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TransitionSystems: give more meaningful names to parallel trsys components
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2 changed files with 16 additions and 16 deletions
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@ -368,16 +368,16 @@ Definition increment_sys := {|
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* system the type of shared state remains the same, we take the Cartesian
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* product of the sets of private state. *)
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Inductive parallel1 shared private1 private2
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Inductive parallel_init shared private1 private2
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(init1 : threaded_state shared private1 -> Prop)
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(init2 : threaded_state shared private2 -> Prop)
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: threaded_state shared (private1 * private2) -> Prop :=
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| Pinit : forall sh pr1 pr2,
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init1 {| Shared := sh; Private := pr1 |}
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-> init2 {| Shared := sh; Private := pr2 |}
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-> parallel1 init1 init2 {| Shared := sh; Private := (pr1, pr2) |}.
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-> parallel_init init1 init2 {| Shared := sh; Private := (pr1, pr2) |}.
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Inductive parallel2 shared private1 private2
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Inductive parallel_step shared private1 private2
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(step1 : threaded_state shared private1 -> threaded_state shared private1 -> Prop)
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(step2 : threaded_state shared private2 -> threaded_state shared private2 -> Prop)
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: threaded_state shared (private1 * private2)
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@ -385,19 +385,19 @@ Inductive parallel2 shared private1 private2
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| Pstep1 : forall sh pr1 pr2 sh' pr1',
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(* First thread gets to run. *)
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step1 {| Shared := sh; Private := pr1 |} {| Shared := sh'; Private := pr1' |}
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-> parallel2 step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
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-> parallel_step step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
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{| Shared := sh'; Private := (pr1', pr2) |}
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| Pstep2 : forall sh pr1 pr2 sh' pr2',
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(* Second thread gets to run. *)
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step2 {| Shared := sh; Private := pr2 |} {| Shared := sh'; Private := pr2' |}
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-> parallel2 step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
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-> parallel_step step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
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{| Shared := sh'; Private := (pr1, pr2') |}.
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Definition parallel shared private1 private2
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(sys1 : trsys (threaded_state shared private1))
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(sys2 : trsys (threaded_state shared private2)) := {|
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Initial := parallel1 sys1.(Initial) sys2.(Initial);
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Step := parallel2 sys1.(Step) sys2.(Step)
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Initial := parallel_init sys1.(Initial) sys2.(Initial);
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Step := parallel_step sys1.(Step) sys2.(Step)
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|}.
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(* Example: composing two threads of the kind we formalized earlier *)
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@ -630,9 +630,9 @@ Proof.
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apply invariant_induction; simplify;
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repeat match goal with
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| [ H : increment2_invariant _ |- _ ] => invert H
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| [ H : parallel1 _ _ _ |- _ ] => invert H
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| [ H : parallel_init _ _ _ |- _ ] => invert H
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| [ H : increment_init _ |- _ ] => invert H
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| [ H : parallel2 _ _ _ _ |- _ ] => invert H
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| [ H : parallel_step _ _ _ _ |- _ ] => invert H
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| [ H : increment_step _ _ |- _ ] => invert H
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| [ pr : increment_program |- _ ] => cases pr; simplify
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end; try equality;
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@ -270,16 +270,16 @@ Definition increment_sys := {|
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* system the type of shared state remains the same, we take the Cartesian
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* product of the sets of private state. *)
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Inductive parallel1 shared private1 private2
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Inductive parallel_init shared private1 private2
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(init1 : threaded_state shared private1 -> Prop)
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(init2 : threaded_state shared private2 -> Prop)
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: threaded_state shared (private1 * private2) -> Prop :=
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| Pinit : forall sh pr1 pr2,
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init1 {| Shared := sh; Private := pr1 |}
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-> init2 {| Shared := sh; Private := pr2 |}
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-> parallel1 init1 init2 {| Shared := sh; Private := (pr1, pr2) |}.
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-> parallel_init init1 init2 {| Shared := sh; Private := (pr1, pr2) |}.
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Inductive parallel2 shared private1 private2
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Inductive parallel_step shared private1 private2
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(step1 : threaded_state shared private1 -> threaded_state shared private1 -> Prop)
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(step2 : threaded_state shared private2 -> threaded_state shared private2 -> Prop)
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: threaded_state shared (private1 * private2)
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@ -287,19 +287,19 @@ Inductive parallel2 shared private1 private2
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| Pstep1 : forall sh pr1 pr2 sh' pr1',
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(* First thread gets to run. *)
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step1 {| Shared := sh; Private := pr1 |} {| Shared := sh'; Private := pr1' |}
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-> parallel2 step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
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-> parallel_step step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
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{| Shared := sh'; Private := (pr1', pr2) |}
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| Pstep2 : forall sh pr1 pr2 sh' pr2',
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(* Second thread gets to run. *)
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step2 {| Shared := sh; Private := pr2 |} {| Shared := sh'; Private := pr2' |}
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-> parallel2 step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
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-> parallel_step step1 step2 {| Shared := sh; Private := (pr1, pr2) |}
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{| Shared := sh'; Private := (pr1, pr2') |}.
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Definition parallel shared private1 private2
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(sys1 : trsys (threaded_state shared private1))
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(sys2 : trsys (threaded_state shared private2)) := {|
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Initial := parallel1 sys1.(Initial) sys2.(Initial);
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Step := parallel2 sys1.(Step) sys2.(Step)
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Initial := parallel_init sys1.(Initial) sys2.(Initial);
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Step := parallel_step sys1.(Step) sys2.(Step)
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|}.
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(* Example: composing two threads of the kind we formalized earlier *)
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