Library Coq.micromega.VarMap

Require Import ZArith.
Require Import Coq.Arith.Max.
Require Import List.
Set Implicit Arguments.


Section MakeVarMap.

  Variable A : Type.
  Variable default : A.

  Inductive t : Type :=
  | Empty : t
  | Leaf : A -> t
  | Node : t -> A -> t -> t .

  Fixpoint find (vm : t) (p:positive) {struct vm} : A :=
    match vm with
      | Empty => default
      | Leaf i => i
      | Node l e r => match p with
                        | xH => e
                        | xO p => find l p
                        | xI p => find r p
                      end
    end.

  Fixpoint singleton (x:positive) (v : A) : t :=
    match x with
    | xH => Leaf v
    | xO p => Node (singleton p v) default Empty
    | xI p => Node Empty default (singleton p v)
    end.

  Fixpoint vm_add (x: positive) (v : A) (m : t) {struct m} : t :=
    match m with
    | Empty => singleton x v
    | Leaf vl =>
      match x with
      | xH => Leaf v
      | xO p => Node (singleton p v) vl Empty
      | xI p => Node Empty vl (singleton p v)
      end
    | Node l o r =>
      match x with
      | xH => Node l v r
      | xI p => Node l o (vm_add p v r)
      | xO p => Node (vm_add p v l) o r
      end
    end.


End MakeVarMap.