Move restricted semantics results to own file.

SoundlyTypedChoreography.v

@@ -8,43 +8,26 @@ Module SoundlyTypedChoreography (E : Expression) (TE : TypedExpression E) (STE :
   Import E. Import TE. Import STE.
   Include (TypedChoreography L E TE).
 
-    Theorem Preservation :
-    forall (Γ : L.t -> nat -> ExprTyp) (Δ : nat -> ChorTyp) (C : Chor) (τ : ChorTyp),
-      Γ;; Δ ⊢c C ::: τ -> forall (R : Redex) (B : list L.t) (C': Chor),
-        RChorStep R B C C' -> Γ;; Δ ⊢c C' ::: τ.
-    Proof.
-      apply RelativePreservation. intros Γ e τ H e' H0.
-      apply ExprPreservation with (e1 := e); auto.
-    Qed.
 
-    Theorem CompletePreservation:
+    Theorem Preservation:
       forall (Γ : L.t -> nat -> ExprTyp) (Δ : nat -> ChorTyp) (C : Chor) (τ : ChorTyp),
         Γ;; Δ ⊢c C ::: τ -> forall (R : Redex) (B : list L.t) (C': Chor),
-          CompleteRChorStep R B C C' -> Γ;; Δ ⊢c C' ::: τ.
+          ChorStep R B C C' -> Γ;; Δ ⊢c C' ::: τ.
     Proof.
-      apply CompleteRelativePreservation. intros Γ e τ H e' H0.
+      apply RelativePreservation. intros Γ e τ H e' H0.
       apply ExprPreservation with (e1 := e); auto.
     Qed.
 
     Theorem Progress :
     forall (C : Chor) (Γ : L.t -> nat -> ExprTyp) (Δ : nat -> ChorTyp) (τ : ChorTyp),
       ChorClosed C -> Γ;; Δ ⊢c C ::: τ ->
-      ChorVal C \/ exists R C', RChorStep R nil C C'.
+      ChorVal C \/ exists R C', ChorStep R nil C C'.
     Proof.
       apply RelativeProgress; auto.
       intros e τ Γ H H0; eapply ExprProgress; eauto.
       intros v Γ H H0; eapply BoolInversion; eauto.
     Qed.
 
-    Theorem CompleteProgress :
-    forall (C : Chor) (Γ : L.t -> nat -> ExprTyp) (Δ : nat -> ChorTyp) (τ : ChorTyp),
-      ChorClosed C -> Γ;; Δ ⊢c C ::: τ ->
-      ChorVal C \/ exists R C', CompleteRChorStep R nil C C'.
-    Proof.
-      apply CompleteRelativeProgress; auto.
-      intros e τ Γ H H0; eapply ExprProgress; eauto.
-      intros v Γ H H0; eapply BoolInversion; eauto.
-    Qed.
 End SoundlyTypedChoreography.
 
 

TypedChoreography.v

@@ -347,14 +347,14 @@ Module TypedChoreography (L : Locations) (E : Expression) (TE : TypedExpression
       rewrite (ExprTypingUnique (Γ l2) e' τ0 τ1 H11 H10); auto.
   Qed.      
 
-  Theorem CompleteRelativePreservation :
+  Theorem RelativePreservation :
     (forall (Γ : nat -> ExprTyp) (e : Expr) (τ : ExprTyp),
         Γ ⊢e e ::: τ
         -> forall e' : Expr, ExprStep e e'
                        -> Γ ⊢e e' ::: τ) ->
     forall (Γ : Loc -> nat -> ExprTyp) (Δ : nat -> ChorTyp) (C : Chor) (τ : ChorTyp),
       Γ;; Δ ⊢c C ::: τ -> forall (R : Redex) (B : list Loc) (C': Chor),
-        CompleteRChorStep R B C C' -> Γ;; Δ ⊢c C' ::: τ.
+        ChorStep R B C C' -> Γ;; Δ ⊢c C' ::: τ.
   Proof using.
     intros expr_pres Γ Δ C τ typing R B C' step; revert Γ Δ τ typing; induction step;
       intros Γ Δ τ typing; inversion typing; subst;
@@ -382,18 +382,6 @@ Module TypedChoreography (L : Locations) (E : Expression) (TE : TypedExpression
       apply AppGlobalSubstTyping; auto.
   Qed.    
   
-  Corollary RelativePreservation :
-    (forall (Γ : nat -> ExprTyp) (e : Expr) (τ : ExprTyp),
-        Γ ⊢e e ::: τ
-        -> forall e' : Expr, ExprStep e e'
-                       -> Γ ⊢e e' ::: τ) ->
-    forall (Γ : Loc -> nat -> ExprTyp) (Δ : nat -> ChorTyp) (C : Chor) (τ : ChorTyp),
-      Γ;; Δ ⊢c C ::: τ -> forall (R : Redex) (B : list Loc) (C': Chor),
-        RChorStep R B C C' -> Γ;; Δ ⊢c C' ::: τ.
-  Proof.
-    intros H Γ Δ C τ H0 R B C' H1; apply LiftRChorStepToComplete in H1.
-    eapply CompleteRelativePreservation in H1; eauto.
-  Qed.
 
   Lemma ChorClosedBelowTyping : forall (Γ1 Γ2 : Loc -> nat -> ExprTyp)
                                   (Δ1 Δ2 : nat -> ChorTyp)
@@ -458,7 +446,8 @@ Module TypedChoreography (L : Locations) (E : Expression) (TE : TypedExpression
     eapply ChorClosedTyping; eauto. apply ChorValuesClosed; auto.
   Qed.
   
-  Theorem RelativeProgress :
+
+  Corollary RelativeProgress :
     (forall (e : Expr) (τ : ExprTyp) (Γ : nat -> ExprTyp),
         Γ ⊢e e ::: τ -> ExprClosed e ->
         ExprVal e \/ exists e' : Expr, ExprStep e e') ->
@@ -466,8 +455,8 @@ Module TypedChoreography (L : Locations) (E : Expression) (TE : TypedExpression
         Γ ⊢e v ::: bool -> ExprVal v -> {v = tt} + {v = ff}) ->
     forall (C : Chor) (Γ : Loc -> nat -> ExprTyp) (Δ : nat -> ChorTyp) (τ : ChorTyp),
       ChorClosed C -> Γ;; Δ ⊢c C ::: τ ->
-      ChorVal C \/ exists R C', RChorStep R nil C C'.
-  Proof.
+      ChorVal C \/ exists R C', ChorStep R nil C C'.
+  Proof using.
     intros ExprProgress BoolInversion C Γ Δ τ cc typ; revert cc; induction typ; intro cc;
       inversion cc; subst.
     2: inversion H2.
@@ -498,21 +487,6 @@ Module TypedChoreography (L : Locations) (E : Expression) (TE : TypedExpression
       all: inversion IHtyp1; subst; inversion typ1; subst.
       all: eexists; eexists; eauto with Chor.
   Qed.
-
-  Corollary CompleteRelativeProgress :
-    (forall (e : Expr) (τ : ExprTyp) (Γ : nat -> ExprTyp),
-        Γ ⊢e e ::: τ -> ExprClosed e ->
-        ExprVal e \/ exists e' : Expr, ExprStep e e') ->
-    (forall (v : Expr) (Γ : nat -> ExprTyp),
-        Γ ⊢e v ::: bool -> ExprVal v -> {v = tt} + {v = ff}) ->
-    forall (C : Chor) (Γ : Loc -> nat -> ExprTyp) (Δ : nat -> ChorTyp) (τ : ChorTyp),
-      ChorClosed C -> Γ;; Δ ⊢c C ::: τ ->
-      ChorVal C \/ exists R C', CompleteRChorStep R nil C C'.
-  Proof using.
-    intros H H0 C Γ Δ τ H1 H2.
-    eapply RelativeProgress in H2; eauto.
-    destruct H2 as [H2 | [R [C' step]]]; [left|right; apply LiftRChorStepToComplete in step; eexists; eexists; eauto]; auto.
-  Qed.
   
 End TypedChoreography.
 

_CoqProject

@@ -11,3 +11,4 @@ FunLMap.v
 Choreography.v
 TypedChoreography.v
 SoundlyTypedChoreography.v
+RestrictedSemantics.v
\ No newline at end of file