source: src/joint/Traces.ma @ 2821

Last change on this file since 2821 was 2821, checked in by tranquil, 7 years ago
  • implemented preclassified system for joint (in joint/joint_fullexec.ma)
File size: 8.8 KB
Line 
1include "joint/joint_semantics.ma".
2include "common/StructuredTraces.ma".
3
4record evaluation_params : Type[1] ≝
5 { globals: list ident
6 ; sparams:> sem_params
7 ; ev_genv: genv sparams globals
8(* ; io_env : state sparams → ∀o:io_out.res (io_in o) *)
9 }.
10
11record prog_params : Type[1] ≝
12 { prog_spars : sem_params
13 ; prog : joint_program prog_spars
14 ; stack_sizes : ident → option ℕ
15(* ; prog_io : state prog_spars → ∀o.res (io_in o) *)
16 }.
17
18lemma map_Exists : ∀A,B,f,P,l.Exists B P (map A B f l) → Exists ? (λx.P (f x)) l.
19#A #B #f #P #l elim l -l [*]
20#hd #tl #IH *
21[ #Phd %1{Phd}
22| #Ptl %2{(IH Ptl)}
23]
24qed.
25
26lemma Exists_In : ∀A,P,l.Exists A P l → ∃x.In A l x ∧ P x.
27#A #P #l elim l -l [*] #hd #tl #IH *
28[ #Phd %{hd} %{Phd} %1 %
29| #Ptl elim (IH Ptl) #x * #H1 #H2 %{x} %{H2} %2{H1}
30]
31qed.
32
33lemma In_Exists : ∀A,P,l,x.In A l x → P x → Exists A P l.
34#A #P #l elim l -l [ #x *] #hd #tl #IH #x *
35[ #EQ >EQ #H %1{H}
36| #Intl #Px %2{(IH … Intl Px)}
37]
38qed.
39
40lemma Exists_mp : ∀A,P,Q,l.(∀x.P x → Q x) → Exists A P l → Exists A Q l.
41#A #P #Q #l #H elim l -l [*] #hd #tl #IH * #G [ %1 | %2 ] /2/ qed.
42
43definition make_global : prog_params → evaluation_params
44
45λpars.
46let p ≝ prog pars in
47let spars ≝ prog_spars pars in
48let genv ≝ globalenv_noinit ? p in
49let get_pc_lbl ≝ λid,lbl.
50  ! bl ← block_of_funct_id … spars genv id ;
51  pc_of_label … genv bl lbl in
52mk_evaluation_params
53  (prog_var_names … p)
54  spars
55  (mk_genv_gen ?? genv ? (stack_sizes pars) get_pc_lbl)
56 (* (prog_io pars) *).
57#s #H
58elim (find_symbol_exists … p s ?)
59[ #bl #EQ >EQ % #ABS destruct(ABS)|*:]
60@Exists_append_r
61@(Exists_mp … H) //
62qed.
63
64coercion prog_params_to_ev_params : ∀p : prog_params.evaluation_params
65≝ make_global on _p : prog_params to evaluation_params.
66
67definition make_initial_state :
68 ∀pars: prog_params.res (state_pc pars) ≝
69λpars.let p ≝ prog pars in
70  let sem_globals : evaluation_params ≝ pars in
71  let ge ≝ ev_genv sem_globals in
72  let m0 ≝ alloc_mem … p in
73  let 〈m,spb〉 as H ≝ alloc … m0 0 external_ram_size in
74  let spp : xpointer ≝
75    «mk_pointer spb (mk_offset (bitvector_of_Z ? external_ram_size)),
76     pi2 … spb» in
77(*  let ispp : xpointer ≝ mk_pointer ispb (mk_offset (bitvector_of_nat ? 47)) in *)
78  let main ≝ prog_main … p in
79  let st0 ≝ mk_state pars (Some ? (empty_framesT …)) empty_is (BBbit false) (empty_regsT … spp) m in
80  (* use exit_pc as ra and call_dest_for_main as dest *)
81  let st0' ≝ mk_state_pc … (set_sp … spp st0) exit_pc exit_pc in
82  ! st0_no_pc ← save_frame ?? sem_globals ID (call_dest_for_main … pars) st0' ;
83  let st0'' ≝ set_no_pc … st0_no_pc st0' in
84  ! bl ← block_of_call … ge (inl … main) st0'';
85  ! 〈i, fn〉 ← fetch_function … ge bl ;
86  match fn with
87  [ Internal ifn ⇒
88    ! st' ← eval_internal_call … ge i ifn (call_args_for_main … pars) st0'' ;
89    let pc' ≝ pc_of_point … bl (joint_if_entry … ifn) in
90    return mk_state_pc … st' pc' exit_pc
91  | External _ ⇒ Error … [MSG BadMain; CTX ? main] (* External main not supported: why? *)
92  ].
93cases m0 in H; #m1 #m2 #m3 #H
94whd in H:(???%); destruct whd in ⊢(??%?); @Zleb_elim_Type0 // #abs @⊥
95@(absurd … (irreflexive_Zlt …)) % #I cases (I OZ) /3 by Zlt_to_Zle_to_Zlt/
96qed.
97
98definition joint_classify_step :
99  ∀p : evaluation_params.joint_step p (globals … p) → status_class ≝
100  λp,stmt.
101  match stmt with
102  [ CALL f args dest ⇒ cl_call
103  | COND _ _ ⇒ cl_jump
104  | _ ⇒ cl_other
105  ].
106
107definition joint_classify_final :
108  ∀p : evaluation_params.joint_fin_step p → status_class ≝
109  λp,stmt.
110  match stmt with
111  [ GOTO _ ⇒ cl_other
112  | RETURN ⇒ cl_return
113  | TAILCALL _ f args ⇒ cl_tailcall
114  ].
115
116definition joint_classify :
117  ∀p : evaluation_params.state_pc p → status_class ≝
118  λp,st.
119  match fetch_statement … (ev_genv p) (pc … st) with
120  [ OK i_fn_s ⇒
121    match \snd i_fn_s with
122    [ sequential s _ ⇒ joint_classify_step p s
123    | final s ⇒ joint_classify_final p s
124    | FCOND _ _ _ _ ⇒ cl_jump
125    ]
126  | _ ⇒ cl_other
127  ].
128
129lemma joint_classify_call : ∀p : evaluation_params.∀st.
130  joint_classify p st = cl_call →
131  ∃i_f,f',args,dest,next.
132  fetch_statement … (ev_genv p) (pc … st) =
133    OK ? 〈i_f, sequential … (CALL … f' args dest) next〉.
134#p #st
135whd in match joint_classify; normalize nodelta
136inversion (fetch_statement … (ev_genv p) (pc … st))
137[2: #e #_ whd in ⊢ (??%?→?); #ABS destruct(ABS) ]
138* #i_f *
139[2,3: [ * [ #lbl | | #fl #f #args ] | #fl #a #ltrue #lfalse ] #_
140  normalize nodelta normalize in ⊢ (%→?); #ABS destruct
141]
142* [ #c | #f' #args #dest | #a #lbl | #s ] #nxt #fetch normalize nodelta
143normalize in ⊢ (%→?); #EQ destruct
144%[|%[|%[|%[|%[| %]]]]]
145qed.
146
147definition joint_after_ret : ∀p:evaluation_params.
148  (Σs : state_pc p.joint_classify p s = cl_call) → state_pc p → Prop ≝
149λp,s1,s2.
150match fetch_statement … (ev_genv p) (pc … s1) with
151[ OK x ⇒
152  match \snd x with
153  [ sequential s next ⇒
154    last_pop … s2 = pc … s1 ∧
155    pc … s2 = succ_pc p (pc … s1) next
156  | _ ⇒ False (* never happens *)
157  ]
158| _ ⇒ False (* never happens *)
159].
160
161definition joint_call_ident : ∀p:evaluation_params.
162  state_pc p → ident ≝
163(* this is a definition without a dummy ident :
164λp,st.
165match ?
166return λx.
167  !〈f, s〉 ← fetch_statement ? p … (ev_genv p) (pc … st) ;
168  match s with
169  [ sequential s next ⇒
170    match s with
171    [ step_seq s ⇒
172      match s with
173      [ CALL f' args dest ⇒
174        function_of_call … (ev_genv p) st f'
175      | _ ⇒ Error … [ ]
176      ]
177    | _ ⇒ Error … [ ]
178    ]
179  | _ ⇒ Error … [ ]
180  ] = x → ? with
181[ OK v ⇒ λ_.v
182| Error e ⇒ λABS.⊥
183] (refl …).
184@hide_prf
185elim (joint_classify_call … (pi2 … st))
186#f *#f' *#args *#dest *#next *#fn *#fd ** #EQ1 #EQ2 #EQ3
187lapply ABS -ABS
188>EQ1 >m_return_bind normalize nodelta >EQ2 #ABS destruct(ABS)
189qed. *)
190(* with a dummy ident (which is never used as seen above in the commented script)
191   I think handling of the function is easier *)
192λp,st.
193let dummy : ident ≝ an_identifier ? one in (* used where it cannot ever happen *)
194match fetch_statement … (ev_genv p) (pc … st) with
195[ OK x ⇒
196  match \snd x with
197  [ sequential s next ⇒
198    match s with
199    [ step_seq s ⇒
200      match s with
201      [ CALL f' args dest ⇒
202        match
203          (! bl ← block_of_call … (ev_genv p) f' st;
204           fetch_internal_function … (ev_genv p) bl) with
205        [ OK i_f ⇒ \fst i_f
206        | _ ⇒ dummy
207        ]
208      | _ ⇒ dummy
209      ]
210    | _ ⇒ dummy
211    ]
212  | _ ⇒ dummy
213  ]
214| _ ⇒ dummy
215].
216
217definition joint_tailcall_ident : ∀p:evaluation_params.
218  state_pc p → ident ≝
219λp,st.
220let dummy : ident ≝ an_identifier ? one in (* used where it cannot ever happen *)
221match fetch_statement … (ev_genv p) (pc … st) with
222[ OK x ⇒
223  match \snd x with
224  [ final s ⇒
225    match s with
226    [ TAILCALL _ f' args ⇒
227      match
228        (! bl ← block_of_call … (ev_genv p) f' st;
229         fetch_internal_function … (ev_genv p) bl) with
230      [ OK i_f ⇒ \fst i_f
231      | _ ⇒ dummy
232      ]
233    | _ ⇒ dummy
234    ]
235  | _ ⇒ dummy
236  ]
237| _ ⇒ dummy
238].
239
240definition pcDeq ≝ mk_DeqSet program_counter eq_program_counter ?.
241*#p1 #EQ1 * #p2 #EQ2 @eq_program_counter_elim
242[ #EQ destruct % #H %
243| * #NEQ % #ABS destruct elim (NEQ ?) %
244]
245qed.
246
247(*
248let rec io_evaluate O I X (env : ∀o.res (I o)) (c : IO O I X) on c : res X ≝
249  match c with
250  [ Value x ⇒ OK … x
251  | Interact o f ⇒
252    ! i ← env o ;
253    io_evaluate O I X env (f i)
254  | Wrong e ⇒ Error … e
255  ].
256*)
257
258definition cost_label_of_stmt :
259  ∀p : evaluation_params.joint_statement p (globals p) → option costlabel ≝
260  λp,s.match s with
261  [ sequential s _ ⇒
262    match s with
263    [  COST_LABEL lbl ⇒ Some ? lbl
264    | _ ⇒ None ?
265    ]
266  | _ ⇒ None ?
267  ].
268
269definition joint_label_of_pc ≝
270  λp : evaluation_params.
271    (λpc.
272      match fetch_statement … (ev_genv p) pc with
273      [ OK fn_stmt ⇒ cost_label_of_stmt … (\snd fn_stmt)
274      | _ ⇒ None ?
275      ]).
276
277definition joint_abstract_status :
278 ∀p : prog_params.
279 abstract_status ≝
280 λp.
281 mk_abstract_status
282   (* as_status ≝ *) (state_pc p)
283   (* as_execute ≝ *)
284    (λs1,s2.eval_state … (ev_genv p) s1 = return s2)
285   (* (* as_init ≝ *) (make_initial_state p) *)
286   (* as_pc ≝ *) pcDeq
287   (* as_pc_of ≝ *) (pc …)
288   (* as_classify ≝ *) (joint_classify p)
289   (* as_label_of_pc ≝ *) (joint_label_of_pc p)
290   (* as_after_return ≝ *) (joint_after_ret p)
291   (* as_result ≝ *) (is_final p  (globals ?) (ev_genv p) exit_pc)
292   (* as_call_ident ≝ *) (λst.joint_call_ident p st)
293   (* as_tailcall_ident ≝ *) (λst.joint_tailcall_ident p st).
294
295(* alternative definition with integrated prog_params constructor *)
296definition joint_status :
297 ∀p : sem_params.
298 joint_program p → (ident → option ℕ) → abstract_status ≝
299λp,prog,stacksizes.joint_abstract_status (mk_prog_params p prog stacksizes).
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