source: src/ASM/Status.ma @ 951

Last change on this file since 951 was 949, checked in by mulligan, 9 years ago

resolved conflict, work from today

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1(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
2(* Interpret.ma: Operational semantics for the 8051/8052 processor.           *)
3(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
4
5include "ASM/ASM.ma".
6include "ASM/Arithmetic.ma".
7include "ASM/BitVectorTrie.ma".
8
9definition Time ≝ nat.
10
11inductive SerialBufferType: Type[0] ≝
12  Eight: Byte → SerialBufferType
13| Nine: Bit → Byte → SerialBufferType.
14
15inductive LineType: Type[0] ≝
16  P1: Byte → LineType
17| P3: Byte → LineType
18| SerialBuffer: SerialBufferType → LineType.
19
20(* What is a continuation, now? *)
21
22inductive 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
43definition 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     
67inductive SFR8052: Type[0] ≝
68   SFR_T2CON: SFR8052
69|  SFR_RCAP2L: SFR8052
70|  SFR_RCAP2H: SFR8052
71|  SFR_TL2: SFR8052
72|  SFR_TH2: SFR8052.
73
74definition 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(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *)
87record 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
105definition Status ≝ PreStatus (BitVectorTrie Byte 16).
106definition PseudoStatus ≝ PreStatus (pseudo_assembly_program).
107
108lemma 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
116qed.
117   
118lemma 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
126qed.
127   
128definition 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   
152definition 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
176definition 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
200definition 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
208qed.
209
210definition 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
218qed.
219
220definition 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)
249qed.
250
251definition 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)
280qed.
281
282definition 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               
306definition set_code_memory ≝
307  λM,M': 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               
330definition 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               
354definition 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               
379definition 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               
403definition 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    ]
415qed.
416
417definition 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 1 ?.
423    normalize
424    repeat (@ (le_S_S ? ?))
425    @ le_O_n
426qed.
427
428definition 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
437qed.
438
439definition 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
448qed.
449
450definition 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
459qed.
460
461definition 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
470qed.
471
472definition 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
481qed.
482
483definition 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
492qed.
493
494definition set_flags ≝
495  λM: Type[0].
496  λs: PreStatus M.
497  λcy: Bit.
498  λac: option Bit.
499  λov: Bit.
500    let old_cy ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) O ? in
501    let old_ac ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 1 ? in
502    let old_fo ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 2 ? in
503    let old_rs1 ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 3 ? in
504    let old_rs0 ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 4 ? in
505    let old_ov ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 5 ? in
506    let old_ud ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 6 ? in
507    let old_p ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 7 ? in
508    let new_ac ≝ match ac with [ None ⇒ old_ac | Some j ⇒ j ] in
509    let new_psw ≝ [[ old_cy ; new_ac ; old_fo ; old_rs1 ;
510                     old_rs0 ; old_ov ; old_ud ; old_p ]] in
511      set_8051_sfr ? s SFR_PSW new_psw.
512    [1,2,3,4,5,6,7,8:
513       normalize
514       repeat (@ le_S_S)
515       @ le_O_n
516    ]
517qed.
518
519definition initialise_status ≝
520  λM: Type[0].
521  λcode_mem: M.
522  let status ≝ mk_PreStatus M code_mem                    (* Code mem. *)
523                         (Stub Byte 7)                      (* Low mem.  *)
524                         (Stub Byte 7)                      (* High mem. *)
525                         (Stub Byte 16)                    (* Ext mem.  *)
526                         (zero 16)                         (* PC.       *)
527                         (replicate Byte 19 (zero 8)) (* 8051 SFR. *)
528                         (replicate Byte 5 (zero 8))     (* 8052 SFR. *)
529                         (zero 8)                           (* P1 latch. *)
530                         (zero 8)                           (* P3 latch. *)
531                         O                                      (* Clock.    *)
532  in
533    set_8051_sfr ? status SFR_SP (bitvector_of_nat 8 7).
534 
535axiom not_implemented: False.
536 
537definition get_bit_addressable_sfr ≝
538  λM: Type[0].
539  λs: PreStatus M.
540  λn: nat.
541  λb: BitVector n.
542  λl: bool.
543    let address ≝ nat_of_bitvector … b in
544      if (eqb address 128) then
545        ?
546      else if (eqb address 144) then
547        if l then
548          (p1_latch ? s)
549        else
550          (get_8051_sfr ? s SFR_P1)
551      else if (eqb address 160) then
552        ?
553      else if (eqb address 176) then
554        if l then
555          (p3_latch ? s)
556        else
557          (get_8051_sfr ? s SFR_P3)
558      else if (eqb address 153) then
559        get_8051_sfr ? s SFR_SBUF
560      else if (eqb address 138) then
561        get_8051_sfr ? s SFR_TL0
562      else if (eqb address 139) then
563        get_8051_sfr ? s SFR_TL1
564      else if (eqb address 140) then
565        get_8051_sfr ? s SFR_TH0
566      else if (eqb address 141) then
567        get_8051_sfr ? s SFR_TH1
568      else if (eqb address 200) then
569        get_8052_sfr ? s SFR_T2CON
570      else if (eqb address 202) then
571        get_8052_sfr ? s SFR_RCAP2L
572      else if (eqb address 203) then
573        get_8052_sfr ? s SFR_RCAP2H
574      else if (eqb address 204) then
575        get_8052_sfr ? s SFR_TL2
576      else if (eqb address 205) then
577        get_8052_sfr ? s SFR_TH2
578      else if (eqb address 135) then
579        get_8051_sfr ? s SFR_PCON
580      else if (eqb address 136) then
581        get_8051_sfr ? s SFR_TCON
582      else if (eqb address 137) then
583        get_8051_sfr ? s SFR_TMOD
584      else if (eqb address 152) then
585        get_8051_sfr ? s SFR_SCON
586      else if (eqb address 168) then
587        get_8051_sfr ? s SFR_IE
588      else if (eqb address 184) then
589        get_8051_sfr ? s SFR_IP
590      else if (eqb address 129) then
591        get_8051_sfr ? s SFR_SP
592      else if (eqb address 130) then
593        get_8051_sfr ? s SFR_DPL
594      else if (eqb address 131) then
595        get_8051_sfr ? s SFR_DPH
596      else if (eqb address 208) then
597        get_8051_sfr ? s SFR_PSW
598      else if (eqb address 224) then
599        get_8051_sfr ? s SFR_ACC_A
600      else if (eqb address 240) then
601        get_8051_sfr ? s SFR_ACC_B
602      else
603        ?.
604      cases not_implemented
605qed.
606
607definition set_bit_addressable_sfr ≝
608  λM: Type[0].
609  λs: PreStatus M.
610  λb: Byte.
611  λv: Byte.
612    let address ≝ nat_of_bitvector … b in
613      if (eqb address 128) then
614        ?
615      else if (eqb address 144) then
616        let status_1 ≝ set_8051_sfr ? s SFR_P1 v in
617        let status_2 ≝ set_p1_latch ? s v in
618          status_2
619      else if (eqb address 160) then
620        ?
621      else if (eqb address 176) then
622        let status_1 ≝ set_8051_sfr ? s SFR_P3 v in
623        let status_2 ≝ set_p3_latch ? s v in
624          status_2
625      else if (eqb address 153) then
626        set_8051_sfr ? s SFR_SBUF v
627      else if (eqb address 138) then
628        set_8051_sfr ? s SFR_TL0 v
629      else if (eqb address 139) then
630        set_8051_sfr ? s SFR_TL1 v
631      else if (eqb address 140) then
632        set_8051_sfr ? s SFR_TH0 v
633      else if (eqb address 141) then
634        set_8051_sfr ? s SFR_TH1 v
635      else if (eqb address 200) then
636        set_8052_sfr ? s SFR_T2CON v
637      else if (eqb address 202) then
638        set_8052_sfr ? s SFR_RCAP2L v
639      else if (eqb address 203) then
640        set_8052_sfr ? s SFR_RCAP2H v
641      else if (eqb address 204) then
642        set_8052_sfr ? s SFR_TL2 v
643      else if (eqb address 205) then
644        set_8052_sfr ? s SFR_TH2 v
645      else if (eqb address 135) then
646        set_8051_sfr ? s SFR_PCON v
647      else if (eqb address 136) then
648        set_8051_sfr ? s SFR_TCON v
649      else if (eqb address 137) then
650        set_8051_sfr ? s SFR_TMOD v
651      else if (eqb address 152) then
652        set_8051_sfr ? s SFR_SCON v
653      else if (eqb address 168) then
654        set_8051_sfr ? s SFR_IE v
655      else if (eqb address 184) then
656        set_8051_sfr ? s SFR_IP v
657      else if (eqb address 129) then
658        set_8051_sfr ? s SFR_SP v
659      else if (eqb address 130) then
660        set_8051_sfr ? s SFR_DPL v
661      else if (eqb address 131) then
662        set_8051_sfr ? s SFR_DPH v
663      else if (eqb address 208) then
664        set_8051_sfr ? s SFR_PSW v
665      else if (eqb address 224) then
666        set_8051_sfr ? s SFR_ACC_A v
667      else if (eqb address 240) then
668        set_8051_sfr ? s SFR_ACC_B v
669      else
670        ?.
671      cases not_implemented
672qed.
673
674definition bit_address_of_register ≝
675  λM: Type[0].
676  λs: PreStatus M.
677  λr: BitVector 3.
678    let b ≝ get_index_v … r O ? in
679    let c ≝ get_index_v … r 1 ? in
680    let d ≝ get_index_v … r 2 ? in
681    let 〈 un, ln 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_PSW) in
682    let 〈 r1, r0 〉 ≝ 〈 get_index_v … 4 un 2 ?, get_index_v … 4 un 3 ? 〉 in
683    let offset ≝
684      if ¬r1 ∧ ¬r0 then
685        O
686      else if ¬r1 ∧ r0 then
687        8
688      else if r1 ∧ r0 then
689        24
690      else
691        16
692    in
693      bitvector_of_nat 7 (offset + (nat_of_bitvector ? [[ false ; b ; c ; d ]])).
694  [1,2,3,4,5:
695    normalize
696    repeat (@ le_S_S)
697    @ le_O_n;
698  ]
699qed.
700
701definition get_register ≝
702  λM: Type[0].
703  λs: PreStatus M.
704  λr: BitVector 3.
705    let address ≝ bit_address_of_register ? s r in
706      lookup … address (low_internal_ram ? s) (zero 8).
707     
708definition set_register ≝
709  λM: Type[0].
710  λs: PreStatus M.
711  λr: BitVector 3.
712  λv: Byte.
713    let address ≝ bit_address_of_register ? s r in
714    let old_low_internal_ram ≝ low_internal_ram ? s in
715    let new_low_internal_ram ≝ insert … address v old_low_internal_ram in
716      set_low_internal_ram ? s new_low_internal_ram.
717     
718definition read_at_stack_pointer ≝
719  λM: Type[0].
720  λs: PreStatus M.
721    let 〈 nu, nl 〉 ≝ split … 4 4 (get_8051_sfr ? s SFR_SP) in
722    let m ≝ get_index_v … nu O ? in
723    let r1 ≝ get_index_v … nu 1 ? in
724    let r2 ≝ get_index_v … nu 2 ? in
725    let r3 ≝ get_index_v … nu 3 ? in
726    let address ≝ [[ r1 ; r2 ; r3 ]] @@ nl in
727    let memory ≝
728      if m then
729        (low_internal_ram ? s)
730      else
731        (high_internal_ram ? s)
732    in
733      lookup … address memory (zero 8).
734  [1,2,3,4:
735     normalize
736     repeat (@ le_S_S)
737     @ le_O_n
738  ]
739qed.
740
741definition write_at_stack_pointer ≝
742  λM: Type[0].
743  λs: PreStatus M.
744  λv: Byte.
745    let 〈 nu, nl 〉 ≝ split … 4 4 (get_8051_sfr ? s SFR_SP) in
746    let bit_zero ≝ get_index_v… nu O ? in
747    let bit_1 ≝ get_index_v… nu 1 ? in
748    let bit_2 ≝ get_index_v… nu 2 ? in
749    let bit_3 ≝ get_index_v… nu 3 ? in
750      if bit_zero then
751        let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl)
752                              v (low_internal_ram ? s) in
753          set_low_internal_ram ? s memory
754      else
755        let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl)
756                              v (high_internal_ram ? s) in
757          set_high_internal_ram ? s memory.
758  [1,2,3,4:
759     normalize
760     repeat (@ le_S_S)
761     @ le_O_n
762  ]
763qed.
764
765definition set_arg_16: ∀M: Type[0]. PreStatus M → Word → [[ dptr ]] → PreStatus M ≝
766  λM.
767  λs.
768  λv.
769  λa.
770   match a return λx. bool_to_Prop (is_in ? [[ dptr ]] x) → ? with
771     [ DPTR ⇒ λ_:True.
772       let 〈 bu, bl 〉 ≝ split … 8 8 v in
773       let status ≝ set_8051_sfr ? s SFR_DPH bu in
774       let status ≝ set_8051_sfr ? status SFR_DPL bl in
775         status
776     | _ ⇒ λK.
777       match K in False with
778       [
779       ]
780     ] (subaddressing_modein … a).
781   
782definition get_arg_16: ∀M: Type[0]. PreStatus M → [[ data16 ]] → Word ≝
783  λm, s, a.
784    match a return λx. bool_to_Prop (is_in ? [[ data16 ]] x) → ? with
785      [ DATA16 d ⇒ λ_:True. d
786      | _ ⇒ λK.
787        match K in False with
788        [
789        ]
790      ] (subaddressing_modein … a).
791     
792definition get_arg_8: ∀M: Type[0]. PreStatus M → bool → [[ direct ; indirect ; registr ;
793                                          acc_a ; acc_b ; data ; acc_dptr ;
794                                          acc_pc ; ext_indirect ;
795                                          ext_indirect_dptr ]] → Byte ≝
796  λm, s, l, a.
797    match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; registr ;
798                                                acc_a ; acc_b ; data ; acc_dptr ;
799                                                acc_pc ; ext_indirect ;
800                                                ext_indirect_dptr ]] x) → ? with
801      [ ACC_A ⇒ λacc_a: True. get_8051_sfr ? s SFR_ACC_A
802      | ACC_B ⇒ λacc_b: True. get_8051_sfr ? s SFR_ACC_B
803      | DATA d ⇒ λdata: True. d
804      | REGISTER r ⇒ λregister: True. get_register ? s r
805      | EXT_INDIRECT_DPTR ⇒
806        λext_indirect_dptr: True.
807          let address ≝ (get_8051_sfr ? s SFR_DPH) @@ (get_8051_sfr ? s SFR_DPL) in
808            lookup … 16 address (external_ram ? s) (zero 8)
809      | EXT_INDIRECT e ⇒
810        λext_indirect: True.
811          let address ≝ get_register ? s [[ false; false; e ]]  in
812          let padded_address ≝ pad 8 8 address in
813            lookup … 16 padded_address (external_ram ? s) (zero 8)
814      | ACC_DPTR ⇒
815        λacc_dptr: True.
816          let dptr ≝ (get_8051_sfr ? s SFR_DPH) @@ (get_8051_sfr ? s SFR_DPL) in
817          let padded_acc ≝ pad 8 8 (get_8051_sfr ? s SFR_ACC_A) in
818          let 〈 carry, address 〉 ≝ half_add 16 dptr padded_acc in
819            lookup … 16 address (external_ram ? s) (zero 8)
820      | ACC_PC ⇒
821        λacc_pc: True.
822          let padded_acc ≝ pad 8 8 (get_8051_sfr ? s SFR_ACC_A) in
823          let 〈 carry, address 〉 ≝ half_add 16 (program_counter ? s) padded_acc in
824            lookup … 16 address (external_ram ? s) (zero 8)
825      | DIRECT d ⇒
826        λdirect: True.
827          let 〈 nu, nl 〉 ≝ split … 4 4 d in
828          let bit_one ≝ get_index_v ? ? nu 0 ? in
829          let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in
830            match bit_one with
831              [ false ⇒
832                  let address ≝ three_bits @@ nl in
833                    lookup ? 7 address (low_internal_ram ? s) (zero 8)
834              | true ⇒ get_bit_addressable_sfr ? s 8 d l
835              ]
836      | INDIRECT i ⇒
837        λindirect: True.
838          let 〈 nu, nl 〉 ≝ split ? 4 4 (get_register ? s [[ false; false; i]]) in
839          let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in
840          let bit_1 ≝ get_index_v … bit_one_v O ? in
841          match  bit_1 with
842            [ false ⇒
843                lookup ? 7 (three_bits @@ nl) (low_internal_ram ? s) (zero 8)
844            | true ⇒
845                lookup ? 7 (three_bits @@ nl) (high_internal_ram ? s) (zero 8)
846            ]
847      | _ ⇒ λother.
848        match other in False with [ ]
849      ] (subaddressing_modein … a).
850  [1,2:
851     normalize
852     repeat (@ le_S_S)
853     @ le_O_n
854  ]
855qed.
856
857definition set_arg_8: ∀M: Type[0]. PreStatus M → [[ direct ; indirect ; registr ;
858                                   acc_a ; acc_b ; ext_indirect ;
859                                   ext_indirect_dptr ]] → Byte → PreStatus M ≝
860  λm, s, a, v.
861    match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; registr ;
862                                                acc_a ; acc_b ; ext_indirect ;
863                                                ext_indirect_dptr ]] x) → ? with
864      [ DIRECT d ⇒
865        λdirect: True.
866          let 〈 nu, nl 〉 ≝ split … 4 4 d in
867          let bit_one ≝ get_index_v ? ? nu 0 ? in
868          let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in
869            match bit_one with
870              [ true ⇒ set_bit_addressable_sfr ? s d v
871              | false ⇒
872                let memory ≝ insert ? 7 (three_bits @@ nl) v (low_internal_ram ? s) in
873                  set_low_internal_ram ? s memory
874              ]
875      | INDIRECT i ⇒
876        λindirect: True.
877          let register ≝ get_register ? s [[ false; false; i ]] in
878          let 〈nu, nl〉 ≝ split ? 4 4 register in
879          let bit_1 ≝ get_index_v … nu 0 ? in
880          let 〈ignore, three_bits〉 ≝ split ? 1 3 nu in
881            match bit_1 with
882              [ false ⇒
883                let memory ≝ insert … (three_bits @@ nl) v (low_internal_ram ? s) in
884                  set_low_internal_ram ? s memory
885              | true ⇒
886                let memory ≝ insert … (three_bits @@ nl) v (high_internal_ram ? s) in
887                  set_high_internal_ram ? s memory
888              ]
889      | REGISTER r ⇒ λregister: True. set_register ? s r v
890      | ACC_A ⇒ λacc_a: True. set_8051_sfr ? s SFR_ACC_A v
891      | ACC_B ⇒ λacc_b: True. set_8051_sfr ? s SFR_ACC_B v
892      | EXT_INDIRECT e ⇒
893        λext_indirect: True.
894          let address ≝ get_register ? s [[ false; false; e ]] in
895          let padded_address ≝ pad 8 8 address in
896          let memory ≝ insert ? 16 padded_address v (external_ram ? s) in
897            set_external_ram ? s memory
898      | EXT_INDIRECT_DPTR ⇒
899        λext_indirect_dptr: True.
900          let address ≝ (get_8051_sfr ? s SFR_DPH) @@ (get_8051_sfr ? s SFR_DPL) in
901          let memory ≝ insert ? 16 address v (external_ram ? s) in
902            set_external_ram ? s memory
903      | _ ⇒
904        λother: False.
905          match other in False with [ ]
906      ] (subaddressing_modein … a).
907  [1,2,3,4:
908     normalize
909     repeat (@ le_S_S)
910     @ le_O_n
911  ]
912qed.
913
914theorem modulus_less_than:
915  ∀m,n: nat. (m mod (S n)) < S n.
916  #n #m
917  normalize
918  @ le_S_S
919  lapply (le_n n)
920  generalize in ⊢ (?%? → ?(??%?)?)
921  elim n in ⊢ (∀_:?. ??% → ?(?%??)?)
922  [ normalize
923    #n
924    @ (less_than_or_equal_b_elim n m)
925    normalize
926    [ //
927    | #H #K
928      inversion K
929      [ # H1
930        < H1
931        //
932      | #x #H1 #H2 #H3
933        destruct
934      ]
935    ]
936  | normalize
937    # y # H1 # n # H2
938    @ (less_than_or_equal_b_elim n m)
939    normalize
940    [ //
941    | # K
942      @ H1
943      cut (n ≤ S y → n - S m ≤ y)
944      /2/
945      cases n
946      normalize
947      //
948      # x # K1
949      lapply (le_S_S_to_le … K1)
950      generalize in match m
951      elim x
952      normalize
953      //
954      # w1 # H # m
955      cases m
956      normalize
957      //
958      # q # K2
959      apply H
960      /3/
961    ]
962  ]
963qed.
964
965definition get_arg_1: ∀M: Type[0]. PreStatus M → [[ bit_addr ; n_bit_addr ; carry ]] →
966                       bool → bool ≝
967  λm, s, a, l.
968    match a return λx. bool_to_Prop (is_in ? [[ bit_addr ;
969                                                 n_bit_addr ;
970                                                 carry ]] x) → ? with
971      [ BIT_ADDR b ⇒
972        λbit_addr: True.
973          let 〈 nu, nl 〉 ≝ split … 4 4 b in
974          let bit_1 ≝ get_index_v … nu 0 ? in
975          let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in
976            match bit_1 with
977              [ true ⇒
978                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
979                let d ≝ address ÷ 8 in
980                let m ≝ address mod 8 in
981                let trans ≝ bitvector_of_nat 8 ((d * 8) + 128) in
982                let sfr ≝ get_bit_addressable_sfr ? s ? trans l in
983                  get_index_v … sfr m ?
984              | false ⇒
985                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
986                let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in
987                let t ≝ lookup … 7 address' (low_internal_ram ? s) (zero 8) in
988                  get_index_v … t (modulus address 8) ?
989              ]
990      | N_BIT_ADDR n ⇒
991        λn_bit_addr: True.
992          let 〈 nu, nl 〉 ≝ split … 4 4 n in
993          let bit_1 ≝ get_index_v … nu 0 ? in
994          let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in
995            match bit_1 with
996              [ true ⇒
997                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
998                let d ≝ address ÷ 8 in
999                let m ≝ address mod 8 in
1000                let trans ≝ bitvector_of_nat 8 ((d * 8) + 128) in
1001                let sfr ≝ get_bit_addressable_sfr ? s ? trans l in
1002                  ¬(get_index_v … sfr m ?)
1003              | false ⇒
1004                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
1005                let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in
1006                let trans ≝ lookup … 7 address' (low_internal_ram ? s) (zero 8) in
1007                  ¬(get_index_v … trans (modulus address 8) ?)
1008              ]
1009      | CARRY ⇒ λcarry: True. get_cy_flag ? s
1010      | _ ⇒ λother.
1011        match other in False with [ ]
1012      ] (subaddressing_modein … a).
1013      [3,6:
1014         normalize
1015         repeat (@ le_S_S)
1016         @ le_O_n
1017      |1,2,4,5:
1018         apply modulus_less_than
1019      ]
1020qed.
1021     
1022definition set_arg_1: ∀M: Type[0]. PreStatus M → [[ bit_addr ; carry ]] →
1023                       Bit → PreStatus M ≝
1024  λm, s, a, v.
1025    match a return λx. bool_to_Prop (is_in ? [[ bit_addr ; carry ]] x) → ? with
1026      [ BIT_ADDR b ⇒ λbit_addr: True.
1027          let 〈 nu, nl 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_PSW) in
1028          let bit_1 ≝ get_index_v … nu 0 ? in
1029          let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in
1030          match bit_1 with
1031            [ true ⇒
1032                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
1033                let d ≝ address ÷ 8 in
1034                let m ≝ address mod 8 in
1035                let t ≝ bitvector_of_nat 8 ((d * 8) + 128) in
1036                let sfr ≝ get_bit_addressable_sfr ? s ? t true in
1037                let new_sfr ≝ set_index … sfr m v ? in
1038                  set_bit_addressable_sfr ? s new_sfr t
1039            | false ⇒
1040                let address ≝ nat_of_bitvector … (three_bits @@ nl) in
1041                let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in
1042                let t ≝ lookup … 7 address' (low_internal_ram ? s) (zero 8) in
1043                let n_bit ≝ set_index … t (modulus address 8) v ? in
1044                let memory ≝ insert ? 7 address' n_bit (low_internal_ram ? s) in
1045                  set_low_internal_ram ? s memory
1046            ]
1047      | CARRY ⇒
1048        λcarry: True.
1049          let 〈 nu, nl 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_PSW) in
1050          let bit_1 ≝ get_index_v… nu 1 ? in
1051          let bit_2 ≝ get_index_v… nu 2 ? in
1052          let bit_3 ≝ get_index_v… nu 3 ? in
1053          let new_psw ≝ [[ v; bit_1 ; bit_2; bit_3 ]] @@ nl in
1054            set_8051_sfr ? s SFR_PSW new_psw
1055      | _ ⇒
1056        λother: False.
1057          match other in False with
1058            [ ]
1059      ] (subaddressing_modein … a).
1060      [1,2,3,6:
1061         normalize
1062         repeat (@ le_S_S)
1063         @ le_O_n
1064      |4,5:
1065         @ modulus_less_than
1066      ]
1067qed.
1068
1069definition load_code_memory ≝
1070 fold_left_i … (
1071   λi, mem, v.
1072     insert … (bitvector_of_nat … i) v mem) (Stub Byte 16).
1073
1074definition load ≝
1075 λl.
1076 λstatus.
1077   set_code_memory (BitVectorTrie Word 16) ? status (load_code_memory l).
1078
1079definition fetch_pseudo_instruction: list labelled_instruction → Word → (pseudo_instruction × Word) ≝
1080  λcode_mem.
1081  λpc: Word.
1082    let 〈lbl, instr〉 ≝ nth (nat_of_bitvector ? pc) … code_mem ? in
1083    let 〈flags, new_pc〉 ≝ half_add ? pc (bitvector_of_nat ? 1) in
1084      〈instr, new_pc〉.
1085    cases not_implemented.
1086qed.
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