Ignore:
Timestamp:
Feb 15, 2013, 11:27:59 AM (7 years ago)
Author:
campbell
Message:

Clean up from recent commits.

File:
1 edited

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  • src/common/FEMeasurable.ma

    r2669 r2670  
    7878
    7979(* TODO: obs eq *)
    80 
    81 definition trace_starts : ∀S. execution S io_out io_in → S → Prop ≝
    82 λS,t,s. match t with [ e_step _ s' _ ⇒ s = s' | _ ⇒ False ].
    83 
    84 (* TODO: too many of these lemmas, slim it down*)
    85 
    86 lemma split_trace_S : ∀fx:trans_system io_out io_in. ∀g,tr,s,n,a,b.
    87   split_trace … (exec_inf_aux ?? fx g (Value … 〈tr,s〉)) (S n) = Some ? 〈a,b〉 →
    88   ∃a'. a = 〈tr,s〉::a' ∧
    89   ((is_final … fx g s = None ? ∧ split_trace … (exec_inf_aux ?? fx g (step … fx g s)) n = Some ? 〈a',b〉) ∨
    90   (∃r. is_final … fx g s = Some ? r ∧ n = 0 ∧ a' = [ ] ∧ b = e_stop … tr r s)).
    91 #fx #g #tr #s #n #a #b
    92 >exec_inf_aux_unfold whd in ⊢ (??(????%?)? → ?);
    93 cases (is_final … s)
    94 [ whd in ⊢ (??%? → ?); cases (split_trace ?????)
    95   [ #E whd in E:(??%%); destruct
    96   | * #a' #b' #E whd in E:(??%%); destruct
    97     %{a'} %{(refl ??)} %1 %{(refl ??)} %
    98   ]
    99 | #r cases n [2:#n'] whd in ⊢ (??%? → ?); #E destruct
    100   %{[ ]} %{(refl ??)} %2 %{r} /4/
    101 ] qed.
    102 
    103 lemma split_trace_S' : ∀fx:trans_system io_out io_in. ∀g,s,n,a,b.
    104   split_trace … (exec_inf_aux ?? fx g (step … fx g s)) (S n) = Some ? 〈a,b〉 →
    105   ∃tr,s'. step … fx g s = Value … 〈tr,s'〉 ∧
    106   ∃a'. a = 〈tr,s'〉::a' ∧
    107   ((is_final … fx g s' = None ? ∧ split_trace … (exec_inf_aux ?? fx g (step … fx g s')) n = Some ? 〈a',b〉) ∨
    108   (∃r. is_final … fx g s' = Some ? r ∧ n = 0 ∧ a' = [ ] ∧ b = e_stop … tr r s')).
    109 #fx #g #s #n #a #b
    110 cases (step … fx g s)
    111 [ #o #i whd in ⊢ (??%? → ?); #E destruct
    112 | * #tr #s' #split %{tr} %{s'} %{(refl …)} @split_trace_S @split
    113 | #err #E whd in E:(??%%); destruct
    114 ] qed.
    115 
    116 lemma split_trace_1 : ∀fx:trans_system io_out io_in. ∀g,tr,s,a,b.
    117   split_trace … (exec_inf_aux ?? fx g (Value … 〈tr,s〉)) 1 = Some ? 〈a,b〉 →
    118   a = [〈tr,s〉] ∧
    119   ((is_final … fx g s = None ? ∧ b = exec_inf_aux ?? fx g (step … fx g s)) ∨
    120   (∃r. is_final … fx g s = Some ? r ∧ b = e_stop … tr r s)).
    121 #fx #g #tr #s #a #b #split
    122 cases (split_trace_S … split)
    123 #a' * #E1 *
    124 [ * #notfinal #split' whd in split':(??%?); destruct %{(refl ??)}
    125   %1 %{notfinal} %
    126 | * #r * * * #final #_ #E2 #E3 destruct %{(refl ??)}
    127   %2 %{r} %{final} %
    128 ] qed.
    129  
    130 
    131 lemma split_trace_SS : ∀fx:trans_system io_out io_in. ∀g,tr,s,n,a,b.
    132   split_trace … (exec_inf_aux ?? fx g (Value … 〈tr,s〉)) (S (S n)) = Some ? 〈a,b〉 →
    133   ∃a'. a = 〈tr,s〉::a' ∧
    134   is_final … fx g s = None ? ∧
    135   ∃tr',s'. step … fx g s = Value … 〈tr',s'〉 ∧
    136   split_trace … (exec_inf_aux ?? fx g (Value … 〈tr',s'〉)) (S n) = Some ? 〈a',b〉.
    137 #fx #g #tr #s #n #a #b #splitSS
    138 cases (split_trace_S … splitSS)
    139 #a' * #E1 *
    140 [ * #notfinal #splitS %{a'} % [ %{E1} @notfinal ]
    141   cases (step … s) in splitS ⊢ %;
    142   [ #o #i #E whd in E:(??%%); destruct
    143   | * #tr' #s' #splitS %{tr'} %{s'} %{(refl ??)} @splitS
    144   | #m  #E whd in E:(??%%); destruct
    145   ]
    146 | * #r * * * #final #En #Ea #Eb destruct
    147 ] qed.
    14880
    14981lemma stack_normal_step : ∀C:preclassified_system. ∀g,s1,trace,s2,stack,current.
     
    344276  measurable (ms_C1 MS) p1 m n stack_cost max →
    345277  ∃m',n'. measurable (ms_C2 MS) p2 m' n' stack_cost max.
    346 * #C1 #C2 #compiled #inv #rel #sim_normal #sim_call_return #sim_cost #sim_init
    347 #p1 #p2 #m #n #stack_cost #max #compiled
    348 whd in ⊢ (% → ?); letin C1' ≝ (mk_classified_system C1 ????) letin g1 ≝ (make_global ?? C1 ?)
    349 * #prefix * #suffix * #subtrace * #remainder
    350 * * * * #split1 #split2 #subtrace_ok #terminates #max_ok
    351 
    352 *)
     278
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