Evolving Recursive Definitions with Applications to Dynamic Programming

TL;DR

This paper introduces a novel approach to recursive definitions inspired by computability logic, distinguishing between static and evolving forms, and proposes a new object-oriented language leveraging these concepts for automatic memoization.

Contribution

It refines recursive function definitions into evolving and non-evolving types and develops a new object-oriented language based on these ideas.

Findings

Evolving recursive definitions enable automatic memoization.

Distinction between blindly-quantified and parallel universally quantified definitions.

Proposal of a new high-level object-oriented language incorporating these concepts.

Abstract

Inspired by computability logic\cite{Jap03}, we refine recursive function definitions into two kinds: blindly-quantified (BQ) ones and parallel universally quantified (PUQ) ones. BQ definitions corresponds to the traditional ones where recursive definitions are $not$ evolving. PUQ definitions are {\it evolving} in the course of computation, leading to automatic memoization. In addition, based on this idea, we propose a new, high-level object-oriented language.