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
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
|
(**********************************************************************)
(* Test call to primitive printers in presence of coercion to *)
(* functions (cf bug #2044) *)
Inductive PAIR := P (n1:nat) (n2:nat).
Coercion P : nat >-> Funclass.
Check (2 3).
(* Check that notations with coercions to functions inserted still work *)
(* (were not working from revision 11886 to 12951) *)
Record Binop := { binop :> nat -> nat -> nat }.
Class Plusop := { plusop : Binop; zero : nat }.
Infix "[+]" := plusop (at level 40).
Instance Plus : Plusop := {| plusop := {| binop := plus |} ; zero := 0 |}.
Check 2[+]3.
(* Test bug #2091 (variable le was printed using <= !) *)
Check forall (A: Set) (le: A -> A -> Prop) (x y: A), le x y \/ le y x.
(* Test recursive notations in cases pattern *)
Remove Printing Let prod.
Check match (0,0,0) with (x,y,z) => x+y+z end.
Check let '(a,b,c) := ((2,3),4) in a.
(* Check printing of notations with mixed reserved binders (see bug #2571) *)
Implicit Type myx : bool.
Check exists myx y, myx = y.
(* Test notation for anonymous functions up to eta-expansion *)
Check fun P:nat->nat->Prop => fun x:nat => ex (P x).
(* Test notations with binders *)
Notation "∃ x .. y , P":= (ex (fun x => .. (ex (fun y => P)) ..))
(x binder, y binder, at level 200, right associativity).
Check (∃ n p, n+p=0).
Check ∃ (a:=0) (x:nat) y (b:=1) (c:=b) (d:=2) z (e:=3) (f:=4), x+y = z+d.
Notation "∀ x .. y , P":= (forall x, .. (forall y, P) ..)
(x binder, at level 200, right associativity).
Check (∀ n p, n+p=0).
Notation "'λ' x .. y , P":= (fun x => .. (fun y => P) ..)
(y binder, at level 200, right associativity).
Check (λ n p, n+p=0).
Generalizable Variable A.
Check `(λ n p : A, n=p).
Check `(∃ n p : A, n=p).
Check `(∀ n p : A, n=p).
Notation "'let'' f x .. y := t 'in' u":=
(let f := fun x => .. (fun y => t) .. in u)
(f ident, x closed binder, y closed binder, at level 200,
right associativity).
Check let' f x y (a:=0) z (b:bool) := x+y+z+1 in f 0 1 2.
(* In practice, only the printing rule is used here *)
(* Note: does not work for pattern *)
Module A.
Notation "f ( x )" := (f x) (at level 10, format "f ( x )").
Open Scope nat_scope.
Check fun f x => f x + S x.
Open Scope list_scope.
Notation list1 := (1::nil)%list.
Notation plus2 n := (S (S n)).
(* plus2 was not correctly printed in the two following tests in 8.3pl1 *)
Print plus2.
Check fun n => match n with list1 => 0 | _ => 2 end.
Unset Printing Allow Match Default Clause.
Check fun n => match n with list1 => 0 | _ => 2 end.
Unset Printing Factorizable Match Patterns.
Check fun n => match n with list1 => 0 | _ => 2 end.
Set Printing Allow Match Default Clause.
Set Printing Factorizable Match Patterns.
End A.
(* This one is not fully satisfactory because binders in the same type
are re-factorized and parentheses are needed even for atomic binder
Notation "'mylet' f [ x ; .. ; y ] := t 'in' u":=
(let f := fun x => .. (fun y => t) .. in u)
(f ident, x closed binder, y closed binder, at level 200,
right associativity).
Check mylet f [x;y;z;(a:bool)] := x+y+z+1 in f 0 1 2.
*)
(* Check notations for functional terms which do not necessarily
depend on their parameter *)
(* Old request mentioned again on coq-club 20/1/2012 *)
Notation "# x : T => t" := (fun x : T => t)
(at level 0, t at level 200, x ident).
Check # x : nat => x.
Check # _ : nat => 2.
(* Check bug 4677 *)
Check fun x (H:le x 0) => exist (le x) 0 H.
Parameters (A : Set) (x y : A) (Q : A -> A -> Prop) (conj : Q x y).
Check (exist (Q x) y conj).
(* Check bug #4854 *)
Notation "% i" := (fun i : nat => i) (at level 0, i ident).
Check %i.
Check %j.
(* Check bug raised on coq-club on Sep 12, 2016 *)
Notation "{ x , y , .. , v }" := (fun a => (or .. (or (a = x) (a = y)) .. (a = v))).
Check ({1, 2}).
(**********************************************************************)
(* Check notations of the form ".a", ".a≡", "a≡" *)
(* Only "a#", "a≡" and ".≡" were working properly for parsing. The *)
(* other ones were working only for printing. *)
Notation "a#" := nat.
Check nat.
Check a#.
Notation "a≡" := nat.
Check nat.
Check a≡.
Notation ".≡" := nat.
Check nat.
Check .≡.
Notation ".a#" := nat.
Check nat.
Check .a#.
Notation ".a≡" := nat.
Check nat.
Check .a≡.
Notation ".α" := nat.
Check nat.
Check .α.
(* A test for #6304 *)
Module M6304.
Notation "'for' m 'from' 0 'to' N 'updating' ( s1 ) {{ b }} ;; rest" :=
(let s1 :=
(fix rec(n: nat) := match n with
| 0 => s1
| S m => let s1 := rec m in b
end) N
in rest)
(at level 20).
Check fun (a b : nat) =>
let res := 0 in
for i from 0 to a updating (res) {{
for j from 0 to b updating (res) {{ S res }};;
res
}};; res.
End M6304.
|
