# recursion theorem (under construction)

## Summary

Many mathematical objects, such as natural numbers, lists, and trees, are defined recursively in terms of basic components and composition rules. The Recursion Theorem shows that functions defined recursively on such objects are well-defined.

## Notes

This concept is still under construction.

## Context

This concept has the prerequisites:

- structural induction (The Recursion Theorem is proved using structural induction.)

## Goals

- be able to use the Recursion Theorem to define functions over recursively defined structures

- prove the Recursion Theorem

## See also

-No Additional Notes-