source: src/LIN/LINToASM.ma @ 1281

Last change on this file since 1281 was 1275, checked in by sacerdot, 9 years ago

RTL ported to joint syntax, but:

  1. bug discovered: opaccs should have taken four registers
  2. push/pop should not be present in RTL :-(

ERTLToLTL and RTLtoERTL not working ATM
File size: 14.7 KB
Line 
1include "ASM/Util.ma".
2include "utilities/BitVectorTrieSet.ma".
3include "LIN/LIN.ma".
4
5let rec association (i: ident) (l: list (ident × nat))
6                    on l: member i (eq_identifier ?) (map ? ? (fst ? ?) l) → nat ≝
7  match l return λl. member i (eq_identifier ?) (map ? ? (fst ? ?) l) → nat with
8  [ nil ⇒ λabsd. ?
9  | cons hd tl ⇒
10    λprf: member i (eq_identifier ?) (map ? ? (fst ? ?) (cons ? hd tl)).
11      (match eq_identifier ? (\fst hd) i return λb. eq_identifier ? (\fst hd) i = b → nat with
12      [ true ⇒ λeq_prf. \snd hd
13      | false ⇒ λeq_prf. association i tl ?
14      ]) (refl ? (eq_identifier ? (\fst hd) i))
15  ].
16  [ cases absd
17  | cases prf
18    [ > eq_prf
19      # H
20      cases H
21    | # H
22      assumption
23    ]
24  ]
25qed.
26
27definition statement_labels ≝
28  λg: list ident.
29  λs: lin_statement g.
30  let 〈label, instr〉 ≝ s in
31  let generated ≝
32    match instr with
33    [ joint_st_sequential instr' _ ⇒
34      match instr' with
35      [ joint_instr_cost_label lbl ⇒ set_insert ? (word_of_identifier ? lbl) (set_empty ?)
36      | joint_instr_cond acc_a_reg lbl ⇒ set_insert ? (word_of_identifier ? lbl) (set_empty ?)
37      | _ ⇒ set_empty ?
38      ]
39    | joint_st_return ⇒ set_empty ?
40    | joint_st_goto lbl ⇒ set_insert ? (word_of_identifier ? lbl) (set_empty ?) ]
41  in
42  match label with
43  [ None ⇒ generated
44  | Some lbl ⇒ set_insert ? (word_of_identifier ? lbl) generated
45  ].
46
47definition function_labels_internal ≝
48  λglobals: list ident.
49  λlabels: BitVectorTrieSet ?.
50  λstatement: lin_statement globals.
51    set_union ? labels (statement_labels globals statement).
52
53
54(* dpm: A = Identifier *)
55definition function_labels: ∀A. ∀globals. ∀f. BitVectorTrieSet ? ≝
56  λA: Type[0].
57  λglobals: list ident.
58  λf: A × (lin_function globals).
59  let 〈ignore, fun_def〉 ≝ f in
60  match fun_def return λ_. BitVectorTrieSet ? with
61  [ Internal stmts ⇒
62      foldl ? ? (function_labels_internal globals) (set_empty ?) (pi1 … (joint_if_code ?? stmts))
63  | External _ ⇒ set_empty ?
64  ].
65 
66definition program_labels_internal: ∀A. ∀globals. ∀labels. ∀funct. BitVectorTrieSet ? ≝
67  λA: Type[0].
68  λglobals: list ident.
69  λlabels: BitVectorTrieSet ?.
70  λfunct: A × (lin_function globals).
71    set_union ? labels (function_labels ? globals funct).
72
73(* CSC: here we are silently throwing away the region information *)
74definition program_labels ≝
75 λprogram: lin_program.
76    foldl … (program_labels_internal … (map … (λx. fst … (fst … x)) (prog_vars … program)))
77              (set_empty …) (prog_funct … program).
78 
79definition data_of_int ≝ λbv. DATA bv.
80definition data16_of_int ≝ λbv. DATA16 (bitvector_of_nat 16 bv).
81definition accumulator_address ≝ DIRECT (bitvector_of_nat 8 224).
82
83definition translate_statements ≝
84  λglobals: list (ident × nat).
85  λglobals_old: list ident.
86  λprf: ∀i: ident. member i (eq_identifier ?) globals_old → member i (eq_identifier ?) (map ? ? (fst ? ?) globals).
87  λstatement: pre_lin_statement globals_old.
88  match statement with
89  [ joint_st_goto lbl ⇒ Jmp (word_of_identifier ? lbl)
90  | joint_st_return ⇒ Instruction (RET ?)
91  | joint_st_sequential instr _ ⇒
92      match instr with
93      [ joint_instr_extension ext ⇒ ⊥
94      | joint_instr_comment comment ⇒ Comment comment
95      | joint_instr_cost_label lbl ⇒ Cost (word_of_identifier ? lbl)
96      | joint_instr_pop _ ⇒ Instruction (POP ? accumulator_address)
97      | joint_instr_push _ ⇒ Instruction (PUSH ? accumulator_address)
98      | joint_instr_clear_carry ⇒ Instruction (CLR ? CARRY)
99      | joint_instr_call_id f _ _ ⇒ Call (word_of_identifier ? f)
100      | joint_instr_opaccs accs _ _ _ _ ⇒
101        match accs with
102        [ Mul ⇒ Instruction (MUL ? ACC_A ACC_B)
103        | DivuModu ⇒ Instruction (DIV ? ACC_A ACC_B)
104        ]
105      | joint_instr_op1 op1 _ _ ⇒
106        match op1 with
107        [ Cmpl ⇒ Instruction (CPL ? ACC_A)
108        | Inc ⇒ Instruction (INC ? ACC_A)
109        ]
110      | joint_instr_op2 op2 _ _ reg ⇒
111        match op2 with
112        [ Add ⇒
113          let reg' ≝ register_address reg in
114          match reg' return λx. bool_to_Prop (is_in … [[ acc_a;
115                                                         direct;
116                                                         registr ]] x) → ? with
117          [ ACC_A ⇒ λacc_a: True.
118            Instruction (ADD ? ACC_A accumulator_address)
119          | DIRECT d ⇒ λdirect1: True.
120            Instruction (ADD ? ACC_A (DIRECT d))
121          | REGISTER r ⇒ λregister1: True.
122            Instruction (ADD ? ACC_A (REGISTER r))
123          | _ ⇒ λother: False. ⊥
124          ] (subaddressing_modein … reg')
125        | Addc ⇒
126          let reg' ≝ register_address reg in
127          match reg' return λx. bool_to_Prop (is_in … [[ acc_a;
128                                                         direct;
129                                                         registr ]] x) → ? with
130          [ ACC_A ⇒ λacc_a: True.
131            Instruction (ADDC ? ACC_A accumulator_address)
132          | DIRECT d ⇒ λdirect2: True.
133            Instruction (ADDC ? ACC_A (DIRECT d))
134          | REGISTER r ⇒ λregister2: True.
135            Instruction (ADDC ? ACC_A (REGISTER r))
136          | _ ⇒ λother: False. ⊥
137          ] (subaddressing_modein … reg')
138        | Sub ⇒
139          let reg' ≝ register_address reg in
140          match reg' return λx. bool_to_Prop (is_in … [[ acc_a;
141                                                         direct;
142                                                         registr ]] x) → ? with
143          [ ACC_A ⇒ λacc_a: True.
144            Instruction (SUBB ? ACC_A accumulator_address)
145          | DIRECT d ⇒ λdirect3: True.
146            Instruction (SUBB ? ACC_A (DIRECT d))
147          | REGISTER r ⇒ λregister3: True.
148            Instruction (SUBB ? ACC_A (REGISTER r))
149          | _ ⇒ λother: False. ⊥
150          ] (subaddressing_modein … reg')
151        | And ⇒
152          let reg' ≝ register_address reg in
153          match reg' return λx. bool_to_Prop (is_in … [[ acc_a;
154                                                         direct;
155                                                         registr ]] x) → ? with
156          [ ACC_A ⇒ λacc_a: True.
157            Instruction (NOP ?)
158          | DIRECT d ⇒ λdirect4: True.
159            Instruction (ANL ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉)))
160          | REGISTER r ⇒ λregister4: True.
161            Instruction (ANL ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉)))
162          | _ ⇒ λother: False. ⊥
163          ] (subaddressing_modein … reg')
164        | Or ⇒
165          let reg' ≝ register_address reg in
166          match reg' return λx. bool_to_Prop (is_in … [[ acc_a;
167                                                         direct;
168                                                         registr ]] x) → ? with
169          [ ACC_A ⇒ λacc_a: True.
170            Instruction (NOP ?)
171          | DIRECT d ⇒ λdirect5: True.
172            Instruction (ORL ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉)))
173          | REGISTER r ⇒ λregister5: True.
174            Instruction (ORL ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉)))
175          | _ ⇒ λother: False. ⊥
176          ] (subaddressing_modein … reg')
177        | Xor ⇒
178          let reg' ≝ register_address reg in
179          match reg' return λx. bool_to_Prop (is_in … [[ acc_a;
180                                                         direct;
181                                                         registr ]] x) → ? with
182          [ ACC_A ⇒ λacc_a: True.
183            Instruction (XRL ? (inr ? ? 〈accumulator_address, ACC_A〉))
184          | DIRECT d ⇒ λdirect6: True.
185            Instruction (XRL ? (inl ? ? 〈ACC_A, DIRECT d〉))
186          | REGISTER r ⇒ λregister6: True.
187            Instruction (XRL ? (inl ? ? 〈ACC_A, REGISTER r〉))
188          | _ ⇒ λother: False. ⊥
189          ] (subaddressing_modein … reg')
190        ]
191      | joint_instr_int reg byte ⇒
192        let reg' ≝ register_address reg in
193          match reg' return λx. bool_to_Prop (is_in … [[ acc_a;
194                                                         direct;
195                                                         registr ]] x) → ? with
196          [ REGISTER r ⇒ λregister7: True.
197            Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈REGISTER r, (data_of_int byte)〉))))))
198          | ACC_A ⇒ λacc: True.
199            Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, (data_of_int byte)〉))))))
200          | DIRECT d ⇒ λdirect7: True.
201            Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈DIRECT d, (data_of_int byte)〉)))))
202          | _ ⇒ λother: False. ⊥
203          ] (subaddressing_modein … reg')
204      | joint_instr_move regs ⇒
205         match regs with
206          [ from_acc reg ⇒
207             let reg' ≝ register_address reg in
208               match reg' return λx. bool_to_Prop (is_in … [[ acc_a;
209                                                              direct;
210                                                              registr ]] x) → ? with
211               [ REGISTER r ⇒ λregister8: True.
212                 Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈REGISTER r, ACC_A〉))))))
213               | ACC_A ⇒ λacc: True.
214                 Instruction (NOP ?)
215               | DIRECT d ⇒ λdirect8: True.
216                 Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈DIRECT d, ACC_A〉)))))
217               | _ ⇒ λother: False. ⊥
218               ] (subaddressing_modein … reg')
219          | to_acc reg ⇒
220             let reg' ≝ register_address reg in
221               match reg' return λx. bool_to_Prop (is_in … [[ acc_a;
222                                                              direct;
223                                                              registr ]] x) → ? with
224               [ REGISTER r ⇒ λregister9: True.
225                 Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉))))))
226               | DIRECT d ⇒ λdirect9: True.
227                 Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉))))))
228               | ACC_A ⇒ λacc_a: True.
229                 Instruction (NOP ?)
230               | _ ⇒ λother: False. ⊥
231               ] (subaddressing_modein … reg')]
232      | joint_instr_load _ _ _ ⇒ Instruction (MOVX ? (inl ? ? 〈ACC_A, EXT_INDIRECT_DPTR〉))
233      | joint_instr_store _ _ _ ⇒ Instruction (MOVX ? (inr ? ? 〈EXT_INDIRECT_DPTR, ACC_A〉))
234      | joint_instr_address addr proof _ _ ⇒
235        let look ≝ association addr globals (prf ? proof) in
236          Instruction (MOV ? (inl ? ? (inl ? ? (inr ? ? (〈DPTR, (data16_of_int look)〉)))))
237      | joint_instr_cond _ lbl ⇒
238        (* dpm: this should be handled in translate_code! *)
239        Instruction (JNZ ? (word_of_identifier ? lbl))
240      | joint_instr_set_carry ⇒
241        Instruction (SETB ? CARRY)
242      ]
243    ].
244  try assumption
245  try @ I
246qed.
247
248(*CSC: XXXXXXXXXXX looks bad: what invariant is needed here? *)
249definition ident_of_label: label → ident ≝
250 λl. an_identifier … (word_of_identifier … l).
251
252definition build_translated_statement ≝
253  λglobals.
254  λglobals_old.
255  λprf.
256  λstatement: lin_statement globals_old.
257    〈option_map … ident_of_label (\fst statement), translate_statements globals globals_old prf (\snd statement)〉.
258
259definition translate_code ≝
260  λglobals: list (ident × nat).
261  λglobals_old: list ident.
262  λprf.
263  λcode: list (lin_statement globals_old).
264    map ? ? (build_translated_statement globals globals_old prf) code.
265   
266lemma translate_code_preserves_WellFormedP:
267  ∀globals, globals_old, prf, code.
268    well_formed_P ? ? code → well_formed_P ? ? (translate_code globals globals_old prf code).
269  #G #GO #P #C
270  elim C
271  [ normalize
272    //
273  | #G2 #G02 #IH (* CSC: understand here *)
274    whd in ⊢ (% → %) whd in match build_translated_statement normalize nodelta
275    cases (\fst G2) normalize // ]
276qed.
277
278definition translate_fun_def ≝
279  λglobals: list (ident × nat).
280  λglobals_old.
281  λprf.
282  λid_def.
283    let 〈id, def〉 ≝ id_def in
284    match def with
285    [ Internal int ⇒
286      let code_proof ≝ joint_if_code … (lin_params globals_old) int in
287      match translate_code globals globals_old prf (pi1 ?? code_proof) return λtranscode. well_formed_P ? ? transcode → list labelled_instruction with
288      [ nil ⇒ λprf2. ⊥
289      | cons hd tl ⇒ λ_.
290        let rest ≝ 〈Some ? id, \snd hd〉 :: tl in
291          map ? ? (
292            λr.
293            match fst ? ? r with
294            [ Some id' ⇒ 〈Some ? (word_of_identifier ? id'), snd ? ? r〉
295            | None ⇒ 〈None ?, \snd r〉
296            ]) rest
297      ] (translate_code_preserves_WellFormedP globals globals_old prf (pi1 ?? code_proof) (pi2 ?? code_proof))
298    | External _ ⇒ [ ]
299    ].
300@prf2
301qed.
302   
303definition translate_functs ≝
304  λglobals.
305  λglobals_old.
306  λprf.
307  λexit_label.
308  λmain.
309  λfuncts.
310  let preamble ≝ [ 〈None ?, Call main〉 ; 〈Some ? exit_label, Jmp exit_label〉 ] in
311   preamble @
312    (flatten ? (map ? ? (translate_fun_def globals globals_old prf) functs)).
313
314(*CSC: region silently thrown away here *)
315definition globals_addr ≝
316 λl.
317  let globals_addr_internal ≝
318   λres_offset.
319   λx_size: ident × region × nat.
320    let 〈res, offset〉 ≝ res_offset in
321    let 〈x, region, size〉 ≝ x_size in
322      〈〈x, offset〉 :: res, offset + size〉
323  in
324    \fst (foldl ? ? globals_addr_internal 〈[ ], 0〉 l).
325
326(* dpm: plays the role of the string "_exit" in the O'caml source *)
327axiom identifier_prefix: Word.
328(*CSC: XXXXXXX wrong anyway since labels from different functions can now
329  clash with each other and with names of functions *)
330axiom fresh_prefix: BitVectorTrieSet 16 → Word → Word.
331
332(* dpm: fresh prefix stuff needs unifying with brian *)
333definition translate : lin_program → pseudo_assembly_program ≝
334  λp.
335  let prog_lbls ≝ program_labels … p in
336  let exit_label ≝ fresh_prefix prog_lbls identifier_prefix in
337  let global_addr ≝ globals_addr (prog_vars … p) in
338  let global_addr' ≝ map ?? (λx_off. let 〈x,off〉 ≝ x_off in 〈word_of_identifier ? x,off〉) global_addr in
339    〈global_addr', translate_functs global_addr (prog_var_names … p) ? exit_label (word_of_identifier … (prog_main … p)) (prog_funct … p)〉.
340 #i normalize nodelta -global_addr' global_addr exit_label prog_lbls;
341 normalize in match prog_var_names normalize nodelta
342 elim (prog_vars … p) //
343 #hd #tl #IH whd in ⊢ (% → %)
344 whd in match globals_addr normalize nodelta
345 whd in match (foldl ???? (hd::tl)) normalize nodelta
346 cases hd * #id #reg #size normalize nodelta
347 cases daemon (*CSC: provable using a pair of lemmas over foldl *)
348qed.
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