On reduction and normalization in the computational core

TL;DR

This paper explores reduction and normalization strategies within a lambda-calculus variant called the computational core, derived from Moggi's monadic framework, focusing on operational intricacies and normalization techniques.

Contribution

It introduces a detailed analysis of reduction rules based on monadic laws and provides factorization results to understand normalization in the computational core.

Findings

Reduction rules derived from monadic laws are complex and require careful analysis.

Factorization results help clarify the relationship between returning values and normal forms.

Strategies for normalization are examined in the context of the computational core.

Abstract

We study the reduction in a lambda-calculus derived from Moggi's computational one, that we call the computational core. The reduction relation consists of rules obtained by orienting three monadic laws. Such laws, in particular associativity and identity, introduce intricacies in the operational analysis. We investigate the central notions of returning a value versus having a normal form, and address the question of normalizing strategies. Our analysis relies on factorization results.