aboutsummaryrefslogtreecommitdiffhomepage
path: root/test-suite/success/Notations2.v
blob: 2655b651a0653cf36aeac2c4d0da19621a05d384 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
(* This file is giving some examples about how implicit arguments and
   scopes are treated when using abbreviations or notations, in terms
   or patterns, or when using @ and parentheses in terms and patterns.

The convention is:

Constant foo with implicit arguments and scopes used in a term or a pattern:

       foo      do not deactivate further arguments and scopes
       @foo     deactivates further arguments and scopes
       (foo x)  deactivates further arguments and scopes
       (@foo x) deactivates further arguments and scopes

Notations binding to foo:

#   := foo      do not deactivate further arguments and scopes
#   := @foo     deactivates further arguments and scopes
# x := foo x    deactivates further arguments and scopes
# x := @foo x   deactivates further arguments and scopes

Abbreviations binding to foo:

f   := foo      do not deactivate further arguments and scopes
f   := @foo     deactivates further arguments and scopes
f x := foo x    do not deactivate further arguments and scopes
f x := @foo x   do not deactivate further arguments and scopes
*)

(* One checks that abbreviations and notations in patterns now behave like in terms *)

Inductive prod' A : Type -> Type :=
| pair' (a:A) B (b:B) (c:bool) : prod' A B.
Arguments pair' [A] a%bool_scope [B] b%bool_scope c%bool_scope.
Notation "0" := true : bool_scope.

(* 1. Abbreviations do not stop implicit arguments to be inserted and scopes to be used *)
Notation c1 x := (pair' x).
Check pair' 0 0 0 : prod' bool bool.
Check (pair' 0) _ 0%bool 0%bool : prod' bool bool. (* parentheses are blocking implicit and scopes *)
Check c1 0 0 0 : prod' bool bool.
Check fun x : prod' bool bool => match x with c1 0 y 0 => 2 | _ => 1 end.

(* 2. Abbreviations do not stop implicit arguments to be inserted and scopes to be used *)
Notation c2 x := (@pair' _ x).
Check (@pair' _ 0) _ 0%bool 0%bool : prod' bool bool. (* parentheses are blocking implicit and scopes *)
Check c2 0 0 0 : prod' bool bool.
Check fun A (x : prod' bool A) => match x with c2 0 y 0 => 2 | _ => 1 end.
Check fun A (x : prod' bool A) => match x with (@pair' _ 0) _ y 0%bool => 2 | _ => 1 end.

(* 3. Abbreviations do not stop implicit arguments to be inserted and scopes to be used *)
Notation c3 x := ((@pair') _ x).
Check (@pair') _ 0%bool _ 0%bool 0%bool : prod' bool bool. (* @ is blocking implicit and scopes *)
Check ((@pair') _ 0%bool) _ 0%bool 0%bool : prod' bool bool. (* parentheses and @ are blocking implicit and scopes *)
Check c3 0 0 0 : prod' nat bool. (* First scope is blocked but not the last two scopes *)
Check fun A (x :prod' nat A) => match x with c3 0 y 0 => 2 | _ => 1 end.

(* 4. Abbreviations do not stop implicit arguments to be inserted and scopes to be used *)
(* unless an atomic @ is given *)
Notation c4 := (@pair').
Check (@pair') _ 0%bool _ 0%bool 0%bool : prod' bool bool.
Check c4 _ 0%bool _ 0%bool 0%bool : prod' bool bool.
Check fun A (x :prod' bool A) => match x with c4 _ 0%bool _ y 0%bool => 2 | _ => 1 end.
Check fun A (x :prod' bool A) => match x with (@pair') _ 0%bool _ y 0%bool => 2 | _ => 1 end.

(* 5. Notations stop further implicit arguments to be inserted and scopes to be used *)
Notation "# x" := (pair' x) (at level 0, x at level 1).
Check pair' 0 0 0 : prod' bool bool.
Check # 0 _ 0%bool 0%bool : prod' bool bool.
Check fun A (x :prod' bool A) => match x with # 0 _ y 0%bool => 2 | _ => 1 end.

(* 6. Notations stop further implicit arguments to be inserted and scopes to be used *)
Notation "## x" := ((@pair') _ x) (at level 0, x at level 1).
Check (@pair') _ 0%bool _ 0%bool 0%bool : prod' bool bool.
Check ((@pair') _ 0%bool) _ 0%bool 0%bool : prod' bool bool.
Check ## 0%bool _ 0%bool 0%bool : prod' bool bool.
Check fun A (x :prod' bool A) => match x with ## 0%bool _ y 0%bool => 2 | _ => 1 end.

(* 7. Notations stop further implicit arguments to be inserted and scopes to be used *)
Notation "###" := (@pair') (at level 0).
Check (@pair') _ 0%bool _ 0%bool 0%bool : prod' bool bool.
Check ### _ 0%bool _ 0%bool 0%bool : prod' bool bool.
Check fun A (x :prod' bool A) => match x with ### _ 0%bool _ y 0%bool => 2 | _ => 1 end.

(* 8. Notations w/o @ preserves implicit arguments and scopes *)
Notation "####" := pair' (at level 0).
Check #### 0 0 0 : prod' bool bool.
Check fun A (x :prod' bool A) => match x with #### 0 y 0 => 2 | _ => 1 end.

(* 9. Notations w/o @ but arguments do not preserve further implicit arguments and scopes *)
Notation "##### x" := (pair' x) (at level 0, x at level 1).
Check ##### 0 _ 0%bool 0%bool : prod' bool bool.
Check fun A (x :prod' bool A) => match x with ##### 0 _ y 0%bool => 2 | _ => 1 end.

(* 10. Check computation of binding variable through other notations *)
(* i should be detected as binding variable and the scopes not being checked *)

Notation "'FUNNAT' i => t" := (fun i : nat => i = t) (at level 200).
Notation "'Funnat' i => t" := (FUNNAT i => t + i%nat) (at level 200).

(* 11. Notations with needed factorization of a recursive pattern *)
(* See https://github.com/coq/coq/issues/6078#issuecomment-342287412 *)
Module A.
Notation "[:: x1 ; .. ; xn & s ]" := (cons x1 .. (cons xn s) ..).
Notation "[:: x1 ; .. ; xn ]" := (cons x1 .. (cons xn nil) ..).
Check [:: 1 ; 2 ; 3 ].
Check [:: 1 ; 2 ; 3 & nil ]. (* was failing *)
End A.