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Split big theroem to manage it
This commit is contained in:
Denis Merigoux
parent
94b1c348d6
commit
8d5aa8e86e
@ -908,7 +908,161 @@ let rec_lemma_works_for_smaller
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=
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lemma
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#push-options "--fuel 2 --ifuel 1 --z3rlimit 70"
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let translation_correctness_exceptions_left_to_right_step_head_not_value
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(de: D.exp)
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(dexceptions: list D.exp {dexceptions << de})
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(djust: D.exp{djust << de})
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(dcons: D.exp{dcons << de})
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(dtau: D.ty)
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(acc: typed_l_exp (L.TOption (translate_ty dtau)))
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(rec_lemma: rec_correctness_step_type de)
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: Pure (nat & typed_l_exp (translate_ty dtau) & nat)
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(requires (
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D.typing_list D.empty dexceptions dtau /\
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D.typing D.empty djust D.TBool /\
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D.typing D.empty dcons dtau /\
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L.is_value acc /\
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Some? (D.step_exceptions_left_to_right de dexceptions djust dcons dtau) /\
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(match dexceptions with hd::tl -> not (D.is_value hd) | _ -> False)
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))
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(ensures (fun (n1, target_e, n2) ->
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translate_empty_is_empty ();
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translation_preserves_typ_exceptions D.empty de dexceptions dtau;
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translation_preserves_empty_typ djust D.TBool;
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translation_preserves_empty_typ dcons dtau;
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let lexceptions = translate_exp_list dexceptions in
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let ljust = translate_exp djust in
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let lcons = translate_exp dcons in
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let Some de' = D.step_exceptions_left_to_right de dexceptions djust dcons dtau in
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let ltau = translate_ty dtau in
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translation_preserves_typ_exceptions D.empty de dexceptions dtau;
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build_default_translation_typing lexceptions acc ljust lcons ltau L.empty;
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take_l_steps ltau (build_default_translation lexceptions acc ljust lcons ltau)
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n1 == Some target_e /\
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begin
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D.preservation_exceptions_left_to_right de dexceptions djust dcons dtau;
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translation_preserves_empty_typ de' dtau;
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let le' = translate_exp de' in
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match de' with
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| D.ELit D.LConflictError -> take_l_steps ltau le' n2 == Some target_e
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| D.EDefault dexceptions' djust' dcons' dtau' ->
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assert(djust' == djust /\ dcons' == dcons /\ dtau' == dtau);
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let lexceptions' = translate_exp_list dexceptions' in
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take_l_steps ltau (build_default_translation lexceptions' acc ljust lcons ltau)
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n2 == Some target_e
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end
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))
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(decreases dexceptions)
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=
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let Some de' = D.step_exceptions_left_to_right de dexceptions djust dcons dtau in
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let le = translate_exp de in
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D.preservation_exceptions_left_to_right de dexceptions djust dcons dtau;
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translate_empty_is_empty ();
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translation_preserves_typ_exceptions D.empty de dexceptions dtau;
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translation_preserves_empty_typ djust D.TBool;
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translation_preserves_empty_typ dcons dtau;
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translation_preserves_empty_typ de' dtau;
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let ltau = translate_ty dtau in
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let le' : typed_l_exp ltau = translate_exp de' in
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let ljust = translate_exp djust in
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let lcons = translate_exp dcons in
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let lexceptions = translate_exp_list dexceptions in
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match dexceptions with
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| [] -> 0, le, 0
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| dhd::dtl ->
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let ltl = translate_exp_list dtl in
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let lhd = translate_exp dhd in
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begin
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match D.step dhd with
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| Some (D.ELit D.LConflictError) ->
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D.preservation dhd dtau;
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translation_preserves_empty_typ dhd dtau;
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let n1_hd, target_hd, n2_hd = rec_lemma dhd dtau in
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translation_preserves_empty_typ dhd dtau;
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translation_preserves_empty_typ djust D.TBool;
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translation_preserves_empty_typ dcons dtau;
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let l_err : typed_l_exp ltau = L.ELit (L.LError L.ConflictError) in
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assert(n2_hd == 0 /\ target_hd == l_err);
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assert(take_l_steps ltau lhd n1_hd == Some l_err);
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translate_list_is_value_list dexceptions;
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build_default_translation_typing_source dexceptions acc djust dcons dtau D.empty;
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lift_multiple_l_steps_exceptions_head ltau ltl acc ljust lcons n1_hd lhd l_err;
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assert(take_l_steps ltau
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(build_default_translation ((L.EThunk lhd)::ltl) acc ljust lcons ltau) (n1_hd + 4) ==
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Some (exceptions_head_lift ltau ltl acc ljust lcons l_err));
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exceptions_head_lift_steps_to_error ltau ltl acc ljust lcons;
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assert(take_l_steps ltau (exceptions_head_lift ltau ltl acc ljust lcons l_err) 5 ==
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Some l_err);
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assert(le' == l_err);
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take_l_steps_transitive ltau
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(build_default_translation ((L.EThunk lhd)::ltl) acc ljust lcons ltau)
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(exceptions_head_lift ltau ltl acc ljust lcons l_err)
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(n1_hd + 4)
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5;
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let lexceptions = translate_exp_list dexceptions in
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assert(take_l_steps ltau (build_default_translation lexceptions acc ljust lcons ltau)
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(n1_hd + 4 + 5) == Some le');
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(n1_hd + 4 + 5, l_err, 0)
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| Some dhd' ->
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D.preservation dhd dtau;
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translation_preserves_empty_typ dhd dtau;
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translation_preserves_empty_typ dhd' dtau;
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let lhd' : typed_l_exp ltau = translate_exp dhd' in
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let n1_hd, target_hd, n2_hd = rec_lemma dhd dtau in
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translation_preserves_empty_typ djust D.TBool;
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translation_preserves_empty_typ dcons dtau;
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assert(take_l_steps ltau lhd n1_hd == Some target_hd);
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assert(take_l_steps ltau lhd' n2_hd == Some target_hd);
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translate_list_is_value_list dexceptions;
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translate_empty_is_empty ();
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build_default_translation_typing_source dexceptions acc djust dcons dtau D.empty;
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assert(L.is_value_list ltl);
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assert(L.typing_list L.empty ltl (L.TArrow L.TUnit ltau));
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lift_multiple_l_steps_exceptions_head ltau ltl acc ljust lcons n1_hd lhd target_hd;
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lift_multiple_l_steps_exceptions_head ltau ltl acc ljust lcons n2_hd lhd' target_hd;
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let target_lexp : typed_l_exp ltau =
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exceptions_head_lift ltau ltl acc ljust lcons target_hd
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in
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assert(take_l_steps ltau (build_default_translation ((L.EThunk lhd)::ltl) acc
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ljust lcons ltau) (n1_hd + 4) == Some target_lexp);
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lift_multiple_l_steps_exceptions_head ltau ltl acc ljust lcons n2_hd lhd' target_hd;
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build_default_translation_typing ((L.EThunk lhd')::ltl) acc ljust lcons ltau
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L.empty;
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assert(take_l_steps ltau (build_default_translation ((L.EThunk lhd')::ltl) acc
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ljust lcons ltau) (n2_hd + 4) == Some target_lexp);
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let lexceptions = translate_exp_list dexceptions in
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assert((L.EThunk lhd)::ltl == lexceptions);
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assert(le' == translate_exp (D.EDefault (dhd'::dtl) djust dcons dtau));
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(n1_hd + 4, target_lexp, n2_hd + 4)
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end
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#pop-options
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#push-options "--fuel 2 --ifuel 1 --z3rlimit 150"
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let step_exceptions_left_to_right_result_shape
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(de: D.exp)
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(dexceptions: list D.exp {dexceptions << de})
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(djust: D.exp{djust << de})
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(dcons: D.exp{dcons << de})
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(dtau: D.ty)
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: Lemma
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(requires (
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Some? (D.step_exceptions_left_to_right de dexceptions djust dcons dtau) /\
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(match dexceptions with dhd::dtl -> D.is_value dhd | _ -> False)
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))
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(ensures (
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let dhd::dtl = dexceptions in
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match D.step_exceptions_left_to_right de dtl djust dcons dtau with
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| Some (D.ELit D.LConflictError) -> True
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| Some (D.EDefault dtl' djust' dcons' dtau') ->
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djust' == djust /\ dcons' == dcons /\ dtau' == dtau
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| _ -> False
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))
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=
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()
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#pop-options
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#push-options "--fuel 2 --ifuel 1 --z3rlimit 70"
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let rec translation_correctness_exceptions_left_to_right_step
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(de: D.exp)
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(dexceptions: list D.exp {dexceptions << de})
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@ -973,6 +1127,7 @@ let rec translation_correctness_exceptions_left_to_right_step
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let ltl = translate_exp_list dtl in
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let lhd = translate_exp dhd in
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if D.is_value dhd then begin
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step_exceptions_left_to_right_result_shape de dexceptions djust dcons dtau;
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match D.step_exceptions_left_to_right de dtl djust dcons dtau with
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| Some (D.ELit D.LConflictError) ->
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assert(de' == D.ELit (D.LConflictError));
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@ -1005,70 +1160,12 @@ let rec translation_correctness_exceptions_left_to_right_step
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assume(take_l_steps ltau le n == Some l_err);
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n, le', 0
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| Some (D.EDefault dtl' djust' dcons' dtau') ->
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admit();
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assert(djust' == djust /\ dcons' == dcons /\ dtau' == dtau);
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admit()
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end else begin
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match D.step dhd with
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| Some (D.ELit D.LConflictError) ->
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D.preservation dhd dtau;
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translation_preserves_empty_typ dhd dtau;
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let n1_hd, target_hd, n2_hd = rec_lemma dhd dtau in
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translation_preserves_empty_typ dhd dtau;
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translation_preserves_empty_typ djust D.TBool;
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translation_preserves_empty_typ dcons dtau;
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let l_err : typed_l_exp ltau = L.ELit (L.LError L.ConflictError) in
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assert(n2_hd == 0 /\ target_hd == l_err);
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assert(take_l_steps ltau lhd n1_hd == Some l_err);
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translate_list_is_value_list dexceptions;
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build_default_translation_typing_source dexceptions acc djust dcons dtau D.empty;
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lift_multiple_l_steps_exceptions_head ltau ltl acc ljust lcons n1_hd lhd l_err;
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assert(take_l_steps ltau
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(build_default_translation ((L.EThunk lhd)::ltl) acc ljust lcons ltau) (n1_hd + 4) ==
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Some (exceptions_head_lift ltau ltl acc ljust lcons l_err));
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exceptions_head_lift_steps_to_error ltau ltl acc ljust lcons;
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assert(take_l_steps ltau (exceptions_head_lift ltau ltl acc ljust lcons l_err) 5 ==
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Some l_err);
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assert(le' == l_err);
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take_l_steps_transitive ltau
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(build_default_translation ((L.EThunk lhd)::ltl) acc ljust lcons ltau)
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(exceptions_head_lift ltau ltl acc ljust lcons l_err)
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(n1_hd + 4)
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5;
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let lexceptions = translate_exp_list dexceptions in
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assert(take_l_steps ltau (build_default_translation lexceptions acc ljust lcons ltau)
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(n1_hd + 4 + 5) == Some le');
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(n1_hd + 4 + 5, l_err, 0)
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| Some dhd' ->
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D.preservation dhd dtau;
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translation_preserves_empty_typ dhd dtau;
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translation_preserves_empty_typ dhd' dtau;
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let lhd' : typed_l_exp ltau = translate_exp dhd' in
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let n1_hd, target_hd, n2_hd = rec_lemma dhd dtau in
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translation_preserves_empty_typ djust D.TBool;
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translation_preserves_empty_typ dcons dtau;
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assert(take_l_steps ltau lhd n1_hd == Some target_hd);
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assert(take_l_steps ltau lhd' n2_hd == Some target_hd);
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translate_list_is_value_list dexceptions;
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translate_empty_is_empty ();
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build_default_translation_typing_source dexceptions acc djust dcons dtau D.empty;
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assert(L.is_value_list ltl);
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assert(L.typing_list L.empty ltl (L.TArrow L.TUnit ltau));
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lift_multiple_l_steps_exceptions_head ltau ltl acc ljust lcons n1_hd lhd target_hd;
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lift_multiple_l_steps_exceptions_head ltau ltl acc ljust lcons n2_hd lhd' target_hd;
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let target_lexp : typed_l_exp ltau =
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exceptions_head_lift ltau ltl acc ljust lcons target_hd
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in
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assert(take_l_steps ltau (build_default_translation ((L.EThunk lhd)::ltl) acc
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ljust lcons ltau) (n1_hd + 4) == Some target_lexp);
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lift_multiple_l_steps_exceptions_head ltau ltl acc ljust lcons n2_hd lhd' target_hd;
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build_default_translation_typing ((L.EThunk lhd')::ltl) acc ljust lcons ltau
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L.empty;
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assert(take_l_steps ltau (build_default_translation ((L.EThunk lhd')::ltl) acc
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ljust lcons ltau) (n2_hd + 4) == Some target_lexp);
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let lexceptions = translate_exp_list dexceptions in
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assert((L.EThunk lhd)::ltl == lexceptions);
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assert(le' == translate_exp (D.EDefault (dhd'::dtl) djust dcons dtau));
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(n1_hd + 4, target_lexp, n2_hd + 4)
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translation_correctness_exceptions_left_to_right_step_head_not_value
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de dexceptions djust dcons dtau acc rec_lemma
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end
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#pop-options
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