The Coq Proof Assistant

# 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.