more bugfixes

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

diff --git a/src/HaskProof.v b/src/HaskProof.v
index 6474665..7e3ef1c 100644 (file)
--- a/src/HaskProof.v
+++ b/src/HaskProof.v
@@ -16,6 +16,7 @@ Require Import HaskKinds.
 Require Import HaskCoreTypes.
 Require Import HaskLiteralsAndTyCons.
 Require Import HaskStrongTypes.
+Require Import HaskWeakVars.
 
 (* A judgment consists of an environment shape (Γ and Δ) and a pair of trees of leveled types (the antecedent and succedent) valid
  * in any context of that shape.  Notice that the succedent contains a tree of types rather than a single type; think
@@ -49,15 +50,14 @@ Definition UJudg2judg {Γ}{Δ}(ej:@UJudg Γ Δ) : Judg :=
   Coercion UJudg2judg : UJudg >-> Judg.
 
 (* information needed to define a case branch in a HaskProof *)
-Record ProofCaseBranch {tc:TyCon}{Γ}{Δ}{lev}{branchtype : HaskType Γ ★}{avars} :=
-{ pcb_scb            :  @StrongAltCon tc
-; pcb_freevars       :  Tree ??(LeveledHaskType Γ ★)
-; pcb_judg           := sac_Γ pcb_scb Γ > sac_Δ pcb_scb Γ avars (map weakCK' Δ)
+Record ProofCaseBranch {tc:TyCon}{Γ}{Δ}{lev}{branchtype : HaskType Γ ★}{avars}{sac:@StrongAltCon tc} :=
+{ pcb_freevars       :  Tree ??(LeveledHaskType Γ ★)
+; pcb_judg           := sac_Γ sac Γ > sac_Δ sac Γ avars (map weakCK' Δ)
                 > (mapOptionTree weakLT' pcb_freevars),,(unleaves (map (fun t => t@@weakL' lev)
-                  (vec2list (sac_types pcb_scb Γ avars))))
+                  (vec2list (sac_types sac Γ avars))))
                 |- [weakLT' (branchtype @@ lev)]
 }.
-Coercion pcb_scb : ProofCaseBranch >-> StrongAltCon.
+(*Coercion pcb_scb : ProofCaseBranch >-> StrongAltCon.*)
 Implicit Arguments ProofCaseBranch [ ].
 
 (* Figure 3, production $\vdash_E$, Uniform rules *)
@@ -85,11 +85,12 @@ Inductive Rule : Tree ??Judg -> Tree ??Judg -> Type :=
 | REsc  : ∀ Γ Δ t v Σ l,                              Rule [Γ > Δ > Σ      |- [<[v|-t]> @@ l]]   [Γ > Δ > Σ     |- [t  @@ (v::l)  ]]
 
 (* Part of GHC, but not explicitly in System FC *)
-| RNote   : ∀ h c,                Note ->             Rule  h                                    [ c ]
+| RNote   : ∀ Γ Δ Σ τ l,          Note ->             Rule  [Γ > Δ > Σ |- [τ @@ l]] [Γ > Δ > Σ |- [τ @@ l]]
 | RLit    : ∀ Γ Δ v       l,                          Rule  [                                ]   [Γ > Δ > []|- [literalType v @@ l]]
 
 (* SystemFC rules *)
 | RVar    : ∀ Γ Δ σ       l,                          Rule [                                 ]   [Γ>Δ> [σ@@l]   |- [σ          @@l]]
+| RGlobal : ∀ Γ Δ τ       l,   WeakExprVar ->         Rule [                                 ]   [Γ>Δ>     []   |- [τ          @@l]]
 | RLam    : forall Γ Δ Σ (tx:HaskType Γ ★) te l,      Rule [Γ>Δ> Σ,,[tx@@l]|- [te@@l]        ]   [Γ>Δ>    Σ     |- [tx--->te   @@l]]
 | RCast   : forall Γ Δ Σ (σ₁ σ₂:HaskType Γ ★) l,
 HaskCoercion Γ Δ (σ₁∼∼∼σ₂) ->
@@ -107,13 +108,13 @@ HaskCoercion Γ Δ (σ₁∼∼∼σ₂) ->
 | RAbsCo  : forall Γ Δ Σ κ (σ₁ σ₂:HaskType Γ κ) σ l,
    Rule [Γ > ((σ₁∼∼∼σ₂)::Δ)            > Σ |- [σ @@ l]]
         [Γ > Δ >                         Σ |- [σ₁∼∼σ₂⇒ σ @@l]]
-| RLetRec        : ∀ Γ Δ Σ₁ τ₁ τ₂, Rule [Γ > Δ > Σ₁,,τ₂ |- τ₁,,τ₂ ] [Γ > Δ > Σ₁ |- τ₁ ]
+| RLetRec        : forall Γ Δ Σ₁ τ₁ τ₂ lev, Rule [Γ > Δ > Σ₁,,(τ₂@@@lev) |- ([τ₁],,τ₂)@@@lev ] [Γ > Δ > Σ₁ |- [τ₁@@lev] ]
 | RCase          : forall Γ Δ lev tc Σ avars tbranches
-  (alts:Tree ??(@ProofCaseBranch tc Γ Δ lev tbranches avars)),
+  (alts:Tree ??{ sac : @StrongAltCon tc & @ProofCaseBranch tc Γ Δ lev tbranches avars sac }),
                    Rule
-                       ((mapOptionTree pcb_judg alts),,
+                       ((mapOptionTree (fun x => pcb_judg (projT2 x)) alts),,
                         [Γ > Δ >                                              Σ |- [ caseType tc avars @@ lev ] ])
-                        [Γ > Δ > (mapOptionTreeAndFlatten pcb_freevars alts),,Σ |- [ tbranches         @@ lev ] ]
+                        [Γ > Δ > (mapOptionTreeAndFlatten (fun x => pcb_freevars (projT2 x)) alts),,Σ |- [ tbranches         @@ lev ] ]
 .
 Coercion RURule : URule >-> Rule.
 
@@ -121,7 +122,8 @@ Coercion RURule : URule >-> Rule.
 (* A rule is considered "flat" if it is neither RBrak nor REsc *)
 Inductive Rule_Flat : forall {h}{c}, Rule h c -> Prop :=
 | Flat_RURule           : ∀ Γ Δ  h c r            ,  Rule_Flat (RURule Γ Δ  h c r)
-| Flat_RNote            : ∀ x y z              ,  Rule_Flat (RNote x y z)
+| Flat_RNote            : ∀ Γ Δ Σ τ l n            ,  Rule_Flat (RNote Γ Δ Σ τ l n)
+| Flat_RLit             : ∀ Γ Δ Σ τ               ,  Rule_Flat (RLit Γ Δ Σ τ  )
 | Flat_RVar             : ∀ Γ Δ  σ               l,  Rule_Flat (RVar Γ Δ  σ         l)
 | Flat_RLam             : ∀ Γ Δ  Σ tx te    q    ,  Rule_Flat (RLam Γ Δ  Σ tx te      q )
 | Flat_RCast            : ∀ Γ Δ  Σ σ τ γ    q     ,  Rule_Flat (RCast Γ Δ  Σ σ τ γ    q )
@@ -132,7 +134,9 @@ Inductive Rule_Flat : forall {h}{c}, Rule h c -> Prop :=
 | 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_RBindingGroup    : ∀ q a b c d e ,  Rule_Flat (RBindingGroup q a b c d e)
-| Flat_RCase            : ∀ Σ Γ  T κlen κ θ l x  , Rule_Flat (RCase Σ Γ T κlen κ θ l x).
+| Flat_REmptyGroup      : ∀ q a                  ,  Rule_Flat (REmptyGroup q a)
+| 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).
 
 (* given a proof that uses only uniform rules, we can produce a general proof *)
 Definition UND_to_ND Γ Δ h c : ND (@URule Γ Δ) h c -> ND Rule (mapOptionTree UJudg2judg h) (mapOptionTree UJudg2judg c)
@@ -208,6 +212,7 @@ 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.