A game-theoretic computational interpretation of proofs in classical analysis

It has been shown by Escardó and the first author that a functional interpretation of proofs in 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.