IO vs OI in Higher-Order Recursion Schemes

TL;DR

This paper investigates the derivation modes of higher-order recursion schemes, showing that innermost-outermost derivations produce the same value trees as unrestricted derivations, linking to call-by-value evaluation.

Contribution

It proves the equivalence of value trees from IO and unrestricted derivations in higher-order recursion schemes, offering insights into evaluation strategies.

Findings

Value trees are identical for IO and unrestricted derivations.

IO derivations model call-by-value evaluation.

Theoretical foundation for evaluation strategies in functional programs.

Abstract

We propose a study of the modes of derivation of higher-order recursion schemes, proving that value trees obtained from schemes using innermost-outermost derivations (IO) are the same as those obtained using unrestricted derivations. Given that higher-order recursion schemes can be used as a model of functional programs, innermost-outermost derivations policy represents a theoretical view point of call by value evaluation strategy.