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Add definition for algorithmic domain

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Yiyun Liu 2025-02-19 17:40:56 -05:00
parent df0b955e4e
commit fe5c16361a
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theories/executable.v
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@ -5,6 +5,90 @@ Require Import algorithmic.
From stdpp Require Import relations (rtc(..), nsteps(..)).
Require Import ssreflect ssrbool.
Inductive algo_dom {n} : PTm n -> PTm n -> Prop :=
| A_AbsAbs a b :
algo_dom a b ->
(* --------------------- *)
algo_dom (PAbs a) (PAbs b)
| A_AbsNeu a u :
ishne u ->
algo_dom a (PApp (ren_PTm shift u) (VarPTm var_zero)) ->
(* --------------------- *)
algo_dom (PAbs a) u
| A_NeuAbs a u :
ishne u ->
algo_dom (PApp (ren_PTm shift u) (VarPTm var_zero)) a ->
(* --------------------- *)
algo_dom u (PAbs a)
| A_PairPair a0 a1 b0 b1 :
algo_dom a0 a1 ->
algo_dom b0 b1 ->
(* ---------------------------- *)
algo_dom (PPair a0 b0) (PPair a1 b1)
| A_PairNeu a0 a1 u :
ishne u ->
algo_dom a0 (PProj PL u) ->
algo_dom a1 (PProj PR u) ->
(* ----------------------- *)
algo_dom (PPair a0 a1) u
| A_NeuPair a0 a1 u :
ishne u ->
algo_dom (PProj PL u) a0 ->
algo_dom (PProj PR u) a1 ->
(* ----------------------- *)
algo_dom u (PPair a0 a1)
| A_UnivCong i j :
(* -------------------------- *)
algo_dom (PUniv i) (PUniv j)
| A_BindCong p0 p1 A0 A1 B0 B1 :
algo_dom A0 A1 ->
algo_dom B0 B1 ->
(* ---------------------------- *)
algo_dom (PBind p0 A0 B0) (PBind p1 A1 B1)
| A_VarCong i j :
(* -------------------------- *)
algo_dom (VarPTm i) (VarPTm j)
| A_ProjCong p0 p1 u0 u1 :
ishne u0 ->
ishne u1 ->
algo_dom u0 u1 ->
(* --------------------- *)
algo_dom (PProj p0 u0) (PProj p1 u1)
| A_AppCong u0 u1 a0 a1 :
ishne u0 ->
ishne u1 ->
algo_dom u0 u1 ->
algo_dom a0 a1 ->
(* ------------------------- *)
algo_dom (PApp u0 a0) (PApp u1 a1)
| A_HRedL a a' b :
HRed.R a a' ->
algo_dom a' b ->
(* ----------------------- *)
algo_dom a b
| A_HRedR a b b' :
ishne a \/ ishf a ->
HRed.R b b' ->
algo_dom a b' ->
(* ----------------------- *)
algo_dom a b.
Search (Bool.reflect (is_true _) _).
Check idP.
Definition metric {n} k (a b : PTm n) :=
exists i j va vb, nsteps LoRed.R i a va /\ nsteps LoRed.R j b vb /\
nf va /\ nf vb /\ size_PTm va + size_PTm vb + i + j <= k.