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Add new definition of eq_view

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Yiyun Liu 2025-03-04 22:20:12 -05:00
parent dcd4465310
commit 5087b8c6ce
1 changed files with 24 additions and 9 deletions
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33
theories/executable.v
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@ -30,20 +30,20 @@ Inductive eq_view : PTm -> PTm -> Type :=
| V_AbsAbs a b : | V_AbsAbs a b :
eq_view (PAbs a) (PAbs b) eq_view (PAbs a) (PAbs b)
| V_AbsNeu a b : | V_AbsNeu a b :
~~ isabs b -> ~~ ishf b ->
eq_view (PAbs a) b eq_view (PAbs a) b
| V_NeuAbs a b : | V_NeuAbs a b :
~~ isabs a -> ~~ ishf a ->
eq_view a (PAbs b) eq_view a (PAbs b)
| V_VarVar i j : | V_VarVar i j :
eq_view (VarPTm i) (VarPTm j) eq_view (VarPTm i) (VarPTm j)
| V_PairPair a0 b0 a1 b1 : | V_PairPair a0 b0 a1 b1 :
eq_view (PPair a0 b0) (PPair a1 b1) eq_view (PPair a0 b0) (PPair a1 b1)
| V_PairNeu a0 b0 u : | V_PairNeu a0 b0 u :
~~ ispair u -> ~~ ishf u ->
eq_view (PPair a0 b0) u eq_view (PPair a0 b0) u
| V_NeuPair u a1 b1 : | V_NeuPair u a1 b1 :
~~ ispair u -> ~~ ishf u ->
eq_view u (PPair a1 b1) eq_view u (PPair a1 b1)
| V_ZeroZero : | V_ZeroZero :
eq_view PZero PZero eq_view PZero PZero
@ -62,16 +62,31 @@ Inductive eq_view : PTm -> PTm -> Type :=
| V_UnivUniv i j : | V_UnivUniv i j :
eq_view (PUniv i) (PUniv j) eq_view (PUniv i) (PUniv j)
| V_Others a b : | V_Others a b :
tm_conf a b ->
eq_view a b. eq_view a b.
Equations tm_to_eq_view (a b : PTm) : eq_view a b := Equations tm_to_eq_view (a b : PTm) : eq_view a b :=
tm_to_eq_view (PAbs a) (PAbs b) := V_AbsAbs a b; tm_to_eq_view (PAbs a) (PAbs b) := V_AbsAbs a b;
tm_to_eq_view (PAbs a) b := V_AbsNeu a b _; tm_to_eq_view (PAbs a) (PApp b0 b1) := V_AbsNeu a (PApp b0 b1) _;
tm_to_eq_view a (PAbs b) := V_NeuAbs a b _; tm_to_eq_view (PAbs a) (VarPTm i) := V_AbsNeu a (VarPTm i) _;
tm_to_eq_view (PAbs a) (PProj p b) := V_AbsNeu a (PProj p b) _;
tm_to_eq_view (PAbs a) (PInd P u b c) := V_AbsNeu a (PInd P u b c) _;
tm_to_eq_view (VarPTm i) (PAbs a) := V_NeuAbs (VarPTm i) a _;
tm_to_eq_view (PApp b0 b1) (PAbs b) := V_NeuAbs (PApp b0 b1) b _;
tm_to_eq_view (PProj p b) (PAbs a) := V_NeuAbs (PProj p b) a _;
tm_to_eq_view (PInd P u b c) (PAbs a) := V_NeuAbs (PInd P u b c) a _;
tm_to_eq_view (VarPTm i) (VarPTm j) := V_VarVar i j; tm_to_eq_view (VarPTm i) (VarPTm j) := V_VarVar i j;
tm_to_eq_view (PPair a0 b0) (PPair a1 b1) := V_PairPair a0 b0 a1 b1; tm_to_eq_view (PPair a0 b0) (PPair a1 b1) := V_PairPair a0 b0 a1 b1;
tm_to_eq_view (PPair a0 b0) u := V_PairNeu a0 b0 u _; (* tm_to_eq_view (PPair a0 b0) u := V_PairNeu a0 b0 u _; *)
tm_to_eq_view u (PPair a1 b1) := V_NeuPair u a1 b1 _; tm_to_eq_view (PPair a0 b0) (VarPTm i) := V_PairNeu a0 b0 (VarPTm i) _;
tm_to_eq_view (PPair a0 b0) (PApp c0 c1) := V_PairNeu a0 b0 (PApp c0 c1) _;
tm_to_eq_view (PPair a0 b0) (PProj p c) := V_PairNeu a0 b0 (PProj p c) _;
tm_to_eq_view (PPair a0 b0) (PInd P t0 t1 t2) := V_PairNeu a0 b0 (PInd P t0 t1 t2) _;
(* tm_to_eq_view u (PPair a1 b1) := V_NeuPair u a1 b1 _; *)
tm_to_eq_view (VarPTm i) (PPair a1 b1) := V_NeuPair (VarPTm i) a1 b1 _;
tm_to_eq_view (PApp t0 t1) (PPair a1 b1) := V_NeuPair (PApp t0 t1) a1 b1 _;
tm_to_eq_view (PProj t0 t1) (PPair a1 b1) := V_NeuPair (PProj t0 t1) a1 b1 _;
tm_to_eq_view (PInd t0 t1 t2 t3) (PPair a1 b1) := V_NeuPair (PInd t0 t1 t2 t3) a1 b1 _;
tm_to_eq_view PZero PZero := V_ZeroZero; tm_to_eq_view PZero PZero := V_ZeroZero;
tm_to_eq_view (PSuc a) (PSuc b) := V_SucSuc a b; tm_to_eq_view (PSuc a) (PSuc b) := V_SucSuc a b;
tm_to_eq_view (PApp a0 b0) (PApp a1 b1) := V_AppApp a0 b0 a1 b1; tm_to_eq_view (PApp a0 b0) (PApp a1 b1) := V_AppApp a0 b0 a1 b1;
@ -80,7 +95,7 @@ Equations tm_to_eq_view (a b : PTm) : eq_view a b :=
tm_to_eq_view PNat PNat := V_NatNat; tm_to_eq_view PNat PNat := V_NatNat;
tm_to_eq_view (PUniv i) (PUniv j) := V_UnivUniv i j; tm_to_eq_view (PUniv i) (PUniv j) := V_UnivUniv i j;
tm_to_eq_view (PBind p0 A0 B0) (PBind p1 A1 B1) := V_BindBind p0 A0 B0 p1 A1 B1; tm_to_eq_view (PBind p0 A0 B0) (PBind p1 A1 B1) := V_BindBind p0 A0 B0 p1 A1 B1;
tm_to_eq_view a b := V_Others a b. tm_to_eq_view a b := V_Others a b _.
Inductive algo_dom : PTm -> PTm -> Prop := Inductive algo_dom : PTm -> PTm -> Prop :=
| A_AbsAbs a b : | A_AbsAbs a b :