A Game-Theoretic Computational Interpretation of Proofs in Classical Analysis

TL;DR

This paper demonstrates how the product of selection functions provides a game-theoretic computational interpretation of classical analysis proofs, linking mathematical theorems to optimal strategies in sequential games.

Contribution

It introduces a novel application of the product of selection functions to interpret classical analysis proofs in a game-theoretic computational framework.

Findings

Provides a natural computational interpretation of mathematical theorems

Connects classical analysis proofs with game-theoretic strategies

Shows practical value of the product of selection functions in analysis

Abstract

It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in sequential games. We argue that this result has genuine practical value by interpreting some well-known theorems of mathematics and demonstrating that the product gives these theorems a natural computational interpretation that can be clearly understood in game theoretic terms.