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 HaskLiteralsAndTyCons.
13 Require Import HaskStrongTypes.
14 Require Import HaskWeakVars.
18 (* any type with decidable equality may be used to represent value variables *)
19 Context `{EQD_VV:EqDecidable VV}.
21 (* a StrongCaseBranchWithVVs contains all the data found in a case branch except the expression itself *)
23 Record StrongCaseBranchWithVVs {tc:TyCon}{Γ}{atypes:IList _ (HaskType Γ) (tyConKind tc)}{sac:@StrongAltCon tc} :=
24 { scbwv_exprvars : vec VV (sac_numExprVars sac)
25 ; scbwv_exprvars_distinct : distinct (vec2list scbwv_exprvars)
26 ; scbwv_varstypes := vec_zip scbwv_exprvars (sac_types sac Γ atypes)
27 ; scbwv_ξ := fun ξ lev => update_ξ (weakLT'○ξ) (weakL' lev) (vec2list scbwv_varstypes)
29 Implicit Arguments StrongCaseBranchWithVVs [[Γ]].
30 (*Coercion scbwv_sac : StrongCaseBranchWithVVs >-> StrongAltCon.*)
32 Inductive Expr : forall Γ (Δ:CoercionEnv Γ), (VV -> LeveledHaskType Γ ★) -> LeveledHaskType Γ ★ -> Type :=
34 (* an "EGlobal" is any variable which is free in the expression which was passed to -fcoqpass (ie bound outside it) *)
35 | EGlobal: ∀ Γ Δ ξ t, WeakExprVar -> Expr Γ Δ ξ t
37 | EVar : ∀ Γ Δ ξ ev, Expr Γ Δ ξ (ξ ev)
38 | ELit : ∀ Γ Δ ξ lit l, Expr Γ Δ ξ (literalType lit@@l)
39 | 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)
40 | ELam : ∀ Γ Δ ξ t1 t2 l ev, Expr Γ Δ (update_ξ ξ l ((ev,t1)::nil)) (t2@@l) -> Expr Γ Δ ξ (t1--->t2@@l)
41 | ELet : ∀ Γ Δ ξ tv t l ev,Expr Γ Δ ξ (tv@@l)->Expr Γ Δ (update_ξ ξ l ((ev,tv)::nil))(t@@l) -> Expr Γ Δ ξ (t@@l)
42 | EEsc : ∀ Γ Δ ξ ec t l, Expr Γ Δ ξ (<[ ec |- t ]> @@ l) -> Expr Γ Δ ξ (t @@ (ec::l))
43 | EBrak : ∀ Γ Δ ξ ec t l, Expr Γ Δ ξ (t @@ (ec::l)) -> Expr Γ Δ ξ (<[ ec |- t ]> @@ l)
44 | ECast : forall Γ Δ ξ t1 t2 (γ:HaskCoercion Γ Δ (t1 ∼∼∼ t2)) l,
45 Expr Γ Δ ξ (t1 @@ l) -> Expr Γ Δ ξ (t2 @@ l)
46 | ENote : ∀ Γ Δ ξ t, Note -> Expr Γ Δ ξ t -> Expr Γ Δ ξ t
47 | ETyApp : ∀ Γ Δ κ σ τ ξ l, Expr Γ Δ ξ (HaskTAll κ σ @@ l) -> Expr Γ Δ ξ (substT σ τ @@ l)
48 | ECoLam : forall Γ Δ κ σ (σ₁ σ₂:HaskType Γ κ) ξ l,
49 Expr Γ (σ₁∼∼∼σ₂::Δ) ξ (σ @@ l) -> Expr Γ Δ ξ (σ₁∼∼σ₂ ⇒ σ @@ l)
50 | ECoApp : forall Γ Δ κ (σ₁ σ₂:HaskType Γ κ) (γ:HaskCoercion Γ Δ (σ₁∼∼∼σ₂)) σ ξ l,
51 Expr Γ Δ ξ (σ₁ ∼∼ σ₂ ⇒ σ @@ l) -> Expr Γ Δ ξ (σ @@l)
52 | ETyLam : ∀ Γ Δ ξ κ σ l,
53 Expr (κ::Γ) (weakCE Δ) (weakLT○ξ) (HaskTApp (weakF σ) (FreshHaskTyVar _)@@(weakL l))-> Expr Γ Δ ξ (HaskTAll κ σ @@ l)
54 | ECase : forall Γ Δ ξ l tc tbranches atypes,
55 Expr Γ Δ ξ (caseType tc atypes @@ l) ->
57 & { scb : StrongCaseBranchWithVVs tc atypes sac
59 (sac_Δ sac Γ atypes (weakCK'' Δ))
61 (weakLT' (tbranches@@l)) } } ->
62 Expr Γ Δ ξ (tbranches @@ l)
64 | ELetRec : ∀ Γ Δ ξ l τ vars,
65 let ξ' := update_ξ ξ l (leaves vars) in
66 ELetRecBindings Γ Δ ξ' l vars ->
70 (* 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 *)
71 with ELetRecBindings : ∀ Γ, CoercionEnv Γ -> (VV -> LeveledHaskType Γ ★) -> HaskLevel Γ -> Tree ??(VV*HaskType Γ ★) -> Type :=
72 | ELR_nil : ∀ Γ Δ ξ l , ELetRecBindings Γ Δ ξ l []
73 | ELR_leaf : ∀ Γ Δ ξ l v t, Expr Γ Δ ξ (t @@ l) -> ELetRecBindings Γ Δ ξ l [(v,t)]
74 | 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)
78 Context {ToStringVV:ToString VV}.
80 Require Import HaskCoreVars.
82 Fixpoint exprToString {Γ}{Δ}{ξ}{τ}(exp:Expr Γ Δ ξ τ) : string :=
84 | EVar Γ' _ ξ' ev => "var."+++ev
85 | EGlobal Γ' _ ξ' t wev => "global." +++(wev:CoreVar)
86 | ELam Γ' _ _ tv _ _ cv e => "\("+++cv+++":t) -> "+++ exprToString e
87 | ELet Γ' _ _ t _ _ ev e1 e2 => "let "+++ev+++" = "+++exprToString e1+++" in "+++exprToString e2
88 | ELit _ _ _ lit _ => "lit."+++lit
89 | EApp Γ' _ _ _ _ _ e1 e2 => "("+++exprToString e1+++")("+++exprToString e2+++")"
90 | EEsc Γ' _ _ ec t _ e => "~~("+++exprToString e+++")"
91 | EBrak Γ' _ _ ec t _ e => "<["+++exprToString e+++"]>"
92 | ENote _ _ _ _ n e => "note."+++exprToString e
93 | ETyApp Γ Δ κ σ τ ξ l e => "("+++exprToString e+++")@("+++τ+++")"
94 | ECoApp Γ Δ κ σ₁ σ₂ γ σ ξ l e => "("+++exprToString e+++")~(co)"
95 | ECast Γ Δ ξ t1 t2 γ l e => "cast ("+++exprToString e+++"):t2"
96 | ETyLam _ _ _ k _ _ e => "\@_ ->"+++ exprToString e
97 | ECoLam Γ Δ κ σ σ₁ σ₂ ξ l e => "\~_ ->"+++ exprToString e
98 | ECase Γ Δ ξ l tc tbranches atypes escrut alts => "case " +++ exprToString escrut +++ " of FIXME"
99 | ELetRec _ _ _ _ _ vars elrb e => "letrec FIXME in " +++ exprToString e
101 Instance ExprToString Γ Δ ξ τ : ToString (Expr Γ Δ ξ τ) := { toString := exprToString }.
104 Implicit Arguments StrongCaseBranchWithVVs [[Γ]].