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OperationalSemantics: automated contextual small-step

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Adam Chlipala 2016-02-21 13:55:18 -05:00
parent ab4420c66f
commit 72ac97a60a
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OperationalSemantics.v
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@ -639,3 +639,48 @@ Proof.
eassumption.
assumption.
Qed.
(* Bonus material: here's how to make these proofs much more automatic. We
* won't explain the features being used here. *)
Hint Constructors plug step0 cstep.
Theorem step_cstep_snazzy : forall v c v' c',
step (v, c) (v', c')
-> cstep (v, c) (v', c').
Proof.
induct 1; repeat match goal with
| [ H : cstep _ _ |- _ ] => invert H
end; eauto.
Qed.
Hint Resolve step_cstep_snazzy.
Lemma step0_step_snazzy : forall v c v' c',
step0 (v, c) (v', c')
-> step (v, c) (v', c').
Proof.
induct 1; eauto.
Qed.
Hint Resolve step0_step_snazzy.
Lemma cstep_step'_snazzy : 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'_snazzy.
Theorem cstep_step_snazzy : forall v c v' c',
cstep (v, c) (v', c')
-> step (v, c) (v', c').
Proof.
induct 1; eauto.
Qed.