view src/coq/Name.v @ 624:354800878b4d

Kind polymorphism through Explify
author Adam Chlipala <adamc@hcoop.net>
date Sun, 22 Feb 2009 16:32:56 -0500
parents d828b143e147
children 75c7a69354d6
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(* Copyright (c) 2009, Adam Chlipala
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Set Implicit Arguments.


Fixpoint name' (n : nat) : Type :=
  match n with
    | O => Empty_set
    | S n' => option (name' n')
  end.

Definition name'_eq_dec : forall n (x y : name' n), {x = y} + {x <> y}.
  Hint Extern 1 (_ = _ -> False) => congruence.

  induction n; simpl; intuition;
    repeat match goal with
             | [ x : Empty_set |- _ ] => destruct x
             | [ x : option _ |- _ ] => destruct x
           end; intuition;
    match goal with
      | [ IH : _, n1 : name' _, n2 : name' _ |- _ ] =>
        destruct (IHn n1 n0); subst; intuition
    end.
Qed.

Definition badName' n (P : name' n -> bool) :
  {nm : _ | P nm = false} + {forall nm, P nm = true}.
  Hint Constructors sig.
  Hint Extern 1 (_ = true) =>
    match goal with
      | [ nm : option _ |- _ ] => destruct nm
    end; auto.

  induction n; simpl; intuition;
    match goal with
      | [ IH : forall P : _ -> _,_ |- _ ] =>
        case_eq (P None);
        destruct (IH (fun nm => P (Some nm))); firstorder eauto
    end.
Qed.

Parameter numNames : nat.
Definition name := name' (S numNames).
Definition name_eq_dec : forall (x y : name), {x = y} + {x <> y} := @name'_eq_dec _.
Definition badName : forall P : name -> bool, {nm : _ | P nm = false} + {forall nm, P nm = true} := @badName' _.
Definition defaultName : name := None.