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rename local makefile; change notation ~ to \neg
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theories/AlgorithmicJudgments.v

Lines changed: 17 additions & 17 deletions
Original file line numberDiff line numberDiff line change
@@ -41,7 +41,7 @@ Section Definitions.
4141
| typeNeuConvAlg {Γ M N T} :
4242
whne M ->
4343
whne N ->
44-
[ Γ |- M ~ N ▹ T] ->
44+
[ Γ |- M ~ N ▹ T] ->
4545
[ Γ |- M ≅h N]
4646
(** **** Conversion of neutral terms *)
4747
with ConvNeuAlg : context -> term -> term -> term -> Type :=
@@ -110,7 +110,7 @@ Section Definitions.
110110
| termFunConvAlg {Γ : context} {f g A B} :
111111
whnf f ->
112112
whnf g ->
113-
[ Γ,, A |- eta_expand f ≅ eta_expand g : B] ->
113+
[ Γ,, A |- eta_expand f ≅ eta_expand g : B] ->
114114
[ Γ |- f ≅h g : tProd A B]
115115
| termSigCongAlg {Γ A B A' B'} :
116116
[ Γ |- A ≅ A' : U] ->
@@ -119,8 +119,8 @@ Section Definitions.
119119
| termPairConvAlg {Γ : context} {p q A B} :
120120
whnf p ->
121121
whnf q ->
122-
[ Γ |- tFst p ≅ tFst q : A] ->
123-
[ Γ |- tSnd p ≅ tSnd q : B[(tFst p)..]] ->
122+
[ Γ |- tFst p ≅ tFst q : A] ->
123+
[ Γ |- tSnd p ≅ tSnd q : B[(tFst p)..]] ->
124124
[ Γ |- p ≅h q : tSig A B]
125125
| termIdCongAlg {Γ A A' x x' y y'} :
126126
[Γ |- A ≅ A' : U] ->
@@ -170,7 +170,7 @@ Section Definitions.
170170
[Γ |- y ◃ A] ->
171171
[Γ |- tId A x y]
172172
| wfTypeUniv {Γ A} :
173-
~ isCanonical A ->
173+
¬ isCanonical A ->
174174
[Γ |- A ▹h U] ->
175175
[Γ |- A]
176176
(** **** Type inference *)
@@ -179,16 +179,16 @@ Section Definitions.
179179
in_ctx Γ n decl ->
180180
[Γ |- tRel n ▹ decl]
181181
| infProd {Γ} {A B} :
182-
[ Γ |- A ▹h U] ->
182+
[ Γ |- A ▹h U] ->
183183
[Γ ,, A |- B ▹h U ] ->
184184
[ Γ |- tProd A B ▹ U ]
185185
| infLam {Γ} {A B t} :
186186
[ Γ |- A] ->
187-
[ Γ ,, A |- t ▹ B ] ->
187+
[ Γ ,, A |- t ▹ B ] ->
188188
[ Γ |- tLambda A t ▹ tProd A B]
189189
| infApp {Γ} {f a A B} :
190-
[ Γ |- f ▹h tProd A B ] ->
191-
[ Γ |- a ◃ A ] ->
190+
[ Γ |- f ▹h tProd A B ] ->
191+
[ Γ |- a ◃ A ] ->
192192
[ Γ |- tApp f a ▹ B[a..] ]
193193
| infNat {Γ} :
194194
[Γ |- tNat ▹ U]
@@ -210,11 +210,11 @@ Section Definitions.
210210
[Γ ,, tEmpty |- P ] ->
211211
[Γ |- tEmptyElim P e ▹ P[e..]]
212212
| infSig {Γ} {A B} :
213-
[ Γ |- A ▹h U] ->
213+
[ Γ |- A ▹h U] ->
214214
[Γ ,, A |- B ▹h U ] ->
215215
[ Γ |- tSig A B ▹ U ]
216216
| infPair {Γ A B a b} :
217-
[ Γ |- A] ->
217+
[ Γ |- A] ->
218218
[Γ ,, A |- B] ->
219219
[Γ |- a ◃ A] ->
220220
[Γ |- b ◃ B[a..]] ->
@@ -252,7 +252,7 @@ Section Definitions.
252252
(** **** Type-checking *)
253253
with CheckAlg : context -> term -> term -> Type :=
254254
| checkConv {Γ t A A'} :
255-
[ Γ |- t ▹ A ] ->
255+
[ Γ |- t ▹ A ] ->
256256
conv_type Γ A A' ->
257257
[ Γ |- t ◃ A' ]
258258

@@ -303,11 +303,11 @@ with UConvRedAlg : term -> term -> Type :=
303303
[tLambda A t ≅h tLambda A' t']
304304
| LambNeUAlg {A t n'} :
305305
whne n' ->
306-
[t ≅ eta_expand n'] ->
306+
[t ≅ eta_expand n'] ->
307307
[tLambda A t ≅h n']
308308
| NeLamUAlg {n A' t'} :
309309
whne n ->
310-
[eta_expand n ≅ t'] ->
310+
[eta_expand n ≅ t'] ->
311311
[n ≅h tLambda A' t']
312312
| SigCongUAlg {A B A' B'} :
313313
[A ≅ A'] ->
@@ -423,13 +423,13 @@ End AlgorithmicTypedConvData.
423423

424424
(** ** Induction principles *)
425425

426-
(** Similarly to declarative typing, we need some massaging to turn the output of
426+
(** Similarly to declarative typing, we need some massaging to turn the output of
427427
Scheme to something that fits our purpose, and we also define a function that computes
428428
the conclusion of a proof by induction. *)
429429
Section InductionPrinciples.
430430
Import AlgorithmicTypingData AlgorithmicTypedConvData.
431431

432-
Scheme
432+
Scheme
433433
Minimality for ConvTypeAlg Sort Type with
434434
Minimality for ConvTypeRedAlg Sort Type with
435435
Minimality for ConvNeuAlg Sort Type with
@@ -514,7 +514,7 @@ Definition AlgoTypingInductionConcl :=
514514
exact t').
515515

516516

517-
Scheme
517+
Scheme
518518
Minimality for UConvAlg Sort Type with
519519
Minimality for UConvRedAlg Sort Type with
520520
Minimality for UConvNeuAlg Sort Type.

theories/Checkers/Completeness.v

Lines changed: 5 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -26,12 +26,12 @@ Context `{!TypingSubst de} `{!TypeConstructorsInj de}.
2626
Let PTyEq (Γ : context) (A B : term) :=
2727
forall v, graph _conv (ty_state;Γ;v;A;B) ok.
2828
Let PTyRedEq (Γ : context) (A B : term) :=
29-
forall v, graph _conv (ty_red_state;Γ;v;A;B) ok.
29+
forall v, graph _conv (ty_red_state;Γ;v;A;B) ok.
3030
Let PNeEq (Γ : context) (A t u : term) :=
3131
forall v, graph _conv (ne_state;Γ;v;t;u) (success A).
3232
Let PNeRedEq (Γ : context) (A t u : term) :=
3333
forall v, graph _conv (ne_red_state;Γ;v;t;u) (success A).
34-
Let PTmEq (Γ : context) (A t u : term) :=
34+
Let PTmEq (Γ : context) (A t u : term) :=
3535
graph _conv (tm_state;Γ;A;t;u) ok.
3636
Let PTmRedEq (Γ : context) (A t u : term) :=
3737
graph _conv (tm_red_state;Γ;A;t;u) ok.
@@ -278,7 +278,7 @@ Hypothesis conv_complete : forall Γ T V,
278278
[Γ |-[de] T ≅ V] ->
279279
graph conv (Γ,T,V) ok.
280280

281-
Definition isCanonical_ty_view1 t (c : ~ isCanonical t) : ne_view1 t.
281+
Definition isCanonical_ty_view1 t (c : ¬ isCanonical t) : ne_view1 t.
282282
Proof.
283283
revert c.
284284
case t ; intros.
@@ -292,7 +292,7 @@ all: try solve [case c ; constructor].
292292
- eapply (ne_view1_dest _ (eIdElim _ _ _ _ _)).
293293
Defined.
294294

295-
Lemma can_ty_view1_small T (c : ~ isCanonical T) :
295+
Lemma can_ty_view1_small T (c : ¬ isCanonical T) :
296296
build_ty_view1 T = ty_view1_small (isCanonical_ty_view1 T c).
297297
Proof.
298298
destruct T ; cbn.
@@ -365,7 +365,7 @@ Proof.
365365
1: exact g0.
366366
econstructor.
367367
1: exact g.
368-
now constructor.
368+
now constructor.
369369
- now constructor.
370370
- econstructor.
371371
1: exact (g0 tt whnf_tEmpty).

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