Require Import Coq.Lists.List.
Require Import General.
Require Import HaskKinds.
-Require Import HaskLiteralsAndTyCons.
+Require Import HaskLiterals.
+Require Import HaskTyCons.
Require Import HaskCoreTypes.
Require Import HaskCoreVars.
Require Import HaskWeakTypes.
Notation "t @@@ l" := (mapOptionTree (fun t' => t' @@ l) t) (at level 20).
Notation "'<[' a '|-' t ']>'" := (@HaskBrak _ a t).
+Definition getlev {Γ}(lt:LeveledHaskType Γ ★) := match lt with _ @@ l => l end.
+
Definition unlev {Γ}{κ}(lht:LeveledHaskType Γ κ) :=
match lht with t@@l => t end.
Coercion glob_tf : Global >-> Funclass.
Coercion glob_wv : Global >-> WeakExprVar.
+(* From (t1->(t2->(t3-> ... t))), return t1::t2::t3::...nil *)
+(* this is a billion times uglier than it needs to be as a result of how primitive Coq's termiation checker is *)
+Fixpoint take_arg_types {TV}{κ}(exp: RawHaskType TV κ) {struct exp} : list (RawHaskType TV κ) :=
+ match exp as E in RawHaskType _ K return list (RawHaskType _ K) with
+ | TApp κ₁ κ₂ x y =>
+ (match κ₁ as K1 return RawHaskType TV (κ₂ ⇛ K1) -> list (RawHaskType TV κ₂) -> list (RawHaskType _ K1) with
+ | KindStar =>
+ match κ₂ as K2 return RawHaskType TV (K2 ⇛ KindStar) -> list (RawHaskType TV K2) -> list (RawHaskType _ KindStar) with
+ | KindStar => fun x' =>
+ match x' return list (RawHaskType TV KindStar) -> list (RawHaskType _ KindStar) with
+ | TApp κ₁'' κ₂'' w'' x'' =>
+ match κ₂'' as K2'' return RawHaskType TV K2'' -> list (RawHaskType TV KindStar) ->
+ list (RawHaskType _ KindStar) with
+ | KindStar =>
+ match w'' with
+ | TArrow => fun a b => a::b
+ | _ => fun _ _ => nil
+ end
+ | _ => fun _ _ => nil
+ end x''
+ | _ => fun _ => nil
+ end
+ | _ => fun _ _ => nil
+ end
+ | _ => fun _ _ => nil
+ end) x (take_arg_types y)
+ | _ => nil
+ end.
+
+Fixpoint count_arg_types {TV}{κ}(exp: RawHaskType TV κ) {struct exp} : nat :=
+ match exp as E in RawHaskType _ K return nat with
+ | TApp κ₁ κ₂ x y =>
+ (match κ₁ as K1 return RawHaskType TV (κ₂ ⇛ K1) -> nat -> nat with
+ | KindStar =>
+ match κ₂ as K2 return RawHaskType TV (K2 ⇛ KindStar) -> nat -> nat with
+ | KindStar => fun x' =>
+ match x' return nat -> nat with
+ | TApp κ₁'' κ₂'' w'' x'' =>
+ match κ₂'' as K2'' return RawHaskType TV K2'' -> nat -> nat with
+ | KindStar =>
+ match w'' with
+ | TArrow => fun a b => S b
+ | _ => fun _ _ => 0
+ end
+ | _ => fun _ _ => 0
+ end x''
+ | _ => fun _ => 0
+ end
+ | _ => fun _ _ => 0
+ end
+ | _ => fun _ _ => 0
+ end) x (count_arg_types y)
+ | _ => 0
+ end.
+
+ Definition ite_unit : ∀ Γ, InstantiatedTypeEnv (fun _ => unit) Γ.
+ intros.
+ induction Γ.
+ apply INil.
+ apply ICons; auto.
+ apply tt.
+ Defined.
+
+Definition take_arg_type {Γ}{κ}(ht:HaskType Γ κ) : (gt (count_arg_types (ht _ (ite_unit _))) 0) -> HaskType Γ κ :=
+ fun pf =>
+ fun TV ite =>
+ match take_arg_types (ht TV ite) with
+ | nil => Prelude_error "impossible"
+ | x::y => x
+ end.
+
+(* From (t1->(t2->(t3-> ... t))), return t *)
+(* this is a billion times uglier than it needs to be as a result of how primitive Coq's termiation checker is *)
+Fixpoint drop_arg_types {TV}{κ}(exp: RawHaskType TV κ) : RawHaskType TV κ :=
+ match exp as E in RawHaskType _ K return RawHaskType _ K with
+ | TApp κ₁ κ₂ x y =>
+ let q :=
+ (match κ₁ as K1 return RawHaskType TV (κ₂ ⇛ K1) -> (RawHaskType TV κ₂) -> ??(RawHaskType _ K1) with
+ | KindStar =>
+ match κ₂ as K2 return RawHaskType TV (K2 ⇛ KindStar) -> (RawHaskType TV K2) -> ??(RawHaskType _ KindStar) with
+ | KindStar => fun x' =>
+ match x' return (RawHaskType TV KindStar) -> ??(RawHaskType _ KindStar) with
+ | TApp κ₁'' κ₂'' w'' x'' =>
+ match κ₂'' as K2'' return RawHaskType TV K2'' -> (RawHaskType TV KindStar) -> ??(RawHaskType _ KindStar) with
+ | KindStar =>
+ match w'' with
+ | TArrow => fun _ b => Some b
+ | _ => fun _ b => None
+ end
+ | _ => fun _ b => None
+ end x''
+ | _ => fun _ => None
+ end
+ | _ => fun _ _ => None
+ end
+ | _ => fun _ _ => None
+ end) x (drop_arg_types y)
+ in match q with
+ | None => TApp x y
+ | Some y => y
+ end
+ | b => b
+ end.
; sac_numExprVars : nat
; sac_ekinds : vec Kind sac_numExTyVars
; sac_kinds := app (tyConKind tc) (vec2list sac_ekinds)
-; sac_Γ := fun Γ => app (vec2list sac_ekinds) Γ
-; sac_coercions : forall Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)), vec (HaskCoercionKind (sac_Γ Γ)) sac_numCoerVars
-; sac_types : forall Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)), vec (HaskType (sac_Γ Γ) ★) sac_numExprVars
-; sac_Δ := fun Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)) Δ => app (vec2list (sac_coercions Γ atypes)) Δ
+; sac_gamma := fun Γ => app (vec2list sac_ekinds) Γ
+; sac_coercions : forall Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)), vec (HaskCoercionKind (sac_gamma Γ)) sac_numCoerVars
+; sac_types : forall Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)), vec (HaskType (sac_gamma Γ) ★) sac_numExprVars
+; sac_delta := fun Γ (atypes:IList _ (HaskType Γ) (tyConKind tc)) Δ => app (vec2list (sac_coercions Γ atypes)) Δ
}.
Coercion sac_tc : StrongAltCon >-> TyCon.
Coercion sac_altcon : StrongAltCon >-> WeakAltCon.
Notation "a ∼∼∼ b" := (@mkHaskCoercionKind _ _ a b) (at level 18).
-Fixpoint update_ξ
+Fixpoint update_xi
`{EQD_VV:EqDecidable VV}{Γ}
(ξ:VV -> LeveledHaskType Γ ★)
(lev:HaskLevel Γ)
: VV -> LeveledHaskType Γ ★ :=
match vt with
| nil => ξ
- | (v,τ)::tl => fun v' => if eqd_dec v v' then τ @@ lev else (update_ξ ξ lev tl) v'
+ | (v,τ)::tl => fun v' => if eqd_dec v v' then τ @@ lev else (update_xi ξ lev tl) v'
end.
-Lemma update_ξ_lemma0 `{EQD_VV:EqDecidable VV} : forall Γ ξ (lev:HaskLevel Γ)(varstypes:list (VV*_)) v,
+Lemma update_xi_lemma0 `{EQD_VV:EqDecidable VV} : forall Γ ξ (lev:HaskLevel Γ)(varstypes:list (VV*_)) v,
not (In v (map (@fst _ _) varstypes)) ->
- (update_ξ ξ lev varstypes) v = ξ v.
+ (update_xi ξ lev varstypes) v = ξ v.
intros.
induction varstypes.
reflexivity.