The Coq Proof Assistant

# Library Coq.micromega.VarMap

Require Import ZArith_base.
Require Import List.
Set Implicit Arguments.
Inductive t {A} : Type :=
| Empty : t
| Elt : A -> t
| Branch : t -> A -> t -> t .
Arguments t : clear implicits.
Register Branch as micromega.VarMap.Branch.
Register Elt as micromega.VarMap.Elt.
Register Empty as micromega.VarMap.Empty.
Register t as micromega.VarMap.type.
Section MakeVarMap.
Variable A : Type.
Variable default : A.
Notation t := (t A).
Fixpoint find (vm : t) (p:positive) {struct vm} : A :=
match vm with
| Empty => default
| Elt i => i
| Branch 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 => Elt v
| xO p => Branch (singleton p v) default Empty
| xI p => Branch 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
| Elt vl =>
match x with
| xH => Elt v
| xO p => Branch (singleton p v) vl Empty
| xI p => Branch Empty vl (singleton p v)
end
| Branch l o r =>
match x with
| xH => Branch l v r
| xI p => Branch l o (vm_add p v r)
| xO p => Branch (vm_add p v l) o r
end
end.
End MakeVarMap.