let RCut take a left environment as well

[coq-hetmet.git] / src / HaskProof.v

diff --git a/src/HaskProof.v b/src/HaskProof.v
index 46009f8..8c6acf4 100644 (file)
--- a/src/HaskProof.v
+++ b/src/HaskProof.v
@@ -65,15 +65,13 @@ Inductive Rule : Tree ??Judg -> Tree ??Judg -> Type :=
 | RCast   : forall Γ Δ Σ (σ₁ σ₂:HaskType Γ ★) l,
                    HaskCoercion Γ Δ (σ₁∼∼∼σ₂) ->      Rule [Γ>Δ> Σ         |- [σ₁]         @l]   [Γ>Δ>    Σ     |- [σ₂         ] @l]
 
-| RJoin  : ∀ Γ Δ Σ₁ Σ₂ τ₁ τ₂ l,   Rule ([Γ > Δ > Σ₁ |- τ₁ @l],,[Γ > Δ > Σ₂ |- τ₂ @l])         [Γ>Δ>  Σ₁,,Σ₂  |- τ₁,,τ₂       @l ]
-
 (* order is important here; we want to be able to skolemize without introducing new AExch'es *)
 | RApp           : ∀ Γ Δ Σ₁ Σ₂ tx te l,  Rule ([Γ>Δ> Σ₁ |- [tx--->te]@l],,[Γ>Δ> Σ₂ |- [tx]@l])  [Γ>Δ> Σ₁,,Σ₂ |- [te]@l]
 
 | RLet           : ∀ Γ Δ Σ₁ Σ₂ σ₁ σ₂ l,  Rule ([Γ>Δ> Σ₁ |- [σ₁]@l],,[Γ>Δ> [σ₁@@l],,Σ₂ |- [σ₂]@l ])     [Γ>Δ> Σ₁,,Σ₂ |- [σ₂   ]@l]
 | RWhere         : ∀ Γ Δ Σ₁ Σ₂ Σ₃ σ₁ σ₂ l,  Rule ([Γ>Δ> Σ₁,,([σ₁@@l],,Σ₃) |- [σ₂]@l ],,[Γ>Δ> Σ₂ |- [σ₁]@l])     [Γ>Δ> Σ₁,,(Σ₂,,Σ₃) |- [σ₂ ]@l]
 
-| RCut           : ∀ Γ Δ Σ₁ Σ₁₂ Σ₂ Σ₃ l,  Rule ([Γ>Δ> Σ₁ |- Σ₁₂ @l],,[Γ>Δ> (Σ₁₂@@@l),,Σ₂ |- Σ₃@l ]) [Γ>Δ> Σ₁,,Σ₂ |- Σ₃@l]
+| RCut           : ∀ Γ Δ Σ Σ₁ Σ₁₂ Σ₂ Σ₃ l, Rule ([Γ>Δ> Σ₁ |- Σ₁₂ @l],,[Γ>Δ> Σ,,((Σ₁₂@@@l),,Σ₂) |- Σ₃@l ]) [Γ>Δ> Σ,,(Σ₁,,Σ₂) |- Σ₃@l]
 | RLeft          : ∀ Γ Δ Σ₁ Σ₂  Σ     l,  Rule  [Γ>Δ> Σ₁ |- Σ₂  @l]                                 [Γ>Δ> (Σ@@@l),,Σ₁ |- Σ,,Σ₂@l]
 | RRight         : ∀ Γ Δ Σ₁ Σ₂  Σ     l,  Rule  [Γ>Δ> Σ₁ |- Σ₂  @l]                                 [Γ>Δ> Σ₁,,(Σ@@@l) |- Σ₂,,Σ@l]
 
@@ -99,6 +97,17 @@ Inductive Rule : Tree ??Judg -> Tree ??Judg -> Type :=
                         [Γ > Δ > (mapOptionTreeAndFlatten (fun x => pcb_freevars (projT2 x)) alts),,Σ |- [ tbranches ] @ lev]
 .
 
+Definition RCut'  : ∀ Γ Δ Σ₁ Σ₁₂ Σ₂ Σ₃ l,
+  ND Rule ([Γ>Δ> Σ₁ |- Σ₁₂ @l],,[Γ>Δ> (Σ₁₂@@@l),,Σ₂ |- Σ₃@l ]) [Γ>Δ> Σ₁,,Σ₂ |- Σ₃@l].
+  intros.
+  eapply nd_comp; [ idtac | eapply nd_rule; eapply RArrange; eapply ACanL ].
+  eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ].
+  apply nd_prod.
+  apply nd_id.
+  apply nd_rule.
+  apply RArrange.
+  apply AuCanL.
+  Defined.
 
 (* A rule is considered "flat" if it is neither RBrak nor REsc *)
 (* TODO: change this to (if RBrak/REsc -> False) *)
@@ -115,7 +124,6 @@ Inductive Rule_Flat : forall {h}{c}, Rule h c -> Prop :=
 | Flat_RAbsCo           : ∀ Γ   Σ κ σ  σ₁ σ₂ q1 q2   , Rule_Flat (RAbsCo Γ   Σ κ σ  σ₁ σ₂  q1 q2   )
 | Flat_RApp             : ∀ Γ Δ  Σ tx te   p     l,  Rule_Flat (RApp Γ Δ  Σ tx te   p l)
 | Flat_RLet             : ∀ Γ Δ  Σ σ₁ σ₂   p     l,  Rule_Flat (RLet Γ Δ  Σ σ₁ σ₂   p l)
-| Flat_RJoin    : ∀ q a b c d e l,  Rule_Flat (RJoin q a b c d e l)
 | Flat_RVoid      : ∀ q a                  l,  Rule_Flat (RVoid q a l)
 | Flat_RCase            : ∀ Σ Γ  T κlen κ θ l x  , Rule_Flat (RCase Σ Γ T κlen κ θ l x)
 | Flat_RLetRec          : ∀ Γ Δ Σ₁ τ₁ τ₂ lev,      Rule_Flat (RLetRec Γ Δ Σ₁ τ₁ τ₂ lev).
@@ -153,7 +161,6 @@ Lemma no_rules_with_multiple_conclusions : forall c h,
     destruct X0; destruct s; inversion e.
     destruct X0; destruct s; inversion e.
     destruct X0; destruct s; inversion e.
-    destruct X0; destruct s; inversion e.
     Qed.
 
 Lemma systemfc_all_rules_one_conclusion : forall h c1 c2 (r:Rule h (c1,,c2)), False.