A counting function for trees and lists of trees.

We define a type of trees based on lists of trees. In this type, an node can have an arbitrary (but finite) number of children, grouped in a list.

Require Export List.

Inductive ltree (A:Set) : Set :=
    lnode : A -> list (ltree A)-> ltree A.

We can define a similar type using mutual inductive types as in the following definition:

Inductive ntree (A:Set) : Set :=
  nnode : A -> nforest A -> ntree A
with nforest (A:Set) : Set :=
  nnil : nforest A | ncons : ntree A -> nforest A -> nforest A.

Define functions ltree_to_ntree and ntree_to_ltree that establish a bijection between the two types and prove the bijection property.

Solution