mirror of
https://github.com/achlipala/frap.git
synced 2024-11-10 00:07:51 +00:00
OperationalSemantics: automated contextual small-step
This commit is contained in:
parent
ab4420c66f
commit
72ac97a60a
1 changed files with 45 additions and 0 deletions
|
@ -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.
|
||||
|
|
Loading…
Reference in a new issue