Mercurial > urweb

comparison src/coq/Name.v @ 620:d828b143e147

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Finish semantics for Featherweight Ur
author Adam Chlipala <adamc@hcoop.net>
date Sat, 21 Feb 2009 14:10:06 -0500
parents
children 75c7a69354d6
comparison
equal deleted inserted replaced
619:f38e009009bb 620:d828b143e147
1 (* Copyright (c) 2009, Adam Chlipala
2 * All rights reserved.
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions are met:
6 *
7 * - Redistributions of source code must retain the above copyright notice,
8 * this list of conditions and the following disclaimer.
9 * - Redistributions in binary form must reproduce the above copyright notice,
10 * this list of conditions and the following disclaimer in the documentation
11 * and/or other materials provided with the distribution.
12 * - The names of contributors may not be used to endorse or promote products
13 * derived from this software without specific prior written permission.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
16 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
19 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
20 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
21 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
22 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
23 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
24 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
25 * POSSIBILITY OF SUCH DAMAGE.
26 *)
27
28 Set Implicit Arguments.
29
30
31 Fixpoint name' (n : nat) : Type :=
32 match n with
33 | O => Empty_set
34 | S n' => option (name' n')
35 end.
36
37 Definition name'_eq_dec : forall n (x y : name' n), {x = y} + {x <> y}.
38 Hint Extern 1 (_ = _ -> False) => congruence.
39
40 induction n; simpl; intuition;
41 repeat match goal with
42 | [ x : Empty_set |- _ ] => destruct x
43 | [ x : option _ |- _ ] => destruct x
44 end; intuition;
45 match goal with
46 | [ IH : _, n1 : name' _, n2 : name' _ |- _ ] =>
47 destruct (IHn n1 n0); subst; intuition
48 end.
49 Qed.
50
51 Definition badName' n (P : name' n -> bool) :
52 {nm : _ | P nm = false} + {forall nm, P nm = true}.
53 Hint Constructors sig.
54 Hint Extern 1 (_ = true) =>
55 match goal with
56 | [ nm : option _ |- _ ] => destruct nm
57 end; auto.
58
59 induction n; simpl; intuition;
60 match goal with
61 | [ IH : forall P : _ -> _,_ |- _ ] =>
62 case_eq (P None);
63 destruct (IH (fun nm => P (Some nm))); firstorder eauto
64 end.
65 Qed.
66
67 Parameter numNames : nat.
68 Definition name := name' (S numNames).
69 Definition name_eq_dec : forall (x y : name), {x = y} + {x <> y} := @name'_eq_dec _.
70 Definition badName : forall P : name -> bool, {nm : _ | P nm = false} + {forall nm, P nm = true} := @badName' _.
71 Definition defaultName : name := None.