(* HIGHER ORDER REDUCIBILITY CANDIDATES ***************************************)
(* An arity is a type of λ→ to be used as carrier for a h.o. r.c. *)
-inductive ARITY: Type[0] ≝
- | SORT: ARITY
- | IMPL: ARITY → ARITY → ARITY
-.
(* The type of the higher order r.c.'s having a given carrier.
* a h.o. r.c is implemented as an inductively defined metalinguistic function
*)
let rec HRC P ≝ match P with
[ SORT ⇒ RC
- | IMPL Q P ⇒ HRC Q → HRC P
+ | ABST Q P ⇒ HRC Q → HRC P
].
(* The default h.o r.c.
*)
let rec defHRC P ≝ match P return λP. HRC P with
[ SORT ⇒ snRC
- | IMPL Q P ⇒ λ_. defHRC P
+ | ABST Q P ⇒ λ_. defHRC P
].
(* extensional equality *******************************************************)
*)
let rec hrceq P ≝ match P return λP. HRC P → HRC P → Prop with
[ SORT ⇒ λC1,C2. C1 ≅ C2
- | IMPL Q P ⇒ λC1,C2. ∀B1,B2. hrceq Q B1 B2 → hrceq P (C1 B1) (C2 B2)
+ | ABST Q P ⇒ λC1,C2. ∀B1,B2. hrceq Q B1 B2 → hrceq P (C1 B1) (C2 B2)
].
interpretation