X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=src%2FHaskProof.v;h=84eaa0b813163cfd2b3fcac740c00dfaee31d494;hp=c887b8a3479a67eec7f088e05498e4ad35b5b72a;hb=3161a8a65cb0190e83d32bde613c3b64dfe31739;hpb=db8c9d54c285980e162e393efd1b7316887e5b80

diff --git a/src/HaskProof.v b/src/HaskProof.v
index c887b8a..84eaa0b 100644
--- a/src/HaskProof.v
+++ b/src/HaskProof.v
@@ -36,14 +36,13 @@ Inductive Judg  :=
   Notation "Γ > Δ > a '|-' s '@' l" := (mkJudg Γ Δ a s l) (at level 52, Δ at level 50, a at level 52, s at level 50, l at level 50).
 
 (* information needed to define a case branch in a HaskProof *)
-Record ProofCaseBranch {tc:TyCon}{Γ}{Δ}{lev}{branchtype : HaskType Γ ★}{avars}{sac:@StrongAltCon tc} :=
-{ pcb_freevars       :  Tree ??(LeveledHaskType Γ ★)
-; pcb_judg           := sac_gamma sac Γ > sac_delta sac Γ avars (map weakCK' Δ)
+Definition pcb_judg
+  {tc:TyCon}{Γ}{Δ}{lev}{branchtype : HaskType Γ ★}{avars}{sac:@StrongAltCon tc}
+  (pcb_freevars       :  Tree ??(LeveledHaskType Γ ★)) :=
+  sac_gamma sac Γ > sac_delta sac Γ avars (map weakCK' Δ)
                 > (mapOptionTree weakLT' pcb_freevars),,(unleaves (map (fun t => t@@weakL' lev)
                   (vec2list (sac_types sac Γ avars))))
-                |- [weakT' branchtype ] @ weakL' lev
-}.
-Implicit Arguments ProofCaseBranch [ ].
+                |- [weakT' branchtype ] @ weakL' lev.
 
 (* Figure 3, production $\vdash_E$, all rules *)
 Inductive Rule : Tree ??Judg -> Tree ??Judg -> Type :=
@@ -65,13 +64,12 @@ 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 RExch'es *)
+(* 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 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]
 
 | RVoid    : ∀ Γ Δ l,               Rule [] [Γ > Δ > [] |- [] @l ]
 
@@ -86,15 +84,43 @@ Inductive Rule : Tree ??Judg -> Tree ??Judg -> Type :=
    Rule [Γ > ((σ₁∼∼∼σ₂)::Δ)            > Σ |- [σ ]@l]
         [Γ > Δ >                         Σ |- [σ₁∼∼σ₂⇒ σ ]@l]
 
-| RLetRec        : forall Γ Δ Σ₁ τ₁ τ₂ lev, Rule [Γ > Δ > Σ₁,,(τ₂@@@lev) |- (τ₂,,[τ₁]) @lev ] [Γ > Δ > Σ₁ |- [τ₁] @lev]
+| RLetRec        : forall Γ Δ Σ₁ τ₁ τ₂ lev, Rule [Γ > Δ > (τ₂@@@lev),,Σ₁ |- (τ₂,,[τ₁]) @lev ] [Γ > Δ > Σ₁ |- [τ₁] @lev]
 | RCase          : forall Γ Δ lev tc Σ avars tbranches
-  (alts:Tree ??{ sac : @StrongAltCon tc & @ProofCaseBranch tc Γ Δ lev tbranches avars sac }),
+  (alts:Tree ??( (@StrongAltCon tc) * (Tree ??(LeveledHaskType Γ ★)) )),
                    Rule
-                       ((mapOptionTree (fun x => pcb_judg (projT2 x)) alts),,
+                       ((mapOptionTree (fun x => @pcb_judg tc Γ Δ lev tbranches avars (fst x) (snd x)) alts),,
                         [Γ > Δ >                                              Σ |- [ caseType tc avars  ] @lev])
-                        [Γ > Δ > (mapOptionTreeAndFlatten (fun x => pcb_freevars (projT2 x)) alts),,Σ |- [ tbranches ] @ lev]
+                        [Γ > Δ > (mapOptionTreeAndFlatten (fun x => (snd 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.
+
+Definition RLet : ∀ Γ Δ Σ₁ Σ₂ σ₁ σ₂ l,
+  ND Rule ([Γ>Δ> Σ₁ |- [σ₁]@l],,[Γ>Δ> [σ₁@@l],,Σ₂ |- [σ₂]@l ])     [Γ>Δ> Σ₁,,Σ₂ |- [σ₂   ]@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.
+  eapply nd_rule; eapply RArrange; eapply AuCanL.
+  Defined.
+
+Definition RWhere : ∀ Γ Δ Σ₁ Σ₂ Σ₃ σ₁ σ₂ l,
+  ND Rule ([Γ>Δ> Σ₁,,([σ₁@@l],,Σ₃) |- [σ₂]@l ],,[Γ>Δ> Σ₂ |- [σ₁]@l])     [Γ>Δ> Σ₁,,(Σ₂,,Σ₃) |- [σ₂ ]@l].
+  intros.
+  eapply nd_comp; [ apply nd_exch | idtac ].
+  eapply nd_rule; eapply RCut.
+  Defined.
 
 (* A rule is considered "flat" if it is neither RBrak nor REsc *)
 (* TODO: change this to (if RBrak/REsc -> False) *)
@@ -110,8 +136,6 @@ Inductive Rule_Flat : forall {h}{c}, Rule h c -> Prop :=
 | Flat_RAppCo           : ∀ Γ Δ  Σ σ₁ σ₂ σ γ q l,  Rule_Flat (RAppCo Γ Δ  Σ  σ₁ σ₂ σ γ  q l)
 | 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).