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