1 (*********************************************************************************************************************************)
2 (* HaskStrong: a dependently-typed version of CoreSyn *)
3 (*********************************************************************************************************************************)
5 Generalizable All Variables.
6 Require Import Preamble.
7 Require Import General.
8 Require Import Coq.Strings.String.
9 Require Import Coq.Lists.List.
10 Require Import HaskKinds.
11 Require Import HaskCoreTypes.
12 Require Import HaskCoreLiterals.
13 Require Import HaskStrongTypes.
17 (* any type with decidable equality may be used to represent value variables *)
18 Context `{EQD_VV:EqDecidable VV}.
20 (* a StrongCaseBranchWithVVs contains all the data found in a case branch except the expression itself *)
21 Record StrongCaseBranchWithVVs {tc:TyCon}{Γ}{atypes:vec (HaskType Γ) tc} :=
22 { scbwv_sac : @StrongAltCon tc
23 ; scbwv_exprvars : vec VV (sac_numExprVars scbwv_sac)
24 ; scbwv_varstypes := vec_zip scbwv_exprvars (sac_types scbwv_sac Γ atypes)
25 ; scbwv_ξ := fun ξ lev => update_ξ (weakLT'○ξ) (vec2list
26 (vec_map (fun x => ((fst x),(snd x @@ weakL' lev))) scbwv_varstypes))
28 Implicit Arguments StrongCaseBranchWithVVs [[Γ]].
29 Coercion scbwv_sac : StrongCaseBranchWithVVs >-> StrongAltCon.
31 Inductive Expr : forall Γ (Δ:CoercionEnv Γ), (VV -> LeveledHaskType Γ) -> LeveledHaskType Γ -> Type :=
32 | EVar : ∀ Γ Δ ξ ev, Expr Γ Δ ξ (ξ ev)
33 | ELit : ∀ Γ Δ ξ lit l, Expr Γ Δ ξ (literalType lit@@l)
34 | 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)
35 | 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)
36 | 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)
37 | EEsc : ∀ Γ Δ ξ ec t l, Expr Γ Δ ξ (<[ ec |- t ]> @@ l) -> Expr Γ Δ ξ (t @@ (ec::l))
38 | EBrak : ∀ Γ Δ ξ ec t l, Expr Γ Δ ξ (t @@ (ec::l)) -> Expr Γ Δ ξ (<[ ec |- t ]> @@ l)
39 | 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)
40 | ENote : ∀ Γ Δ ξ t, Note -> Expr Γ Δ ξ t -> Expr Γ Δ ξ t
41 | 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)
42 | 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)
43 | 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)
44 | ETyLam : ∀ Γ Δ ξ κ σ l,
45 Expr (κ::Γ) (weakCE Δ) (weakLT○ξ) (HaskTApp (weakF σ) (FreshHaskTyVar _)@@(weakL l))-> Expr Γ Δ ξ (HaskTAll κ σ @@ l)
47 | ECase : forall Γ Δ ξ l tc atypes tbranches,
48 Expr Γ Δ ξ (caseType tc atypes @@ l) ->
49 Tree ??{ scb : StrongCaseBranchWithVVs tc atypes
51 (sac_Δ scb Γ atypes (weakCK'' Δ))
53 (weakLT' (tbranches@@l)) } ->
54 Expr Γ Δ ξ (tbranches @@ l)
56 | ELetRec : ∀ Γ Δ ξ l τ vars, let ξ' := update_ξ ξ (map (fun x => ((fst x),(snd x @@ l))) (leaves vars)) in
57 ELetRecBindings Γ Δ ξ' l vars ->
61 (* 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 *)
62 with ELetRecBindings : forall Γ (Δ:CoercionEnv Γ), (VV -> LeveledHaskType Γ) -> HaskLevel Γ -> Tree ??(VV*HaskType Γ) -> Type :=
63 | ELR_nil : ∀ Γ Δ ξ l , ELetRecBindings Γ Δ ξ l []
64 | ELR_leaf : ∀ Γ Δ ξ t l v, Expr Γ Δ ξ (t @@ l) -> ELetRecBindings Γ Δ ξ l [(v,t)]
65 | 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)
69 Implicit Arguments StrongCaseBranchWithVVs [[Γ]].