source: src/joint/semantics.ma @ 1359

Last change on this file since 1359 was 1359, checked in by sacerdot, 9 years ago
  1. more work on the RTL semantics
  2. changes to joint/semantics to accomodate the RTL one
File size: 16.0 KB
Line 
1include "utilities/lists.ma".
2include "common/Globalenvs.ma".
3include "common/IO.ma".
4include "common/SmallstepExec.ma".
5include "joint/Joint.ma".
6include "joint/BEMem.ma".
7
8(* CSC: external functions never fail (??) and always return something of the
9   size of one register, both in the frontend and in the backend.
10   Is this reasonable??? In OCaml it always return a list, but in the frontend
11   only the head is kept (or Undef if the list is empty) ??? *)
12
13record more_sem_params (p:params_): Type[1] ≝
14 { framesT: Type[0]
15 ; regsT: Type[0]
16
17 ; succ_pc: succ p → address → address
18 ; greg_store_: generic_reg p → beval → regsT → res regsT
19 ; greg_retrieve_: regsT → generic_reg p → res beval
20 ; acca_store_: acc_a_reg p → beval → regsT → res regsT
21 ; acca_retrieve_: regsT → acc_a_reg p → res beval
22 ; accb_store_: acc_b_reg p → beval → regsT → res regsT
23 ; accb_retrieve_: regsT → acc_b_reg p → res beval
24 ; dpl_store_: dpl_reg p → beval → regsT → res regsT
25 ; dpl_retrieve_: regsT → dpl_reg p → res beval
26 ; dph_store_: dph_reg p → beval → regsT → res regsT
27 ; dph_retrieve_: regsT → dph_reg p → res beval
28 ; pair_reg_move_: regsT → pair_reg p → res regsT
29 
30 ; pointer_of_label: label → Σp:pointer. ptype p = Code
31 }.
32
33record sem_params: Type[1] ≝
34 { spp :> params_
35 ; more_sem_pars :> more_sem_params spp
36 }.
37
38record state (p: sem_params): Type[0] ≝
39 { st_frms: framesT ? p
40 ; pc: address
41 ; sp: pointer
42 ; carry: beval
43 ; regs: regsT ? p
44 ; m: bemem
45 }.
46
47record more_sem_params1 (succT: Type[0]) (p:params1): Type[1] ≝
48 { more_sparams :> more_sem_params (mk_params_ p succT)
49
50   (* Functions that manipulate the st_frms component of the state *)
51 ; init_locals : localsT p → regsT … more_sparams → regsT … more_sparams
52 ; pop_frame: list beval → state (mk_sem_params … more_sparams) → res (state (mk_sem_params … more_sparams))
53 ; save_frame: call_dest p → state (mk_sem_params … more_sparams) → state (mk_sem_params … more_sparams)
54 }.
55
56record sem_params1: Type[1] ≝
57 { spp1 :> params1
58 ; ssucc_ : Type[0]
59 ; more_sem_params1 :> more_sem_params1 ssucc_ spp1
60 }.
61
62definition sem_params_of_sem_params1 ≝ λsp1: sem_params1. mk_sem_params … sp1.
63coercion sem_params_of_sem_params1 : ∀_x:sem_params1. sem_params
64 ≝ sem_params_of_sem_params1 on _x: sem_params1 to sem_params.
65
66definition genv ≝ λglobals.λp:params globals. (genv_t Genv) (joint_function globals p).
67
68record more_sem_params2 (globals: list ident) (p: params globals) : Type[1] ≝
69 { more_sparams1 :> more_sem_params1 (succ p) p
70
71 ; fetch_statement: genv … p → state (mk_sem_params … more_sparams1) → res (joint_statement (mk_sem_params … more_sparams1) globals)
72 ; fetch_result: state (mk_sem_params … more_sparams1) → res (list beval)
73
74 ; fetch_external_args: external_function → state (mk_sem_params … more_sparams1) → res (list val)
75 ; set_result: list val → state (mk_sem_params … more_sparams1) → res (state (mk_sem_params … more_sparams1))
76
77 ; exec_extended: genv globals p → extend_statements (mk_sem_params … more_sparams1) → succ p → state (mk_sem_params … more_sparams1) → IO io_out io_in (trace × (state (mk_sem_params … more_sparams1)))
78 }.
79
80record sem_params2 (globals: list ident): Type[1] ≝
81 { p2:> params globals
82 ; more_sparams2:> more_sem_params2 globals p2
83 }.
84
85definition sem_params_of_sem_params2 ≝ λglobals. λsp2: sem_params2 globals. mk_sem_params sp2 sp2.
86coercion sem_params_of_sem_params2 : ∀globals. ∀_x:sem_params2 globals. sem_params
87 ≝ sem_params_of_sem_params2 on _x: sem_params2 ? to sem_params.
88(*
89unification hint  0 ≔ globals: (list ident), p: sem_params2 globals;
90   S ≟ sem_params_of_sem_params2 globals p
91(* ---------------------------------------- *) ⊢
92   pars_ (spp (mk_sem_params (p2 globals p)
93    (more_sparams (p2 globals p) globals
94    (more_sparams2 globals p)))) ≡ spp__o__pars_ S.
95*)
96definition sem_params1_of_sem_params2 ≝ λglobals. λsp2: sem_params2 globals. mk_sem_params1 sp2 (succ sp2) sp2.
97coercion sem_params1_of_sem_params2 : ∀globals. ∀_x:sem_params2 globals. sem_params1
98 ≝ sem_params1_of_sem_params2 on _x: sem_params2 ? to sem_params1.
99
100definition address_of_label: sem_params → label → address.
101 #p #l generalize in match (refl … (address_of_pointer (pointer_of_label … p l)))
102 cases (address_of_pointer (pointer_of_label … p l)) in ⊢ (???% → ?)
103  [ #res #_ @res
104  | #msg cases (pointer_of_label … p l) * * #q #com #off #E1 #E2 try destruct
105    normalize in E2; destruct ]
106qed.
107
108definition set_m: ∀p. bemem → state p → state p ≝
109 λp,m,st. mk_state p (st_frms … st) (pc … st) (sp … st) (carry … st) (regs … st) m.
110
111definition set_regs: ∀p:sem_params. regsT ? p → state p → state p ≝
112 λp,regs,st. mk_state p (st_frms … st) (pc … st) (sp … st) (carry … st) regs (m … st).
113
114definition set_sp: ∀p. pointer → state p → state p ≝
115 λp,sp,st. mk_state … (st_frms … st) (pc … st) sp (carry … st) (regs … st) (m … st).
116
117definition set_carry: ∀p. beval → state p → state p ≝
118 λp,carry,st. mk_state … (st_frms … st) (pc … st) (sp … st) carry (regs … st) (m … st).
119
120definition set_pc: ∀p. address → state p → state p ≝
121 λp,pc,st. mk_state … (st_frms … st) pc (sp … st) (carry … st) (regs … st) (m … st).
122
123definition set_frms: ∀p:sem_params. framesT ? p → state p → state p ≝
124 λp,frms,st. mk_state … frms (pc … st) (sp … st) (carry … st) (regs … st) (m … st).
125
126definition goto: ∀p:sem_params. label → state p → state p ≝
127 λp,l,st. set_pc … (address_of_label p l) st.
128
129definition next: ∀p:sem_params. succ … p → state p → state p ≝
130 λp,l,st. set_pc … (succ_pc … (more_sem_pars p) l (pc … st)) st.
131
132definition greg_store: ∀p:sem_params. generic_reg p → beval → state p → res (state p) ≝
133 λp,dst,v,st.
134  do regs  ← greg_store_ … dst v (regs … st);
135  OK ? (set_regs … regs st).
136
137definition greg_retrieve: ∀p:sem_params. state p → generic_reg p → res beval ≝
138 λp,st,dst.greg_retrieve_ … (regs … st) dst.
139
140definition acca_store: ∀p:sem_params. acc_a_reg p → beval → state p → res (state p) ≝
141 λp,dst,v,st.
142  do regs ← acca_store_ … dst v (regs … st);
143  OK ? (set_regs … regs st).
144
145definition acca_retrieve: ∀p:sem_params. state p → acc_a_reg p → res beval ≝
146 λp,st,dst.acca_retrieve_ … (regs … st) dst.
147
148definition accb_store: ∀p:sem_params. acc_b_reg p → beval → state p → res (state p) ≝
149 λp,dst,v,st.
150  do regs ← accb_store_ … dst v (regs … st);
151  OK ? (set_regs … regs st).
152
153definition accb_retrieve: ∀p:sem_params. state p → acc_b_reg p → res beval ≝
154 λp,st,dst.accb_retrieve_ … (regs … st) dst.
155
156definition dpl_store: ∀p:sem_params. dpl_reg p → beval → state p → res (state p) ≝
157 λp,dst,v,st.
158  do regs ← dpl_store_ … dst v (regs … st);
159  OK ? (set_regs … regs st).
160
161definition dpl_retrieve: ∀p:sem_params. state p → dpl_reg p → res beval ≝
162 λp,st,dst.dpl_retrieve_ … (regs … st) dst.
163
164definition dph_store: ∀p:sem_params. dph_reg p → beval → state p → res (state p) ≝
165 λp,dst,v,st.
166  do regs ← dph_store_ … dst v (regs … st);
167  OK ? (set_regs … regs st).
168
169definition dph_retrieve: ∀p:sem_params. state p → dph_reg p → res beval ≝
170 λp,st,dst.dph_retrieve_ … (regs … st) dst.
171
172definition pair_reg_move: ∀p:sem_params. state p → pair_reg p → res (state p) ≝
173 λp,st,rs.
174  do regs ← pair_reg_move_ … (regs … st) rs;
175  OK … (set_regs … regs st).
176
177axiom FailedStore: String.
178
179definition push: ∀p. state p → beval → res (state p) ≝
180 λp,st,v.
181  let sp ≝ sp … st in
182  do m ← opt_to_res … (msg FailedStore) (bestorev (m … st) sp v);
183  let sp ≝ shift_pointer … sp [[false;false;false;false;false;false;false;true]] in
184  OK … (set_m … m (set_sp … sp st)).
185
186definition pop: ∀p. state p → res (state p × beval) ≝
187 λp,st.
188  let sp ≝ sp ? st in
189  let sp ≝ neg_shift_pointer ? sp [[false;false;false;false;false;false;false;true]] in
190  let st ≝ set_sp … sp st in
191  do v ← opt_to_res ? (msg FailedStore) (beloadv (m ? st) sp);
192  OK ? 〈st,v〉.
193
194definition save_ra : ∀p. state p → succ p → res (state p) ≝
195 λp,st,l.
196  let 〈addrl,addrh〉 ≝ succ_pc … (more_sem_pars p) l (pc … st) in
197  do st ← push … st addrl;
198  push … st addrh.
199
200definition fetch_ra : ∀p.state p → res (state p × address) ≝
201 λp,st.
202  do 〈st,addrh〉 ← pop … st;
203  do 〈st,addrl〉 ← pop … st;
204  OK ? 〈st, 〈addrl,addrh〉〉.
205
206axiom MissingSymbol : String.
207axiom FailedLoad : String.
208axiom BadFunction : String.
209
210definition eval_statement : ∀globals: list ident.∀p:sem_params2 globals. genv globals p → state p → IO io_out io_in (trace × (state p)) ≝
211 λglobals,p,ge,st.
212  ! s ← fetch_statement … ge st;
213  match s with
214    [ GOTO l ⇒ ret ? 〈E0, goto … l st〉
215    | sequential seq l ⇒
216      match seq with
217      [ extension c ⇒ exec_extended … p ge c l st
218      | COST_LABEL cl ⇒ ret ? 〈Echarge cl, next … l st〉
219      | COMMENT c ⇒ ret ? 〈E0, next … l st〉
220      | INT dest v ⇒
221        ! st ← greg_store p dest (BVByte v) st;
222          ret ? 〈E0, next … l st〉
223      | LOAD dst addrl addrh ⇒
224        ! vaddrh ← dph_retrieve … st addrh;
225        ! vaddrl ← dpl_retrieve … st addrl;
226        ! vaddr ← pointer_of_address 〈vaddrl,vaddrh〉;
227        ! v ← opt_to_res … (msg FailedLoad) (beloadv (m … st) vaddr);
228        ! st ← acca_store p … dst v st;
229          ret ? 〈E0, next … l st〉
230      | STORE addrl addrh src ⇒
231        ! vaddrh ← dph_retrieve … st addrh;
232        ! vaddrl ← dpl_retrieve … st addrl;
233        ! vaddr ← pointer_of_address 〈vaddrl,vaddrh〉;
234        ! v ← acca_retrieve … st src;
235        ! m' ← opt_to_res … (msg FailedStore) (bestorev (m … st) vaddr v);
236          ret ? 〈E0, next … l (set_m … m' st)〉
237      | COND src ltrue ⇒
238        ! v ← acca_retrieve … st src;
239        ! b ← bool_of_beval v;
240          ret ? 〈E0, (if b then goto … ltrue else next … l) st〉
241      | ADDRESS ident prf ldest hdest ⇒
242        ! addr ← opt_to_res ? [MSG MissingSymbol; CTX … ident] (find_symbol ?? ge ident);
243        ! 〈laddr,haddr〉 ← address_of_pointer (mk_pointer (block_region addr) addr ? zero_offset);
244        ! st ← dpl_store p ldest laddr st;
245        ! st ← dph_store p hdest haddr st;
246          ret ? 〈E0, next … l st〉
247      | OP1 op dacc_a sacc_a ⇒
248        ! v ← acca_retrieve … st sacc_a;
249        ! v ← Byte_of_val v;
250          let v' ≝ BVByte (op1 eval op v) in
251        ! st ← acca_store p dacc_a v' st;
252          ret ? 〈E0, next … l st〉
253      | OP2 op dacc_a sacc_a src ⇒
254        ! v1 ← acca_retrieve … st sacc_a;
255        ! v1 ← Byte_of_val v1;
256        ! v2 ← greg_retrieve … st src;
257        ! v2 ← Byte_of_val v2;
258        ! carry ← bool_of_beval (carry … st);
259          let 〈v',carry〉 ≝ op2 eval carry op v1 v2 in
260          let v' ≝ BVByte v' in
261          let carry ≝ beval_of_bool carry in
262        ! st ← acca_store p dacc_a v' st;
263          ret ? 〈E0, next … l (set_carry … carry st)〉
264      | CLEAR_CARRY ⇒ ret ? 〈E0, next … l (set_carry … BVfalse st)〉
265      | SET_CARRY ⇒ ret ? 〈E0, next … l (set_carry … BVtrue st)〉
266      | OPACCS op dacc_a_reg dacc_b_reg sacc_a_reg sacc_b_reg ⇒
267        ! v1 ← acca_retrieve … st sacc_a_reg;
268        ! v1 ← Byte_of_val v1;
269        ! v2 ← accb_retrieve … st sacc_b_reg;
270        ! v2 ← Byte_of_val v2;
271          let 〈v1',v2'〉 ≝ opaccs eval op v1 v2 in
272          let v1' ≝ BVByte v1' in
273          let v2' ≝ BVByte v2' in
274        ! st ← acca_store p dacc_a_reg v1' st;
275        ! st ← accb_store p dacc_b_reg v2' st;
276          ret ? 〈E0, next … l st〉
277      | POP dst ⇒
278        ! 〈st,v〉 ← pop … st;
279        ! st ← acca_store p dst v st;
280          ret ? 〈E0, next … l st〉
281      | PUSH src ⇒
282        ! v ← acca_retrieve … st src;
283        ! st ← push … st v;
284          ret ? 〈E0, next … l st〉
285      | MOVE dst_src ⇒
286        ! st ← pair_reg_move … st dst_src ;
287          ret ? 〈E0, next … l st〉
288      | CALL_ID id argsno dest ⇒
289        ! b ← opt_to_res … [MSG MissingSymbol; CTX ? id] (find_symbol ?? ge id);
290        ! fd ← opt_to_res … [MSG BadFunction; CTX ? id] (find_funct_ptr ?? ge b);
291          match fd with
292          [ Internal fn ⇒
293            ! st ← save_ra … st l;
294              let st ≝ save_frame … dest st in
295              let regs ≝ init_locals … (joint_if_locals … fn) (regs … st) in
296(*+ USARE GLI ARGSNO CHE SONO IN VERITA' I VALORI DEI PARAMETRI COME IN RTLABS
297+ ALLOCARE LO STACK FRAME*)
298              let l' ≝ joint_if_entry … fn in
299             ret ? 〈 E0, goto … l' (set_regs p regs st)〉
300          | External fn ⇒
301            ! params ← fetch_external_args … fn st;
302            ! evargs ← check_eventval_list params (sig_args (ef_sig fn));
303            ! evres ← do_io (ef_id fn) evargs (proj_sig_res (ef_sig fn));
304            (* CSC: XXX bug here; I think I should split it into Byte-long
305               components; instead I am making a singleton out of it *)
306              let vs ≝ [mk_val ? evres] in
307            ! st ← set_result … vs st;
308              ret ? 〈Eextcall (ef_id fn) evargs (mk_eventval ? evres), next … l st〉
309          ]]
310    | RETURN ⇒
311(* + DEALLOCARE LO STACK FRAME*)
312      ! res ← fetch_result … st;
313      ! st ← pop_frame … res st;
314      ! 〈st,pch〉 ← pop … st;
315      ! 〈st,pcl〉 ← pop … st;
316        ret ? 〈E0,set_pc … 〈pcl,pch〉 st〉].
317cases addr //
318qed.
319
320definition is_final: ∀globals:list ident. ∀p: sem_params2 globals. genv … p → address → state p → option int ≝
321 λglobals,p,ge,exit,st.res_to_opt ? (
322  do s ← fetch_statement … ge st;
323  match s with
324   [ RETURN ⇒
325      do 〈st,l〉 ← fetch_ra … st;
326      if eq_address l exit then
327       do vals ← fetch_result … st ;
328       Word_of_list_beval vals
329      else
330       Error ? []
331   | _ ⇒ Error ? []]).
332
333record evaluation_parameters : Type[1] ≝
334 { globals: list ident
335 ; sparams2: sem_params2 globals
336 ; exit: address
337 ; genv2: genv globals sparams2
338 }.
339
340definition joint_exec: trans_system io_out io_in ≝
341  mk_trans_system … evaluation_parameters (λG. state (sparams2 G))
342   (λG.is_final (globals G) (sparams2 G) (genv2 G) (exit G))
343   (λG.eval_statement (globals G) (sparams2 G) (genv2 G)).
344
345definition make_global :
346 ∀pars:∀globals.params globals. ∀sparams:∀p: joint_program pars. more_sem_params2 … (pars (prog_var_names … p)).
347  joint_program pars → evaluation_parameters
348
349 λpars,sparams.
350  (λp. mk_evaluation_parameters (prog_var_names … p) (mk_sem_params2 … (sparams p)) ? (globalenv Genv … (λx.[Init_space x]) p)).
351cases daemon (*CSC: XXXXXXXXXXXXX*)
352qed.
353
354definition make_initial_state :
355 ∀pars:∀globals.params globals. ∀sparams:∀p: joint_program pars. more_sem_params2 … (pars (prog_var_names … p)).
356 ∀p: joint_program … pars. res (state (mk_sem_params (pars (prog_var_names … p)) (sparams p))) ≝
357λpars,sparams,p.
358  let ge ≝ genv2 (make_global pars sparams p) in
359  do m ← init_mem Genv … (λx.[Init_space x]) p;
360  let main ≝ prog_main … p in
361  do b ← opt_to_res ? [MSG MissingSymbol; CTX ? main] (find_symbol ? ? ge main);
362  do f ← opt_to_res ? [MSG BadFunction; CTX ? main] (find_funct_ptr ? ? ge b);
363  ?.(* OK ? 〈ge,Callstate f (nil ?) [ ] (nil ?) m〉.*)
364cases daemon qed.
365(*
366RTL:
367 init_prog == init_mem
368 init_sp: inizializzare lo stack pointer
369 init_isp: inizializzare l'altro stack pointer
370 init_renv: inizializzare i registri fisici
371 init_main_call: chiamata di funzione
372   --- init_fun_call: cambia fra ERTL e LTL
373 change_carry: a 0
374*)
375
376definition joint_fullexec :
377 ∀pars:∀globals.params globals.
378 ∀sparams:∀p: joint_program pars. more_sem_params2 … (pars (prog_var_names … p)).
379 fullexec io_out io_in ≝
380 λpars,sparams.
381  mk_fullexec ??? joint_exec (make_global pars sparams) (make_initial_state pars sparams).
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