forked from coq/coq
-
Notifications
You must be signed in to change notification settings - Fork 2
/
simpl.v
191 lines (155 loc) · 4.73 KB
/
simpl.v
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
Require Import TestSuite.admit.
(* Check that inversion of names of mutual inductive fixpoints works *)
(* (cf BZ#1031) *)
Inductive tree : Set :=
| node : nat -> forest -> tree
with forest : Set :=
| leaf : forest
| cons : tree -> forest -> forest
.
Definition copy_of_compute_size_forest :=
fix copy_of_compute_size_forest (f:forest) : nat :=
match f with
| leaf => 1
| cons t f0 => copy_of_compute_size_forest f0 + copy_of_compute_size_tree t
end
with copy_of_compute_size_tree (t:tree) : nat :=
match t with
| node _ f => 1 + copy_of_compute_size_forest f
end for copy_of_compute_size_forest
.
Eval simpl in (copy_of_compute_size_forest leaf).
(* Another interesting case: Hrec has two occurrences: one cannot be folded
back to f while the second can. *)
Parameter g : (nat->nat)->nat->nat->nat.
Definition f (n n':nat) :=
nat_rec (fun _ => nat -> nat)
(fun x => x)
(fun k Hrec => g Hrec (Hrec k))
n n'.
Goal forall a b, f (S a) b = b.
intros.
simpl.
match goal with [ |- g (f a) (f a a) b = b ] => idtac end.
admit.
Qed.
(* Yet another example. *)
Require Import List.
Goal forall A B (a:A) l f (i:B), fold_right f i ((a :: l))=i.
intros.
simpl.
match goal with [ |- f0 a (fold_right f0 i l) = i ] => idtac end.
admit.
Qed. (* Qed will fail if simplification is incorrect (de Bruijn!) *)
(* Check that maximally inserted arguments do not break interpretation
of references in simpl, vm_compute etc. *)
Arguments fst {A} {B} p.
Goal fst (0,0) = 0.
simpl fst.
Fail set (fst _).
Abort.
Goal fst (0,0) = 0.
vm_compute fst.
Fail set (fst _).
Abort.
Goal let f x := x + 0 in f 0 = 0.
intro.
vm_compute f.
Fail set (f _).
Abort.
(* This is a change wrt 8.4 (waiting to know if it breaks script a lot or not)*)
Goal 0+0=0.
Fail simpl @eq.
Abort.
(* Check reference by notation in simpl *)
Goal 0+0 = 0.
simpl "+".
Fail set (_ + _).
Abort.
(* Check occurrences *)
Record box A := Box { unbox : A }.
Goal unbox _ (unbox _ (unbox _ (Box _ (Box _ (Box _ True))))) =
unbox _ (unbox _ (unbox _ (Box _ (Box _ (Box _ True))))).
simpl (unbox _ (unbox _ _)) at 1.
match goal with |- True = unbox _ (unbox _ (unbox _ (Box _ (Box _ (Box _ True))))) => idtac end.
Undo 2.
Fail simpl (unbox _ (unbox _ _)) at 5.
simpl (unbox _ (unbox _ _)) at 1 4.
match goal with |- True = unbox _ (Box _ True) => idtac end.
Undo 2.
Fail simpl (unbox _ (unbox _ _)) at 3 4. (* Nested and even overlapping *)
simpl (unbox _ (unbox _ _)) at 2 4.
match goal with |- unbox _ (Box _ True) = unbox _ (Box _ True) => idtac end.
Abort.
(* Check interpretation of ltac variables (was broken in 8.5 beta 1 and 2 *)
Goal 2=1+1.
match goal with |- (_ = ?c) => simpl c end.
match goal with |- 2 = 2 => idtac end. (* Check that it reduced *)
Abort.
Module FurtherAppliedPrimitiveProjections.
Set Primitive Projections.
Record T := { u : nat -> nat }.
Goal {| u:= fun x => x |}.(u) 0 = 0.
simpl u.
match goal with |- 0 = 0 => idtac end. (* Check that it reduced *)
Abort.
End FurtherAppliedPrimitiveProjections.
Module BugUniverseMutualFix.
Set Universe Polymorphism.
Fixpoint foo1@{u v} (A : Type@{u}) n : Type@{v} := match n with 0 => A | S n => (foo2 A n * A)%type end
with foo2@{u v} (A : Type@{u}) n : Type@{v} := match n with 0 => A | S n => (foo1 A n * A)%type end.
Set Printing Universes.
Definition bar@{u} (A : Type@{u}) n := foo1@{u u} A n.
Goal forall n, bar unit (S n) = unit.
simpl.
Abort.
End BugUniverseMutualFix.
Module PolyUniverses.
(* An example showing that the cache needs to take universes into account *)
Set Universe Polymorphism.
Record cell T S := Cell { hd : T; tl : S }.
Arguments Cell {_ _}.
Arguments hd {_ _}.
Arguments tl {_ _}.
Notation "x ::: y" := (Cell x y) (at level 60).
Definition ilist T n := @Nat.iter n Type (cell T) unit.
Fixpoint imap@{u u0 u1 u2} (T:Type@{u}) (S:Type@{u0}) (f : T -> S) n : ilist@{u2 u1} T n -> ilist@{u0 u1} S n :=
match n with
| 0 => fun l => tt
| S n => fun l => f l.(hd) ::: imap _ _ f _ l.(tl)
end.
Lemma imap_eq (T S : Type) (f g : T -> S) :
forall n, forall x, @imap _ _ f n x = @imap _ _ g n x.
induction n. intro; auto.
intros [].
Abort.
End PolyUniverses.
Module WithLet.
Section S.
Variable a : nat.
Let b := 0.
Variable c : nat.
Fixpoint f n :=
match n with
| 0 => a + b + c
| S n => f n
end.
End S.
Definition f' a c n := f a c n.
Lemma L a c n : f' a c (S n) = f a c (S n).
simpl.
match goal with [ |- f' a c n = f a c n ] => idtac end.
Abort.
End WithLet.
Module WithLetMutual.
Section S.
Context (a : nat) (b := 0) (c : nat).
Fixpoint f n := match n with 0 => a + b + c | S n => g n end
with g n := match n with 0 => a + b + c | S n => f n end.
End S.
Definition f' a c n := f a c n.
Lemma L a c n : f' a c (S n) = f a c (S n).
simpl.
match goal with [ |- g a c n = g a c n ] => idtac end.
Abort.
End WithLetMutual.