source: src/common/SmallstepExec.ma @ 1077

Last change on this file since 1077 was 797, checked in by campbell, 9 years ago

Add error messages wherever the error monad is used.
Sticks to CompCert? style strings+identifiers for the moment.
Use axioms for strings as we currently have no representation or literals
for them - still *very* useful for animation in the proof assistant.

File size: 4.5 KB
RevLine 
[24]1
[700]2include "utilities/extralib.ma".
3include "common/IOMonad.ma".
4include "common/Integers.ma".
5include "common/Events.ma".
6include "common/Mem.ma".
[24]7
[731]8record execstep (outty:Type[0]) (inty:outty → Type[0]) : Type[1] ≝
[693]9{ genv  : Type[0]
10; state : Type[0]
11; is_final : state → option int
12; mem_of_state : state → mem
[731]13; step : genv → state → IO outty inty (trace×state)
[24]14}.
15
[731]16let rec repeat (n:nat) (outty:Type[0]) (inty:outty → Type[0]) (exec:execstep outty inty)
17               (g:genv ?? exec) (s:state ?? exec)
18 : IO outty inty (trace × (state ?? exec)) ≝
[24]19match n with
[25]20[ O ⇒ Value ??? 〈E0, s〉
[731]21| S n' ⇒ ! 〈t1,s1〉 ← step ?? exec g s;
22         repeat n' ?? exec g s1
[24]23].
24
[751]25let rec trace_map (A,B:Type[0]) (f:A → res (trace × B))
26                  (l:list A) on l : res (trace × (list B)) ≝
27match l with
28[ nil ⇒ OK ? 〈E0, [ ]〉
29| cons h t ⇒
30    do 〈tr,h'〉 ← f h;
31    do 〈tr',t'〉 ← trace_map … f t;
32    OK ? 〈tr ⧺ tr',h'::t'〉
33].
34
[693]35(* A (possibly non-terminating) execution.   *)
36coinductive execution (state:Type[0]) (output:Type[0]) (input:output → Type[0]) : Type[0] ≝
37| e_stop : trace → int → mem → execution state output input
38| e_step : trace → state → execution state output input → execution state output input
[797]39| e_wrong : errmsg → execution state output input
[693]40| e_interact : ∀o:output. (input o → execution state output input) → execution state output input.
41
42(* This definition is slightly awkward because of the need to provide resumptions.
43   It records the last trace/state passed in, then recursively processes the next
44   state. *)
45
[731]46let corec exec_inf_aux (output:Type[0]) (input:output → Type[0])
47                       (exec:execstep output input) (ge:genv ?? exec)
48                       (s:IO output input (trace×(state ?? exec)))
[693]49                       : execution ??? ≝
50match s with
[797]51[ Wrong m ⇒ e_wrong ??? m
[693]52| Value v ⇒ match v with [ pair t s' ⇒
[731]53    match is_final ?? exec s' with
54    [ Some r ⇒ e_stop ??? t r (mem_of_state ?? exec s')
55    | None ⇒ e_step ??? t s' (exec_inf_aux ??? ge (step ?? exec ge s')) ] ]
56| Interact out k' ⇒ e_interact ??? out (λv. exec_inf_aux ??? ge (k' v))
[693]57].
58
[731]59lemma execution_cases: ∀o,i,s.∀e:execution s o i.
[693]60 e = match e with [ e_stop tr r m ⇒ e_stop ??? tr r m
61 | e_step tr s e ⇒ e_step ??? tr s e
[797]62 | e_wrong m ⇒ e_wrong ??? m | e_interact o k ⇒ e_interact ??? o k ].
[731]63#o #i #s #e cases e; //; qed.
[693]64
[731]65axiom exec_inf_aux_unfold: ∀o,i,exec,ge,s. exec_inf_aux o i exec ge s =
[693]66match s with
[797]67[ Wrong m ⇒ e_wrong ??? m
[693]68| Value v ⇒ match v with [ pair t s' ⇒
[731]69    match is_final ?? exec s' with
70    [ Some r ⇒ e_stop ??? t r (mem_of_state ?? exec s')
71    | None ⇒ e_step ??? t s' (exec_inf_aux ??? ge (step ?? exec ge s')) ] ]
72| Interact out k' ⇒ e_interact ??? out (λv. exec_inf_aux ??? ge (k' v))
[693]73].
74(*
75#exec #ge #s >(execution_cases ? (exec_inf_aux …)) cases s
76[ #o #k
77| #x cases x #tr #s' (* XXX Can't unfold exec_inf_aux here *)
78| ]
79whd in ⊢ (??%%); //;
80qed.
81*)
82
[731]83record fullexec (outty:Type[0]) (inty:outty → Type[0]) : Type[1] ≝
84{ es1 :> execstep outty inty
85; program : Type[0]
86; make_initial_state : program → res (genv ?? es1 × (state ?? es1))
[702]87}.
[693]88
[731]89definition exec_inf : ∀o,i.∀fx:fullexec o i. ∀p:program ?? fx. execution (state ?? fx) o i ≝
90λo,i,fx,p.
91  match make_initial_state ?? fx p with
92  [ OK gs ⇒ exec_inf_aux ?? fx (\fst gs) (Value … 〈E0,\snd gs〉)
[797]93  | Error m ⇒ e_wrong ??? m
[731]94  ].
[693]95
[731]96
97record execstep' (outty:Type[0]) (inty:outty → Type[0]) : Type[1] ≝
98{ es0 :> execstep outty inty
99; initial : state ?? es0 → Prop
100}.
101
102
[24]103alias symbol "and" (instance 2) = "logical and".
[693]104record related_semantics : Type[1] ≝
[731]105{ output : Type[0]
106; input : output → Type[0]
107; sem1 : execstep' output input
108; sem2 : execstep' output input
109; ge1 : genv ?? sem1
110; ge2 : genv ?? sem2
111; match_states : state ?? sem1 → state ?? sem2 → Prop
112; match_initial_states : ∀st1. (initial ?? sem1) st1 → ∃st2. (initial ?? sem2) st2 ∧ match_states st1 st2
113; match_final_states : ∀st1,st2,r. match_states st1 st2 → (is_final ?? sem1) st1 = Some ? r → (is_final ?? sem2) st2 = Some ? r
[24]114}.
115
116
117
[693]118record simulation : Type[1] ≝
[24]119{ sems :> related_semantics
120; sim : ∀st1,st2,t,st1'.
[731]121        P_io' ?? (trace × (state ?? (sem1 sems))) (λr. r = 〈t,st1'〉) (step ?? (sem1 sems) (ge1 sems) st1) →
[24]122        match_states sems st1 st2 →
[731]123        ∃st2':(state ?? (sem2 sems)).(∃n:nat.P_io' ?? (trace × (state ?? (sem2 sems))) (λr. r = 〈t,st2'〉) (repeat n ?? (sem2 sems) (ge2 sems) st2)) ∧
[24]124          match_states sems st1' st2'
125}.
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