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comparison src/coq/Name.v @ 635:75c7a69354d6

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Coq formalization uses TDisjoint
author Adam Chlipala <adamc@hcoop.net>
date Tue, 24 Feb 2009 16:08:14 -0500
parents d828b143e147
children
comparison
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634:6302b10dbe0e 635:75c7a69354d6
23 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 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 24 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
25 * POSSIBILITY OF SUCH DAMAGE. 25 * POSSIBILITY OF SUCH DAMAGE.
26 *) 26 *)
27 27
28 Set Implicit Arguments. 28 Require Import String.
29 29
30 30 Definition name := string.
31 Fixpoint name' (n : nat) : Type := 31 Definition name_eq_dec : forall x y : name, {x = y} + {x <> y} := string_dec.
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.