A Metalanguage for Guarded Iteration

TL;DR

This paper introduces a generic metalanguage for guarded iteration that unifies various notions of recursion in programming languages, supported by categorical semantics and operational validation.

Contribution

It combines guardedness with call-by-value to create a unifying language for guarded and unguarded iteration with effects, supported by categorical semantics.

Findings

Categorical semantics for the metalanguage are developed.

A concrete operational semantics is provided for a specific instance.

Soundness and adequacy of the semantics are established.

Abstract

Notions of guardedness serve to delineate admissible recursive definitions in various settings in a compositional manner. In recent work, we have introduced an axiomatic notion of guardedness in symmetric monoidal categories, which serves as a unifying framework for various examples from program semantics, process algebra, and beyond. In the present paper, we propose a generic metalanguage for guarded iteration based on combining this notion with the fine-grain call-by-value paradigm, which we intend as a unifying programming language for guarded and unguarded iteration in the presence of computational effects. We give a generic (categorical) semantics of this language over a suitable class of strong monads supporting guarded iteration, and show it to be in touch with the standard operational behaviour of iteration by giving a concrete big-step operational semantics for a certain specific instance of the metalanguage and establishing soundness and (computational) adequacy for this case.