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
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
|
Set Primitive Projections.
Set Record Elimination Schemes.
Module Prim.
Record F := { a : nat; b : a = a }.
Record G (A : Type) := { c : A; d : F }.
Check c.
End Prim.
Module Univ.
Set Universe Polymorphism.
Set Implicit Arguments.
Record Foo (A : Type) := { foo : A }.
Record G (A : Type) := { c : A; d : c = c; e : Foo A }.
Definition Foon : Foo nat := {| foo := 0 |}.
Definition Foonp : nat := Foon.(foo).
Definition Gt : G nat := {| c:= 0; d:=eq_refl; e:= Foon |}.
Check (Gt.(e)).
Section bla.
Record bar := { baz : nat; def := 0; baz' : forall x, x = baz \/ x = def }.
End bla.
End Univ.
Set Primitive Projections.
Unset Elimination Schemes.
Set Implicit Arguments.
Check nat.
Inductive X (U:Type) := { k : nat; a: k = k -> X U; b : let x := a eq_refl in X U }.
Parameter x:X nat.
Check (a x : forall _ : @eq nat (k x) (k x), X nat).
Check (b x : X nat).
Inductive Y := { next : option Y }.
Check _.(next) : option Y.
Lemma eta_ind (y : Y) : y = Build_Y y.(next).
Proof. Fail reflexivity. Abort.
Inductive Fdef := { Fa : nat ; Fb := Fa; Fc : Fdef }.
Fail Scheme Fdef_rec := Induction for Fdef Sort Prop.
(*
Rules for parsing and printing of primitive projections and their eta expansions.
If r : R A where R is a primitive record with implicit parameter A.
If p : forall {A} (r : R A) {A : Set}, list (A * B).
*)
Record R {A : Type} := { p : forall {X : Set}, A * X }.
Arguments R : clear implicits.
Record R' {A : Type} := { p' : forall X : Set, A * X }.
Arguments R' : clear implicits.
Unset Printing All.
Parameter r : R nat.
Check (r.(p)).
Set Printing Projections.
Check (r.(p)).
Unset Printing Projections.
Set Printing All.
Check (r.(p)).
Unset Printing All.
(* Check (r.(p)).
Elaborates to a primitive application, X arg implicit.
Of type nat * ?ex
No Printing All: p r
Set Printing Projections.: r.(p)
Printing All: r.(@p) ?ex
*)
Check p r.
Set Printing Projections.
Check p r.
Unset Printing Projections.
Set Printing All.
Check p r.
Unset Printing All.
Check p r (X:=nat).
Set Printing Projections.
Check p r (X:=nat).
Unset Printing Projections.
Set Printing All.
Check p r (X:=nat).
Unset Printing All.
(* Same elaboration, printing for p r *)
(** Explicit version of the primitive projection, under applied w.r.t implicit arguments
can be printed only using projection notation. r.(@p) *)
Check r.(@p _).
Set Printing Projections.
Check r.(@p _).
Unset Printing Projections.
Set Printing All.
Check r.(@p _).
Unset Printing All.
(** Explicit version of the primitive projection, applied to its implicit arguments
can be printed using application notation r.(p), r.(@p) in fully explicit form *)
Check r.(@p _) nat.
Set Printing Projections.
Check r.(@p _) nat.
Unset Printing Projections.
Set Printing All.
Check r.(@p _) nat.
Unset Printing All.
Parameter r' : R' nat.
Check (r'.(p')).
Set Printing Projections.
Check (r'.(p')).
Unset Printing Projections.
Set Printing All.
Check (r'.(p')).
Unset Printing All.
(* Check (r'.(p')).
Elaborates to a primitive application, X arg explicit.
Of type forall X : Set, nat * X
No Printing All: p' r'
Set Printing Projections.: r'.(p')
Printing All: r'.(@p')
*)
Check p' r'.
Set Printing Projections.
Check p' r'.
Unset Printing Projections.
Set Printing All.
Check p' r'.
Unset Printing All.
(* Same elaboration, printing for p r *)
(** Explicit version of the primitive projection, under applied w.r.t implicit arguments
can be printed only using projection notation. r.(@p) *)
Check r'.(@p' _).
Set Printing Projections.
Check r'.(@p' _).
Unset Printing Projections.
Set Printing All.
Check r'.(@p' _).
Unset Printing All.
(** Explicit version of the primitive projection, applied to its implicit arguments
can be printed only using projection notation r.(p), r.(@p) in fully explicit form *)
Check p' r' nat.
Set Printing Projections.
Check p' r' nat.
Unset Printing Projections.
Set Printing All.
Check p' r' nat.
Unset Printing All.
Check (@p' nat).
Check p'.
Set Printing All.
Check (@p' nat).
Check p'.
Unset Printing All.
Record wrap (A : Type) := { unwrap : A; unwrap2 : A }.
Definition term (x : wrap nat) := x.(unwrap).
Definition term' (x : wrap nat) := let f := (@unwrap2 nat) in f x.
Require Coq.extraction.Extraction.
Recursive Extraction term term'.
Extraction TestCompile term term'.
(*Unset Printing Primitive Projection Parameters.*)
(* Primitive projections in the presence of let-ins (was not failing in beta3)*)
Set Primitive Projections.
Record s (x:nat) (y:=S x) := {c:=x; d:x=c}.
Lemma f : 0=1.
Proof.
Fail apply d.
(*
split.
reflexivity.
Qed.
*)
|