source: src/common/Animation.ma @ 1881

Last change on this file since 1881 was 1881, checked in by campbell, 8 years ago

Resurrect version of exec_up_to which shows the final state.

File size: 4.6 KB
RevLine 
[409]1
[731]2include "common/IO.ma".
3include "common/SmallstepExec.ma".
[963]4include "arithmetics/nat.ma".
[409]5
6(* Functions to allow programs to be executed up to some number of steps, given
7   a predetermined set of input values.  Note that we throw away the state if
8   we stop at a continuation - it can be too large to work with. *)
9
[487]10definition get_input : ∀o:io_out. eventval → res (io_in o) ≝
[409]11λo,ev.
12match io_in_typ o return λt. res (eventval_type t) with
[961]13[ ASTint sz _ ⇒ match ev with [ EVint sz' i ⇒ intsize_eq_elim ? sz' sz ? i (λi.OK ? i) (Error ? (msg IllTypedEvent)) | _ ⇒ Error ? (msg IllTypedEvent) ]
[879]14| ASTfloat _ ⇒ match ev with [ EVfloat f ⇒ OK ? f | _ ⇒ Error ? (msg IllTypedEvent) ]
[797]15| ASTptr _ ⇒ Error ? (msg IllTypedEvent)
[409]16].
17
[731]18inductive snapshot (state:Type[0]) : Type[0] ≝
19| running : trace → state → snapshot state
[1213]20| finished : trace → int → state → snapshot state
[731]21| input_exhausted : trace → snapshot state.
22
[797]23axiom StoppedMidIO : String.
24
[1231]25let rec up_to_nth_step (n:nat) (state:Type[0]) (input:list eventval) (e:execution state io_out io_in) (t:trace) : res (snapshot state) ≝
[409]26match n with
[731]27[ O ⇒ match e with [ e_step tr s _ ⇒ OK ? (running ? (t⧺tr) s)
28                   | e_stop tr r m ⇒ OK ? (finished ? (t⧺tr) r m)
[797]29                   | e_interact o k ⇒ Error ? (msg StoppedMidIO)
30                   | e_wrong m ⇒ Error ? m ]
[1231]31| S m ⇒ match e with [ e_step tr s e' ⇒ up_to_nth_step m state input e' (t⧺tr)
[731]32                     | e_stop tr r m ⇒ OK ? (finished ? (t⧺tr) r m)
[409]33                     | e_interact o k ⇒
34                         match input with
[731]35                         [ nil ⇒ OK ? (input_exhausted ? t)
[409]36                         | cons h tl ⇒ do i ← get_input o h;
[1231]37                                       up_to_nth_step m state tl (k i) t
[409]38                         ]
[797]39                     | e_wrong m ⇒ Error ? m
[409]40                     ]
41].
42
[1231]43definition exec_up_to : ∀fx:fullexec io_out io_in. ∀p:program ?? fx. nat → list eventval → res (snapshot (state ?? fx (make_global … p))) ≝
44λfx,p,n,i. up_to_nth_step n ? i (exec_inf ?? fx p) E0.
[409]45
[963]46(* A version of exec_up_to that reports the state prior to failure. *)
47
48inductive snapshot' (state:Type[0]) : Type[0] ≝
49| running' : trace → state → snapshot' state
[1213]50| finished' : nat → trace → int → state → snapshot' state
[963]51| input_exhausted' : trace → snapshot' state
52| failed' : errmsg → nat → state → snapshot' state
53| init_state_fail' : errmsg → snapshot' state.
[1881]54
55let rec up_to_nth_step' (n:nat) (total:nat) (state:Type[0]) (input:list eventval) (e:execution state io_out io_in) (prev:state) (t:trace) : snapshot' state ≝
[963]56match n with
57[ O ⇒ match e with [ e_step tr s _ ⇒ running' ? (t⧺tr) s
58                   | e_stop tr r m ⇒ finished' ? total (t⧺tr) r m
59                   | e_interact o k ⇒ failed' ? (msg StoppedMidIO) total prev
60                   | e_wrong m ⇒ failed' ? m total prev ]
[1881]61| S m ⇒ match e with [ e_step tr s e' ⇒ up_to_nth_step' m total state input e' s (t⧺tr)
[963]62                     | e_stop tr r m ⇒ finished' ? (minus total n) (t⧺tr) r m
63                     | e_interact o k ⇒
64                         match input with
65                         [ nil ⇒ input_exhausted' ? t
66                         | cons h tl ⇒ match get_input o h with
[1881]67                                       [ OK i ⇒ up_to_nth_step' m total state tl (k i) prev t
[963]68                                       | Error m ⇒ failed' ? m (minus total n) prev
69                                       ]
70                         ]
71                     | e_wrong m ⇒ failed' ? m (minus total n) prev
72                     ]
73].
74
[1881]75definition exec_up_to' : ∀fx:fullexec io_out io_in. ∀p:program ?? fx. nat → list eventval → snapshot' (state ?? fx (make_global … p)) ≝
[963]76λfx,p,n,i.
77match make_initial_state ?? fx p with
[1881]78[ OK s ⇒ up_to_nth_step' n n (state ?? fx (make_global … p)) i (exec_inf ?? fx p) s E0
[963]79| Error m ⇒ init_state_fail' ? m
80].
[1881]81
[409]82(* Provide an easy way to get a term in proof mode for reduction.
83   For example,
84   
[487]85   example exec: result ? (exec_up_to myprog 20 [EVint (repr 12)]).
86   normalize  (* you can examine the result here *)
87   % qed.
[409]88   
89 *)
90
[487]91inductive result (A:Type[0]) : A → Type[0] ≝
[409]92| witness : ∀a:A. result A a.
93
[1876]94inductive finishes_with : int → ∀S.res (snapshot S) → Prop ≝
95fw_ok : ∀r,S,t,s. finishes_with r S (OK ? (finished S t r s)).
[731]96
[1213]97include "common/Mem.ma".
98
[409]99(* Hide the representation of memory to make displaying the results easier. *)
100
101notation < "'MEM'" with precedence 1 for @{ 'mem }.
102interpretation "hide memory" 'mem = (mk_mem ???).
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