diff --git a/OperationalSemantics_template.v b/OperationalSemantics_template.v index cc915b9..ca49851 100644 --- a/OperationalSemantics_template.v +++ b/OperationalSemantics_template.v @@ -367,7 +367,7 @@ Theorem big_small : forall v c v', eval v c v' Proof. Admitted. -Theorem small_big_snazzy : forall v c v', step^* (v, c) (v', Skip) +Theorem small_big : forall v c v', step^* (v, c) (v', Skip) -> eval v c v'. Proof. Admitted. @@ -741,33 +741,8 @@ Module Concurrent. Proof. eexists; propositional. unfold prog. + Admitted. - econstructor. - eapply CStep with (C := CPar1 (CSeq Hole _) _); eauto. - - econstructor. - eapply CStep with (C := CPar2 _ (CSeq Hole _)); eauto. - - econstructor. - eapply CStep with (C := CPar1 Hole _); eauto. - - econstructor. - eapply CStep with (C := CPar2 _ Hole); eauto. - - econstructor. - eapply CStep with (C := CPar1 Hole _); eauto. - - econstructor. - eapply CStep with (C := Hole); eauto. - - econstructor. - eapply CStep with (C := Hole); eauto. - - econstructor. - - simplify. - equality. - Qed. (** Proving equivalence with non-contextual semantics *) @@ -806,49 +781,8 @@ Module Concurrent. Hint Constructors step. (* Now, an automated proof of equivalence. Actually, it's *exactly* the same - * proof we used for the old feature set! *) - - Theorem step_cstep : forall v c v' c', - step (v, c) (v', c') - -> cstep (v, c) (v', c'). - Proof. - induct 1; repeat match goal with - | [ H : forall a b c d, _ = _ -> _ = _ -> _ |- _ ] => - specialize (H _ _ _ _ eq_refl eq_refl) - | [ H : cstep _ _ |- _ ] => invert H - end; eauto. - Qed. - - Hint Resolve step_cstep. - - Lemma step0_step : forall v c v' c', - step0 (v, c) (v', c') - -> step (v, c) (v', c'). - Proof. - induct 1; eauto. - Qed. - - Hint Resolve step0_step. - - Lemma cstep_step' : forall C c0 c, - plug C c0 c - -> forall v' c'0 v c', step0 (v, c0) (v', c'0) - -> plug C c'0 c' - -> step (v, c) (v', c'). - Proof. - induct 1; simplify; repeat match goal with - | [ H : plug _ _ _ |- _ ] => invert1 H - end; eauto. - Qed. - - Hint Resolve cstep_step'. - - Theorem cstep_step : forall v c v' c', - cstep (v, c) (v', c') - -> step (v, c) (v', c'). - Proof. - induct 1; eauto. - Qed. + * proof we used for the old feature set! For full dramatic effect, copy and + * paste here from above. *) End Concurrent.