero).
426    nrepeat (napply (less_than_or_equal_monotone ? ?)).
427    napply (less_than_or_equal_zero).
428nqed.
429
430ndefinition get_rs0_flag ≝
431  λs: Status.
432    let sfr ≝ special_function_registers_8051 s in
433    let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in
434      get_index Bool eight psw four ?.
435    nnormalize.
436    nrepeat (napply (less_than_or_equal_monotone ? ?)).
437    napply (less_than_or_equal_zero).
438    nrepeat (napply (less_than_or_equal_monotone ? ?)).
439    napply (less_than_or_equal_zero).
440nqed.
441
442ndefinition get_ov_flag ≝
443  λs: Status.
444    let sfr ≝ special_function_registers_8051 s in
445    let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in
446      get_index Bool eight psw five ?.
447    nnormalize.
448    nrepeat (napply (less_than_or_equal_monotone ? ?)).
449    napply (less_than_or_equal_zero).
450    nrepeat (napply (less_than_or_equal_monotone ? ?)).
451    napply (less_than_or_equal_zero).
452nqed.
453
454ndefinition get_ud_flag ≝
455  λs: Status.
456    let sfr ≝ special_function_registers_8051 s in
457    let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in
458      get_index Bool eight psw six ?.
459    nnormalize.
460    nrepeat (napply (less_than_or_equal_monotone ? ?)).
461    napply (less_than_or_equal_zero).
462    nrepeat (napply (less_than_or_equal_monotone ? ?)).
463    napply (less_than_or_equal_zero).
464nqed.
465
466ndefinition get_p_flag ≝
467  λs: Status.
468    let sfr ≝ special_function_registers_8051 s in
469    let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in
470      get_index Bool eight psw seven ?.
471    nnormalize.
472    nrepeat (napply (less_than_or_equal_monotone ? ?)).
473    napply (less_than_or_equal_zero).
474    nrepeat (napply (less_than_or_equal_monotone ? ?)).
475    napply (less_than_or_equal_zero).
476nqed.
477
478ndefinition set_flags ≝
479  λs: Status.
480  λcy: Bit.
481  λac: Maybe Bit.
482  λov: Bit.
483    let 〈 nu, nl 〉 ≝ split … four four (get_8051_sfr s SFR_PSW) in
484    let old_cy ≝ get_index … nu Z ? in
485    let old_ac ≝ get_index … nu one ? in
486    let old_fo ≝ get_index … nu two ? in
487    let old_rs1 ≝ get_index … nu three ? in
488    let old_rs0 ≝ get_index … nl Z ? in
489    let old_ov ≝ get_index … nl one ? in
490    let old_ud ≝ get_index … nl two ? in
491    let old_p ≝ get_index … nl three ? in
492    let new_ac ≝ match ac with [ Nothing ⇒ old_ac | Just j ⇒ j ] in
493    let new_psw ≝ [[ old_cy ; new_ac ; old_fo ; old_rs1 ;
494                     old_rs0 ; old_ov ; old_ud ; old_p ]] in
495      set_8051_sfr s SFR_PSW new_psw.
496    ##[##1,2,3,4,5,6,7,8:
497        nnormalize;
498        nrepeat (napply less_than_or_equal_monotone);
499        napply (less_than_or_equal_zero);
500    ##]
501nqed.
502
503ndefinition initialise_status ≝
504  let status ≝ mk_Status (Stub Byte sixteen)                    (* Code mem. *)
505                         (Stub Byte seven)                      (* Low mem.  *)
506                         (Stub Byte seven)                      (* High mem. *)
507                         (Stub Byte sixteen)                    (* Ext mem.  *)
508                         (zero sixteen)                         (* PC.       *)
509                         (replicate Byte nineteen (zero eight)) (* 8051 SFR. *)
510                         (replicate Byte five (zero eight))     (* 8052 SFR. *)
511                         (zero eight)                           (* P1 latch. *)
512                         (zero eight)                           (* P3 latch. *)
513                         Z                                      (* Clock.    *)
514  in
515    set_program_counter status (bitvector_of_nat sixteen seven).
516 
517naxiom not_implemented: False.
518 
519include "Arithmetic.ma".
520 
521ndefinition get_bit_addressable_sfr ≝
522  λs: Status.
523  λn: Nat.
524  λb: BitVector n.
525  λl: Bool.
526    let address ≝ nat_of_bitvector … b in
527      if (decidable_equality address one_hundred_and_twenty_eight) then
528        ?
529      else if (decidable_equality address one_hundred_and_forty_four) then
530        if l then
531          (p1_latch s)
532        else
533          (get_8051_sfr s SFR_P1)
534      else if (decidable_equality address one_hundred_and_sixty) then
535        ?
536      else if (decidable_equality address one_hundred_and_seventy_six) then
537        if l then
538          (p3_latch s)
539        else
540          (get_8051_sfr s SFR_P3)
541      else if (decidable_equality address one_hundred_and_fifty_three) then
542        get_8051_sfr s SFR_SBUF
543      else if (decidable_equality address one_hundred_and_thirty_eight) then
544        get_8051_sfr s SFR_TL0
545      else if (decidable_equality address one_hundred_and_thirty_nine) then
546        get_8051_sfr s SFR_TL1
547      else if (decidable_equality address one_hundred_and_forty) then
548        get_8051_sfr s SFR_TH0
549      else if (decidable_equality address one_hundred_and_forty_one) then
550        get_8051_sfr s SFR_TH1
551      else if (decidable_equality address two_hundred) then
552        get_8052_sfr s SFR_T2CON
553      else if (decidable_equality address two_hundred_and_two) then
554        get_8052_sfr s SFR_RCAP2L
555      else if (decidable_equality address two_hundred_and_three) then
556        get_8052_sfr s SFR_RCAP2H
557      else if (decidable_equality address two_hundred_and_four) then
558        get_8052_sfr s SFR_TL2
559      else if (decidable_equality address two_hundred_and_five) then
560        get_8052_sfr s SFR_TH2
561      else if (decidable_equality address one_hundred_and_thirty_five) then
562        get_8051_sfr s SFR_PCON
563      else if (decidable_equality address one_hundred_and_thirty_six) then
564        get_8051_sfr s SFR_TCON
565      else if (decidable_equality address one_hundred_and_thirty_seven) then
566        get_8051_sfr s SFR_TMOD
567      else if (decidable_equality address one_hundred_and_fifty_two) then
568        get_8051_sfr s SFR_SCON
569      else if (decidable_equality address one_hundred_and_sixty_eight) then
570        get_8051_sfr s SFR_IE
571      else if (decidable_equality address one_hundred_and_eighty_four) then
572        get_8051_sfr s SFR_IP
573      else if (decidable_equality address one_hundred_and_twenty_nine) then
574        get_8051_sfr s SFR_SP
575      else if (decidable_equality address one_hundred_and_thirty) then
576        get_8051_sfr s SFR_DPL
577      else if (decidable_equality address one_hundred_and_thirty_one) then
578        get_8051_sfr s SFR_DPH
579      else if (decidable_equality address two_hundred_and_eight) then
580        get_8051_sfr s SFR_PSW
581      else if (decidable_equality address two_hundred_and_twenty_four) then
582        get_8051_sfr s SFR_ACC_A
583      else if (decidable_equality address two_hundred_and_forty) then
584        get_8051_sfr s SFR_ACC_B
585      else
586        ?.
587      ncases not_implemented.
588nqed.
589
590ndefinition set_bit_addressable_sfr ≝
591  λs: Status.
592  λb: Byte.
593  λv: Byte.
594    let address ≝ nat_of_bitvector … b in
595      if (decidable_equality address one_hundred_and_twenty_eight) then
596        ?
597      else if (decidable_equality address one_hundred_and_forty_four) then
598        let status_1 ≝ set_8051_sfr s SFR_P1 v in
599        let status_2 ≝ set_p1_latch s v in
600          status_2
601      else if (decidable_equality address one_hundred_and_sixty) then
602        ?
603      else if (decidable_equality address one_hundred_and_seventy_six) then
604        let status_1 ≝ set_8051_sfr s SFR_P3 v in
605        let status_2 ≝ set_p3_latch s v in
606          status_2
607      else if (decidable_equality address one_hundred_and_fifty_three) then
608        set_8051_sfr s SFR_SBUF v
609      else if (decidable_equality address one_hundred_and_thirty_eight) then
610        set_8051_sfr s SFR_TL0 v
611      else if (decidable_equality address one_hundred_and_thirty_nine) then
612        set_8051_sfr s SFR_TL1 v
613      else if (decidable_equality address one_hundred_and_forty) then
614        set_8051_sfr s SFR_TH0 v
615      else if (decidable_equality address one_hundred_and_forty_one) then
616        set_8051_sfr s SFR_TH1 v
617      else if (decidable_equality address two_hundred) then
618        set_8052_sfr s SFR_T2CON v
619      else if (decidable_equality address two_hundred_and_two) then
620        set_8052_sfr s SFR_RCAP2L v
621      else if (decidable_equality address two_hundred_and_three) then
622        set_8052_sfr s SFR_RCAP2H v
623      else if (decidable_equality address two_hundred_and_four) then
624        set_8052_sfr s SFR_TL2 v
625      else if (decidable_equality address two_hundred_and_five) then
626        set_8052_sfr s SFR_TH2 v
627      else if (decidable_equality address one_hundred_and_thirty_five) then
628        set_8051_sfr s SFR_PCON v
629      else if (decidable_equality address one_hundred_and_thirty_six) then
630        set_8051_sfr s SFR_TCON v
631      else if (decidable_equality address one_hundred_and_thirty_seven) then
632        set_8051_sfr s SFR_TMOD v
633      else if (decidable_equality address one_hundred_and_fifty_two) then
634        set_8051_sfr s SFR_SCON v
635      else if (decidable_equality address one_hundred_and_sixty_eight) then
636        set_8051_sfr s SFR_IE v
637      else if (decidable_equality address one_hundred_and_eighty_four) then
638        set_8051_sfr s SFR_IP v
639      else if (decidable_equality address one_hundred_and_twenty_nine) then
640        set_8051_sfr s SFR_SP v
641      else if (decidable_equality address one_hundred_and_thirty) then
642        set_8051_sfr s SFR_DPL v
643      else if (decidable_equality address one_hundred_and_thirty_one) then
644        set_8051_sfr s SFR_DPH v
645      else if (decidable_equality address two_hundred_and_eight) then
646        set_8051_sfr s SFR_PSW v
647      else if (decidable_equality address two_hundred_and_twenty_four) then
648        set_8051_sfr s SFR_ACC_A v
649      else if (decidable_equality address two_hundred_and_forty) then
650        set_8051_sfr s SFR_ACC_B v
651      else
652        ?.
653      ncases not_implemented.
654nqed.
655
656ndefinition bit_address_of_register ≝
657  λs: Status.
658  λr: BitVector three.
659    let b ≝ get_index ? r Z ? in
660    let c ≝ get_index ? r one ? in
661    let d ≝ get_index ? r two ? in
662    let 〈 un, ln 〉 ≝ split ? four four (get_8051_sfr s SFR_PSW) in
663    let 〈 r1, r0 〉 ≝ mk_Cartesian … (get_index four un two ?) (get_index four un three ?) in
664    let offset ≝
665      if conjunction (negation r1) (negation r0) then
666        Z
667      else if conjunction (negation r1) r0 then
668        eight
669      else if conjunction r1 r0 then
670        twenty_four
671      else
672        sixteen
673    in
674      bitvector_of_nat seven (offset + (nat_of_bitvector ? [[ false ; b ; c ; d ]])).
675  ##[##1,2,3,4,5:
676      nnormalize;
677      nrepeat (napply less_than_or_equal_monotone);
678      napply less_than_or_equal_zero;
679  ##]
680nqed.
681
682ndefinition get_register ≝
683  λs: Status.
684  λr: BitVector three.
685    let address ≝ bit_address_of_register s r in
686      lookup … address (low_internal_ram s) (zero eight).
687     
688ndefinition set_register ≝
689  λs: Status.
690  λr: BitVector three.
691  λv: Byte.
692    let address ≝ bit_address_of_register s r in
693    let old_low_internal_ram ≝ low_internal_ram s in
694    let new_low_internal_ram ≝ insert … address v old_low_internal_ram in
695      set_low_internal_ram s new_low_internal_ram.
696     
697alias id "get_index" = "cic:/matita/ng/BitVector/get_index.def(3)".
698ndefinition read_at_stack_pointer ≝
699  λs: Status.
700    let 〈 nu, nl 〉 ≝ split … four four (get_8051_sfr s SFR_SP) in
701    let m ≝ get_index … nu Z ? in
702    let r1 ≝ get_index … nu one ? in
703    let r2 ≝ get_index … nu two ? in
704    let r3 ≝ get_index … nu three ? in
705    let address ≝ [[ r1 ; r2 ; r3 ]] @@ nl in
706    let memory ≝
707      if m then
708        (low_internal_ram s)
709      else
710        (high_internal_ram s)
711    in
712      lookup … address memory (zero eight).
713    ##[##1,2,3,4:
714        nnormalize;
715        nrepeat (napply less_than_or_equal_monotone);
716        napply less_than_or_equal_zero;
717    ##]
718nqed.
719
720ndefinition write_at_stack_pointer ≝
721  λs: Status.
722  λv: Byte.
723    let 〈 nu, nl 〉 ≝ split … four four (get_8051_sfr s SFR_SP) in
724    let bit_zero ≝ get_index … nu Z ? in
725    let bit_one ≝ get_index … nu one ? in
726    let bit_two ≝ get_index … nu two ? in
727    let bit_three ≝ get_index … nu three ? in
728      if bit_zero then
729        let memory ≝ insert … ([[ bit_one ; bit_two ; bit_three ]] @@ nl)
730                              v (low_internal_ram s) in
731          set_low_internal_ram s memory
732      else
733        let memory ≝ insert … ([[ bit_one ; bit_two ; bit_three ]] @@ nl)
734                              v (high_internal_ram s) in
735          set_high_internal_ram s memory.
736    ##[##1,2,3,4:
737        nnormalize;
738        nrepeat (napply less_than_or_equal_monotone);
739        napply less_than_or_equal_zero;
740    ##]
741nqed.
742
743ndefinition set_arg_16: Status → Word → [[ dptr ]] → Status ≝
744  λs,v,a.
745   match a return λx. bool_to_Prop (is_in ? [[ dptr ]] x) → ? with
746     [ DPTR ⇒ λ_:True.
747       let 〈 bu, bl 〉 ≝ split … eight eight v in
748       let status ≝ set_8051_sfr s SFR_DPH bu in
749       let status ≝ set_8051_sfr status SFR_DPL bl in
750         status
751     | _ ⇒ λK.
752       match K in False with
753       [
754       ]
755     ] (subaddressing_modein … a).
756   
757ndefinition get_arg_16: Status → [[ data16 ]] → Word ≝
758  λs, a.
759    match a return λx. bool_to_Prop (is_in ? [[ data16 ]] x) → ? with
760      [ DATA16 d ⇒ λ_:True. d
761      | _ ⇒ λK.
762        match K in False with
763        [
764        ]
765      ] (subaddressing_modein … a).
766     
767ndefinition get_arg_8: Status → Bool → [[ direct ; indirect ; register ;
768                                          acc_a ; acc_b ; data ; acc_dptr ;
769                                          acc_pc ; ext_indirect ;
770                                          ext_indirect_dptr ]] → Byte ≝
771  λs, l, a.
772    match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; register ;
773                                                acc_a ; acc_b ; data ; acc_dptr ;
774                                                acc_pc ; ext_indirect ;
775                                                ext_indirect_dptr ]] x) → ? with
776      [ ACC_A ⇒ λacc_a: True. get_8051_sfr s SFR_ACC_A
777      | ACC_B ⇒ λacc_b: True. get_8051_sfr s SFR_ACC_B
778      | DATA d ⇒ λdata: True. d
779      | REGISTER r ⇒ λregister: True. get_register s r
780      | EXT_INDIRECT_DPTR ⇒
781        λext_indirect_dptr: True.
782          let address ≝ (get_8051_sfr s SFR_DPH) @@ (get_8051_sfr s SFR_DPL) in
783            lookup … sixteen address (external_ram s) (zero eight)
784      | EXT_INDIRECT e ⇒
785        λext_indirect: True.
786          let address ≝ get_register s [[ false; false; e ]]  in
787          let padded_address ≝ pad eight eight address in
788            lookup … sixteen padded_address (external_ram s) (zero eight)
789      | ACC_DPTR ⇒
790        λacc_dptr: True.
791          let dptr ≝ (get_8051_sfr s SFR_DPH) @@ (get_8051_sfr s SFR_DPL) in
792          let padded_acc ≝ pad eight eight (get_8051_sfr s SFR_ACC_A) in
793          let 〈 carry, address 〉 ≝ half_add sixteen dptr padded_acc in
794            lookup … sixteen address (external_ram s) (zero eight)
795      | ACC_PC ⇒
796        λacc_pc: True.
797          let padded_acc ≝ pad eight eight (get_8051_sfr s SFR_ACC_A) in
798          let 〈 carry, address 〉 ≝ half_add sixteen (program_counter s) padded_acc in
799            lookup … sixteen address (external_ram s) (zero eight)
800      | DIRECT d ⇒
801        λdirect: True.
802          let 〈 nu, nl 〉 ≝ split … four four d in
803          let bit_one ≝ get_index … nu one ? in
804            match bit_one with
805              [ true ⇒
806                  let 〈 bit_one, three_bits 〉 ≝ split ? one three nu in
807                  let address ≝ three_bits @@ nl in
808                    lookup ? seven address (low_internal_ram s) (zero eight)
809              | false ⇒ get_bit_addressable_sfr s eight d l
810              ]
811      | INDIRECT i ⇒
812        λindirect: True.
813          let 〈 nu, nl 〉 ≝ split ? four four (get_register s [[ false; false; i]]) in
814          let 〈 bit_one_v, three_bits 〉 ≝ split ? one three nu in
815          let bit_one ≝ get_index … bit_one_v Z ? in
816          match bit_one with
817            [ true ⇒
818                lookup ? seven (three_bits @@ nl) (low_internal_ram s) (zero eight)
819            | false ⇒
820                lookup ? seven (three_bits @@ nl) (high_internal_ram s) (zero eight)
821            ]
822      | _ ⇒ λother.
823        match other in False with [ ]
824      ] (subaddressing_modein … a).
825      ##[##1,2:
826          nnormalize;
827          nrepeat (napply less_than_or_equal_monotone);
828          napply less_than_or_equal_zero;
829      ##]
830nqed.
831
832ndefinition set_arg_8: Status → [[ direct ; indirect ; register ;
833                                   acc_a ; acc_b ; ext_indirect ;
834                                   ext_indirect_dptr ]] → Byte → Status ≝
835  λs, a, v.
836    match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; register ;
837                                                acc_a ; acc_b ; ext_indirect ;
838                                                ext_indirect_dptr ]] x) → ? with
839      [ DIRECT d ⇒
840        λdirect: True.
841          let 〈 nu, nl 〉 ≝ split … four four d in
842          let bit_one ≝ get_index … nu one ? in
843          let 〈 ignore, three_bits 〉 ≝ split ? one three nu in
844            match bit_one with
845              [ true ⇒ set_bit_addressable_sfr s d v
846              | false ⇒
847                let memory ≝ insert ? seven (three_bits @@ nl) v (low_internal_ram s) in
848                  set_low_internal_ram s memory
849              ]
850      | INDIRECT i ⇒
851        λindirect: True.
852          let register ≝ get_register s [[ false; false; i ]] in
853          let 〈 nu, nl 〉 ≝ split ? four four register in
854          let bit_one ≝ get_index ? nu one ? in
855          let 〈 ignore, three_bits 〉 ≝ split ? one three nu in
856          match bit_one with
857            [ true ⇒
858              let memory ≝ insert … (three_bits @@ nl) v (low_internal_ram s) in
859                set_low_internal_ram s memory
860            | false ⇒
861              let memory ≝ insert … (three_bits @@ nl) v (high_internal_ram s) in
862                set_high_internal_ram s memory
863            ]
864      | REGISTER r ⇒ λregister: True. set_register s r v
865      | ACC_A ⇒ λacc_a: True. set_8051_sfr s SFR_ACC_A v
866      | ACC_B ⇒ λacc_b: True. set_8051_sfr s SFR_ACC_B v
867      | EXT_INDIRECT e ⇒
868        λext_indirect: True.
869          let address ≝ get_register s [[ false; false; e ]] in
870          let padded_address ≝ pad eight eight address in
871          let memory ≝ insert ? sixteen padded_address v (external_ram s) in
872            set_external_ram s memory
873      | EXT_INDIRECT_DPTR ⇒
874        λext_indirect_dptr: True.
875          let address ≝ (get_8051_sfr s SFR_DPH) @@ (get_8051_sfr s SFR_DPL) in
876          let memory ≝ insert ? sixteen address v (external_ram s) in
877            set_external_ram s memory
878      | _ ⇒
879        λother: False.
880          match other in False with [ ]
881      ] (subaddressing_modein … a).
882      ##[##1,2:
883          nnormalize;
884          nrepeat (napply less_than_or_equal_monotone);
885          napply less_than_or_equal_zero
886      ##]
887nqed.
888
889naxiom modulus_less_than:
890  ∀m,n: Nat.
891    (m mod n) < n.
892
893ndefinition get_arg_1: Status → [[ bit_addr ; n_bit_addr ; carry ]] →
894                       Bool → Bool ≝
895  λs, a, l.
896    match a return λx. bool_to_Prop (is_in ? [[ bit_addr ;
897                                                 n_bit_addr ;
898                                                 carry ]] x) → ? with
899      [ BIT_ADDR b ⇒
900        λbit_addr: True.
901          let 〈 nu, nl 〉 ≝ split … four four b in
902          let bit_one ≝ get_index … nu one ? in
903          let 〈 bit_one_v, three_bits 〉 ≝ split ? one three nu in
904            match bit_one with
905              [ true ⇒
906                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
907                let d ≝ address ÷ eight in
908                let m ≝ address mod eight in
909                let trans ≝ bitvector_of_nat eight ((d * eight) + one_hundred_and_twenty_eight) in
910                let sfr ≝ get_bit_addressable_sfr s ? trans l in
911                  get_index ? sfr m ?
912              | false ⇒
913                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
914                let address' ≝ bitvector_of_nat seven ((address ÷ eight) + thirty_two) in
915                let t ≝ lookup … seven address' (low_internal_ram s) (zero eight) in
916                  get_index ? t (modulus address eight) ?
917              ]
918      | N_BIT_ADDR n ⇒
919        λn_bit_addr: True.
920          let 〈 nu, nl 〉 ≝ split … four four n in
921          let bit_one ≝ get_index … nu one ? in
922          let 〈 bit_one_v, three_bits 〉 ≝ split ? one three nu in
923            match bit_one with
924              [ true ⇒
925                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
926                let d ≝ address ÷ eight in
927                let m ≝ address mod eight in
928                let trans ≝ bitvector_of_nat eight ((d * eight) + one_hundred_and_twenty_eight) in
929                let sfr ≝ get_bit_addressable_sfr s ? trans l in
930                  negation (get_index ? sfr m ?)
931              | false ⇒
932                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
933                let address' ≝ bitvector_of_nat seven ((address ÷ eight) + thirty_two) in
934                let trans ≝ lookup … seven address' (low_internal_ram s) (zero eight) in
935                  negation (get_index ? trans (modulus address eight) ?)
936              ]
937      | CARRY ⇒ λcarry: True. get_cy_flag s
938      | _ ⇒ λother.
939        match other in False with [ ]
940      ] (subaddressing_modein … a).
941      ##[##3,6:
942          nnormalize;
943          nrepeat (napply less_than_or_equal_monotone);
944          napply less_than_or_equal_zero;
945      ##|##1,2,4,5:
946          napply modulus_less_than;
947      ##]
948nqed.
949     
950ndefinition set_arg_1: Status → [[ bit_addr ; carry ]] →
951                       Bit → Status ≝
952  λs, a, v.
953    match a return λx. bool_to_Prop (is_in ? [[ bit_addr ; carry ]] x) → ? with
954      [ BIT_ADDR b ⇒ λbit_addr: True.
955          let 〈 nu, nl 〉 ≝ split ? four four (get_8051_sfr s SFR_PSW) in
956          let bit_one ≝ get_index ? nu one ? in
957          let 〈 ignore, three_bits 〉 ≝ split ? one three nu in
958          match bit_one with
959            [ true ⇒
960                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
961                let d ≝ address ÷ eight in
962                let m ≝ address mod eight in
963                let t ≝ bitvector_of_nat eight ((d * eight) + one_hundred_and_twenty_eight) in
964                let sfr ≝ get_bit_addressable_sfr s ? t true in
965                let new_sfr ≝ set_index … sfr m v ? in
966                  set_bit_addressable_sfr s new_sfr t
967            | false ⇒
968                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
969                let address' ≝ bitvector_of_nat seven ((address ÷ eight) + thirty_two) in
970                let t ≝ lookup … seven address' (low_internal_ram s) (zero eight) in
971                let n_bit ≝ set_index … t (modulus address eight) v ? in
972                let memory ≝ insert ? seven address' n_bit (low_internal_ram s) in
973                  set_low_internal_ram s memory
974            ]
975      | CARRY ⇒
976        λcarry: True.
977          let 〈 nu, nl 〉 ≝ split ? four four (get_8051_sfr s SFR_PSW) in
978          let bit_one ≝ get_index … nu one ? in
979          let bit_two ≝ get_index … nu two ? in
980          let bit_three ≝ get_index … nu three ? in
981          let new_psw ≝ [[ v; bit_one ; bit_two; bit_three ]] @@ nl in
982            set_8051_sfr s SFR_PSW new_psw
983      | _ ⇒
984        λother: False.
985          match other in False with
986            [ ]
987      ] (subaddressing_modein … a).
988      ##[##1,2,3,6:
989          nnormalize;
990          nrepeat (napply less_than_or_equal_monotone);
991          napply less_than_or_equal_zero;
992      ##|##4,5:
993          napply (modulus_less_than address eight);
994      ##]
995nqed.
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