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Require Import List.
Require Import Program.
Inductive Tree : Set :=
| Br : Tree -> Tree -> Tree
| No : nat -> Tree
.
(* given a tree, we want to know which lists can
be used to navigate exactly to a node *)
Inductive Exact : Tree -> list bool -> Prop :=
| exDone n : Exact (No n) nil
| exLeft l r p: Exact l p -> Exact (Br l r) (true::p)
| exRight l r p: Exact r p -> Exact (Br l r) (false::p)
.
Definition unreachable A : False -> A.
intros.
destruct H.
Defined.
Program Fixpoint fetch t p (x:Exact t p) {struct t} :=
match t, p with
| No p' , nil => p'
| No p' , _::_ => unreachable nat _
| Br l r, nil => unreachable nat _
| Br l r, true::t => fetch l t _
| Br l r, false::t => fetch r t _
end.
Next Obligation. inversion x. Qed.
Next Obligation. inversion x. Qed.
Next Obligation. inversion x; trivial. Qed.
Next Obligation. inversion x; trivial. Qed.
|
