Make the HaskStrong type representation Kind-indexed, and many supporting changes...

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

diff --git a/src/HaskStrong.v b/src/HaskStrong.v
index 50e7ab3..b7229d0 100644 (file)
--- a/src/HaskStrong.v
+++ b/src/HaskStrong.v
@@ -8,6 +8,7 @@ Require Import General.
 Require Import Coq.Strings.String.
 Require Import Coq.Lists.List.
 Require Import HaskKinds.
+Require Import HaskWeakVars.
 Require Import HaskCoreTypes.
 Require Import HaskCoreLiterals.
 Require Import HaskStrongTypes.
@@ -18,8 +19,9 @@ Section HaskStrong.
   Context `{EQD_VV:EqDecidable VV}.
 
   (* a StrongCaseBranchWithVVs contains all the data found in a case branch except the expression itself *)
-  Record StrongCaseBranchWithVVs {tc:TyCon}{Γ}{atypes:vec (HaskType Γ) tc} :=
-  { scbwv_sac       :  @StrongAltCon tc
+
+  Record StrongCaseBranchWithVVs {tc:TyCon}{Γ}{sac:@StrongAltCon tc}{atypes:IList _ (HaskType Γ) (tyConKind sac)} :=
+  { scbwv_sac       := sac
   ; scbwv_exprvars  :  vec VV (sac_numExprVars scbwv_sac)
   ; scbwv_varstypes := vec_zip scbwv_exprvars (sac_types scbwv_sac Γ atypes)
   ; scbwv_ξ         := fun ξ lev =>  update_ξ (weakLT'○ξ) (vec2list
@@ -28,25 +30,27 @@ Section HaskStrong.
   Implicit Arguments StrongCaseBranchWithVVs [[Γ]].
   Coercion scbwv_sac : StrongCaseBranchWithVVs >-> StrongAltCon.
 
-  Inductive Expr : forall Γ (Δ:CoercionEnv Γ), (VV -> LeveledHaskType Γ) -> LeveledHaskType Γ -> Type :=
+  Inductive Expr : forall Γ (Δ:CoercionEnv Γ), (VV -> LeveledHaskType Γ ★) -> LeveledHaskType Γ ★ -> Type :=
   | EVar   : ∀ Γ Δ ξ ev,                                                                             Expr Γ Δ ξ (ξ ev)
   | ELit   : ∀ Γ Δ ξ lit   l,                                                                        Expr Γ Δ ξ (literalType lit@@l)
   | EApp   : ∀ Γ Δ ξ t1 t2 l,        Expr Γ Δ ξ (t2--->t1 @@ l)   -> Expr Γ Δ ξ (t2 @@ l)         -> Expr Γ Δ ξ (t1 @@ l)
-  | ELam   : ∀ Γ Δ ξ t1 t2 l ev, Γ ⊢ᴛy t1:★ ->Expr Γ Δ (update_ξ ξ ((ev,t1@@l)::nil)) (t2@@l)     -> Expr Γ Δ ξ (t1--->t2@@l)
+  | ELam   : ∀ Γ Δ ξ t1 t2 l ev,              Expr Γ Δ (update_ξ ξ ((ev,t1@@l)::nil)) (t2@@l)     -> Expr Γ Δ ξ (t1--->t2@@l)
   | ELet   : ∀ Γ Δ ξ tv t  l ev,Expr Γ Δ ξ (tv@@l)->Expr Γ Δ (update_ξ ξ ((ev,tv@@l)::nil))(t@@l) -> Expr Γ Δ ξ (t@@l)
   | EEsc   : ∀ Γ Δ ξ ec t  l,     Expr Γ Δ ξ (<[ ec |- t ]> @@ l)                                 -> Expr Γ Δ ξ (t @@ (ec::l))
   | EBrak  : ∀ Γ Δ ξ ec t  l,     Expr Γ Δ ξ (t @@ (ec::l))                                       -> Expr Γ Δ ξ (<[ ec |- t ]> @@ l)
-  | ECast  : ∀ Γ Δ ξ γ t1 t2 l, Δ ⊢ᴄᴏ γ : t1 ∼ t2 ->  Expr Γ Δ ξ (t1 @@ l)                        -> Expr Γ Δ ξ (t2 @@ l)
+  | ECast  : forall Γ Δ ξ t1 t2 (γ:HaskCoercion Γ Δ (t1 ∼∼∼ t2)) l,
+    Expr Γ Δ ξ (t1 @@ l)                        -> Expr Γ Δ ξ (t2 @@ l)
   | ENote  : ∀ Γ Δ ξ t, Note                      -> Expr Γ Δ ξ t                                 -> Expr Γ Δ ξ t
-  | ETyApp : ∀ Γ Δ κ σ τ ξ l,     Γ ⊢ᴛy τ : κ -> Expr Γ Δ ξ (HaskTAll κ σ @@ l)                   -> Expr Γ Δ ξ (substT σ τ @@ l)
-  | ECoLam : ∀ Γ Δ κ σ σ₁ σ₂ ξ l,   Γ ⊢ᴛy σ₁:κ -> Γ ⊢ᴛy σ₂:κ -> Expr Γ (σ₁∼∼∼σ₂::Δ) ξ (σ @@ l)    -> Expr Γ Δ ξ (σ₁∼∼σ₂    ⇒ σ @@ l)
-  | ECoApp : ∀ Γ Δ   γ σ₁ σ₂ σ ξ l, Δ ⊢ᴄᴏ γ  : σ₁∼σ₂ -> Expr Γ Δ ξ (σ₁ ∼∼ σ₂ ⇒ σ @@ l)            -> Expr Γ Δ ξ (σ        @@l)
+  | ETyApp : ∀ Γ Δ κ σ τ ξ l,                    Expr Γ Δ ξ (HaskTAll κ σ @@ l)                   -> Expr Γ Δ ξ (substT σ τ @@ l)
+  | ECoLam : forall Γ Δ κ σ (σ₁ σ₂:HaskType Γ κ) ξ l,
+    Expr Γ (σ₁∼∼∼σ₂::Δ) ξ (σ @@ l)    -> Expr Γ Δ ξ (σ₁∼∼σ₂    ⇒ σ @@ l)
+  | ECoApp : forall Γ Δ κ (σ₁ σ₂:HaskType Γ κ) (γ:HaskCoercion Γ Δ (σ₁∼∼∼σ₂)) σ ξ l,
+    Expr Γ Δ ξ (σ₁ ∼∼ σ₂ ⇒ σ @@ l)            -> Expr Γ Δ ξ (σ        @@l)
   | ETyLam : ∀ Γ Δ ξ κ σ l,
     Expr (κ::Γ) (weakCE Δ) (weakLT○ξ) (HaskTApp (weakF σ) (FreshHaskTyVar _)@@(weakL l))-> Expr Γ Δ ξ (HaskTAll κ σ @@ l)
-
-  | ECase    : forall Γ Δ ξ l tc atypes tbranches,
+  | ECase    : forall Γ Δ ξ l tc tbranches sac atypes,
                Expr Γ Δ ξ (caseType tc atypes @@ l) ->
-               Tree ??{ scb : StrongCaseBranchWithVVs tc atypes
+               Tree ??{ scb : StrongCaseBranchWithVVs tc sac atypes
                             & Expr (sac_Γ scb Γ)
                                    (sac_Δ scb Γ atypes (weakCK'' Δ))
                                    (scbwv_ξ scb ξ l)
@@ -59,7 +63,7 @@ Section HaskStrong.
     Expr            Γ Δ ξ  (τ@@l)
 
   (* can't avoid having an additional inductive: it is a tree of Expr's, each of whose ξ depends on the type of the entire tree *)
-  with ELetRecBindings : forall Γ (Δ:CoercionEnv Γ), (VV -> LeveledHaskType Γ) -> HaskLevel Γ -> Tree ??(VV*HaskType Γ) -> Type :=
+  with ELetRecBindings : ∀ Γ, CoercionEnv Γ -> (VV -> LeveledHaskType Γ ★) -> HaskLevel Γ -> Tree ??(VV*HaskType Γ ★) -> Type :=
   | ELR_nil    : ∀ Γ Δ ξ l  ,                                                                 ELetRecBindings Γ Δ ξ l []
   | ELR_leaf   : ∀ Γ Δ ξ t l v,                                        Expr Γ Δ ξ (t @@ l) -> ELetRecBindings Γ Δ ξ l [(v,t)]
   | ELR_branch : ∀ Γ Δ ξ l t1 t2, ELetRecBindings Γ Δ ξ l t1 -> ELetRecBindings Γ Δ ξ l t2 -> ELetRecBindings Γ Δ ξ l (t1,,t2)