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Revise reduction rules

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Yiyun Liu 2024-12-16 18:00:08 -05:00
parent ace1325da8
commit d723ee4675
1 changed files with 46 additions and 3 deletions
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49
theories/fp_red.v
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@ -32,16 +32,23 @@ Module Par.
(****************** Eta ***********************) (****************** Eta ***********************)
| AppEta a0 a1 : | AppEta a0 a1 :
R a0 a1 -> R a0 a1 ->
R a0 (Abs (ren_Tm shift a1)) R a0 (Abs (App (ren_Tm shift a1) (VarTm var_zero)))
| PairEta a0 a1 : | PairEta a0 a1 :
R a0 a1 -> R a0 a1 ->
R a0 (Pair a1 a1) R a0 (Pair a1 a1)
(*************** Congruence ********************) (*************** Congruence ********************)
| AbsCong a0 a1 :
R a0 a1 ->
R (Abs a0) (Abs a1)
| AppCong a0 a1 b0 b1 : | AppCong a0 a1 b0 b1 :
R a0 a1 -> R a0 a1 ->
R b0 b1 -> R b0 b1 ->
R (App a0 b0) (App a1 b1) R (App a0 b0) (App a1 b1)
| PairCong a0 a1 b0 b1 :
R a0 a1 ->
R b0 b1 ->
R (Pair a0 b0) (Pair a1 b1)
| Proj1Cong a0 a1 : | Proj1Cong a0 a1 :
R a0 a1 -> R a0 a1 ->
R (Proj1 a0) (Proj1 a1) R (Proj1 a0) (Proj1 a1)
@ -78,10 +85,17 @@ Module RPar.
R (Proj2 (Pair a0 b)) a1 R (Proj2 (Pair a0 b)) a1
(*************** Congruence ********************) (*************** Congruence ********************)
| AbsCong a0 a1 :
R a0 a1 ->
R (Abs a0) (Abs a1)
| AppCong a0 a1 b0 b1 : | AppCong a0 a1 b0 b1 :
R a0 a1 -> R a0 a1 ->
R b0 b1 -> R b0 b1 ->
R (App a0 b0) (App a1 b1) R (App a0 b0) (App a1 b1)
| PairCong a0 a1 b0 b1 :
R a0 a1 ->
R b0 b1 ->
R (Pair a0 b0) (Pair a1 b1)
| Proj1Cong a0 a1 : | Proj1Cong a0 a1 :
R a0 a1 -> R a0 a1 ->
R (Proj1 a0) (Proj1 a1) R (Proj1 a0) (Proj1 a1)
@ -95,16 +109,23 @@ Module EPar.
(****************** Eta ***********************) (****************** Eta ***********************)
| AppEta a0 a1 : | AppEta a0 a1 :
R a0 a1 -> R a0 a1 ->
R a0 (Abs (ren_Tm shift a1)) R a0 (Abs (App (ren_Tm shift a1) (VarTm var_zero)))
| PairEta a0 a1 : | PairEta a0 a1 :
R a0 a1 -> R a0 a1 ->
R a0 (Pair a1 a1) R a0 (Pair a1 a1)
(*************** Congruence ********************) (*************** Congruence ********************)
| AbsCong a0 a1 :
R a0 a1 ->
R (Abs a0) (Abs a1)
| AppCong a0 a1 b0 b1 : | AppCong a0 a1 b0 b1 :
R a0 a1 -> R a0 a1 ->
R b0 b1 -> R b0 b1 ->
R (App a0 b0) (App a1 b1) R (App a0 b0) (App a1 b1)
| PairCong a0 a1 b0 b1 :
R a0 a1 ->
R b0 b1 ->
R (Pair a0 b0) (Pair a1 b1)
| Proj1Cong a0 a1 : | Proj1Cong a0 a1 :
R a0 a1 -> R a0 a1 ->
R (Proj1 a0) (Proj1 a1) R (Proj1 a0) (Proj1 a1)
@ -116,4 +137,26 @@ End EPar.
Lemma EPar_Par n (a b : Tm n) : EPar.R a b -> Par.R a b. Lemma EPar_Par n (a b : Tm n) : EPar.R a b -> Par.R a b.
Proof. induction 1; hauto lq:on ctrs:Par.R. Qed. Proof. induction 1; hauto lq:on ctrs:Par.R. Qed.
Lemma EPar_ Lemma RPar_Par n (a b : Tm n) : RPar.R a b -> Par.R a b.
Proof. induction 1; hauto lq:on ctrs:Par.R. Qed.
Lemma merge n (t a u : Tm n) :
EPar.R t a ->
RPar.R a u ->
Par.R t u.
Proof.
move => h. move : u.
elim:t a/h.
- move => n0 a0 a1 ha iha u hu.
apply iha.
inversion hu; subst.
- hauto lq:on inv:RPar.R.
- move => a0 a1 b0 b1 ha iha hb ihb u.
inversion 1; subst.
+ inversion ha.
best use:EPar_Par, RPar_Par.
best ctrs:Par.R inv:EPar.R,RPar.R use:EPar_Par, RPar_Par.