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fix warnings in MessagesAndRefinement.v
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1 changed files with 25 additions and 25 deletions
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@ -241,7 +241,7 @@ Inductive couldGenerate : proc -> list action -> Prop :=
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(* Skip ahead to [refines_couldGenerate] to see the top-level connection from
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* [refines]. *)
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Hint Constructors couldGenerate.
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Hint Constructors couldGenerate : core.
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Lemma lstepSilent_couldGenerate : forall pr1 pr2,
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lstepSilent^* pr1 pr2
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@ -251,7 +251,7 @@ Proof.
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induct 1; eauto.
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Qed.
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Hint Resolve lstepSilent_couldGenerate.
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Hint Resolve lstepSilent_couldGenerate : core.
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Lemma simulates_couldGenerate' : forall (R : proc -> proc -> Prop),
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(forall pr1 pr2, R pr1 pr2
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@ -305,8 +305,8 @@ Ltac inverter :=
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| [ H : lstepSilent _ _ |- _ ] => invert H
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end.
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Hint Constructors lstep.
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Hint Unfold lstepSilent.
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Hint Constructors lstep : core.
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Hint Unfold lstepSilent : core.
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Ltac lists' :=
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repeat match goal with
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@ -316,7 +316,7 @@ Ltac lists' :=
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Ltac lists := solve [ lists' ].
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Hint Extern 1 (NoDup _) => lists.
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Hint Extern 1 (NoDup _) => lists : core.
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(** * Examples *)
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@ -361,7 +361,7 @@ Inductive R_add2 : proc -> proc -> Prop :=
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(Block intermediate; Done || Done)
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Done.
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Hint Constructors R_add2.
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Hint Constructors R_add2 : core.
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Theorem add2_once_refines_addN : forall input output,
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input <> output
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@ -462,9 +462,9 @@ Inductive RDup (R : proc -> proc -> Prop) : proc -> proc -> Prop :=
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-> RDup R pr2 pr2'
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-> RDup R (Par pr1 pr2) (Par pr1' pr2').
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Hint Constructors RDup.
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Hint Constructors RDup : core.
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Hint Unfold lstepSilent.
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Hint Unfold lstepSilent : core.
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Lemma lstepSilent_Par1 : forall pr1 pr1' pr2,
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lstepSilent^* pr1 pr1'
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@ -480,7 +480,7 @@ Proof.
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induct 1; eauto.
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Qed.
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Hint Resolve lstepSilent_Par1 lstepSilent_Par2.
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Hint Resolve lstepSilent_Par1 lstepSilent_Par2 : core.
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Lemma refines_Dup_Action : forall R : _ -> _ -> Prop,
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(forall pr1 pr2, R pr1 pr2
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@ -593,7 +593,7 @@ Inductive RPar (R1 R2 : proc -> proc -> Prop) : proc -> proc -> Prop :=
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-> R2 pr2 pr2'
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-> RPar R1 R2 (pr1 || pr2) (pr1' || pr2').
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Hint Constructors RPar.
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Hint Constructors RPar : core.
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Lemma refines_Par_Action : forall R1 R2 : _ -> _ -> Prop,
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(forall pr1 pr2, R1 pr1 pr2
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@ -706,8 +706,8 @@ Inductive RBlock (R : proc -> proc -> Prop) : proc -> proc -> Prop :=
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R pr1 pr2
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-> RBlock R (Block ch; pr1) (Block ch; pr2).
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Hint Constructors RBlock.
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Hint Unfold notUse.
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Hint Constructors RBlock : core.
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Hint Unfold notUse : core.
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Lemma lstepSilent_Block : forall ch pr1 pr2,
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lstepSilent^* pr1 pr2
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@ -716,7 +716,7 @@ Proof.
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induct 1; eauto.
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Qed.
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Hint Resolve lstepSilent_Block.
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Hint Resolve lstepSilent_Block : core.
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Theorem refines_Block : forall pr1 pr2 ch,
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pr1 <| pr2
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@ -743,7 +743,7 @@ Inductive RBlock2 : proc -> proc -> Prop :=
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| RBlock2_1 : forall ch1 ch2 pr,
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RBlock2 (Block ch1; Block ch2; pr) (Block ch2; Block ch1; pr).
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Hint Constructors RBlock2.
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Hint Constructors RBlock2 : core.
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Theorem refines_Block2 : forall ch1 ch2 pr,
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Block ch1; Block ch2; pr <| Block ch2; Block ch1; pr.
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@ -783,7 +783,7 @@ Inductive neverUses (ch : channel) : proc -> Prop :=
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| NuDone :
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neverUses ch Done.
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Hint Constructors neverUses.
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Hint Constructors neverUses : core.
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Lemma neverUses_step : forall ch pr1,
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neverUses ch pr1
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@ -793,14 +793,14 @@ Proof.
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induct 1; invert 1; eauto.
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Qed.
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Hint Resolve neverUses_step.
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Hint Resolve neverUses_step : core.
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Inductive RBlockS : proc -> proc -> Prop :=
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| RBlockS1 : forall ch pr1 pr2,
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neverUses ch pr2
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-> RBlockS (Block ch; pr1 || pr2) ((Block ch; pr1) || pr2).
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Hint Constructors RBlockS.
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Hint Constructors RBlockS : core.
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Lemma neverUses_notUse : forall ch pr l,
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neverUses ch pr
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@ -824,7 +824,7 @@ Proof.
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simplify; auto.
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Qed.
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Hint Resolve neverUses_notUse.
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Hint Resolve neverUses_notUse : core.
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Theorem refines_BlockS : forall ch pr1 pr2,
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neverUses ch pr2
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@ -1008,7 +1008,7 @@ Inductive RTree (t : tree) (input output : channel) : proc -> proc -> Prop :=
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(Block output'; threads || Done)
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Done.
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Hint Constructors TreeThreads RTree.
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Hint Constructors TreeThreads RTree : core.
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Lemma TreeThreads_actionIs : forall ch maySend pr,
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TreeThreads ch maySend pr
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@ -1055,7 +1055,7 @@ Proof.
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induct 1; eauto.
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Qed.
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Hint Resolve TreeThreads_silent TreeThreads_maySend TreeThreads_action TreeThreads_weaken.
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Hint Resolve TreeThreads_silent TreeThreads_maySend TreeThreads_action TreeThreads_weaken : core.
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Lemma TreeThreads_inTree_par' : forall n ch t,
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TreeThreads ch (mem n t) (inTree_par' n t ch).
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@ -1066,7 +1066,7 @@ Proof.
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cases (mem n t2); simplify; eauto.
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Qed.
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Hint Resolve TreeThreads_inTree_par'.
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Hint Resolve TreeThreads_inTree_par' : core.
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(* Finally, the main theorem: *)
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Theorem refines_inTree_par : forall t input output,
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@ -1186,7 +1186,7 @@ Inductive Rhandoff (ch : channel) (A : Type) (v : A) (k : A -> proc) : proc -> p
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-> manyOf (??ch(x : A); k x) recvs
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-> Rhandoff ch v k (Block ch; Done || recvs) rest.
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Hint Constructors manyOf manyOfAndOneOf Rhandoff.
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Hint Constructors manyOf manyOfAndOneOf Rhandoff : core.
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Lemma manyOf_action : forall this pr,
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manyOf this pr
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@ -1226,7 +1226,7 @@ Proof.
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invert H1; eauto.
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Qed.
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Hint Resolve manyOf_silent manyOf_rendezvous.
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Hint Resolve manyOf_silent manyOf_rendezvous : core.
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Lemma manyOfAndOneOf_output : forall ch (A : Type) (k : A -> _) rest ch0 (A0 : Type) (v0 : A0) pr,
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manyOfAndOneOf (Recv ch k) rest pr
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@ -1260,7 +1260,7 @@ Proof.
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induct 1; simplify; eauto.
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Qed.
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Hint Resolve manyOf_manyOfAndOneOf.
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Hint Resolve manyOf_manyOfAndOneOf : core.
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Lemma no_rendezvous : forall ch0 (A0 : Type) (v : A0) pr1 rest (k : A0 -> _),
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manyOfAndOneOf (??ch0 (x : _); k x) rest pr1
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@ -1335,7 +1335,7 @@ Proof.
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invert H.
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Qed.
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Hint Resolve manyOfAndOneOf_silent manyOf_rendezvous.
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Hint Resolve manyOfAndOneOf_silent manyOf_rendezvous : core.
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Lemma manyOfAndOneOf_action : forall ch (A : Type) (k : A -> _) rest pr,
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manyOfAndOneOf (Recv ch k) rest pr
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