Add [parallel] to libary

This commit is contained in:
Adam Chlipala 2016-02-22 17:28:40 -05:00
parent 06b5592c89
commit cc19c1708b

View file

@ -42,3 +42,41 @@ Proof.
clear H1.
induction H2; eauto.
Qed.
(** * General parallel composition *)
Record threaded_state shared private := {
Shared : shared;
Private : private
}.
Inductive parallel1 shared private1 private2
(init1 : threaded_state shared private1 -> Prop)
(init2 : threaded_state shared private2 -> Prop)
: threaded_state shared (private1 * private2) -> Prop :=
| Pinit : forall sh pr1 pr2,
init1 {| Shared := sh; Private := pr1 |}
-> init2 {| Shared := sh; Private := pr2 |}
-> parallel1 init1 init2 {| Shared := sh; Private := (pr1, pr2) |}.
Inductive parallel2 shared private1 private2
(step1 : threaded_state shared private1 -> threaded_state shared private1 -> Prop)
(step2 : threaded_state shared private2 -> threaded_state shared private2 -> Prop)
: threaded_state shared (private1 * private2)
-> threaded_state shared (private1 * private2) -> Prop :=
| Pstep1 : forall sh pr1 pr2 sh' pr1',
step1 {| Shared := sh; Private := pr1 |} {| Shared := sh'; Private := pr1' |}
-> parallel2 step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
{| Shared := sh'; Private := (pr1', pr2) |}
| Pstep2 : forall sh pr1 pr2 sh' pr2',
step2 {| Shared := sh; Private := pr2 |} {| Shared := sh'; Private := pr2' |}
-> parallel2 step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
{| Shared := sh'; Private := (pr1, pr2') |}.
Definition parallel shared private1 private2
(sys1 : trsys (threaded_state shared private1))
(sys2 : trsys (threaded_state shared private2)) := {|
Initial := parallel1 sys1.(Initial) sys2.(Initial);
Step := parallel2 sys1.(Step) sys2.(Step)
|}.