A call-by-value lambda-calculus with lists and control

TL;DR

This paper introduces a simply typed call-by-value lambda calculus that incorporates control operators, list data types, and primitive recursion, with formal proofs of key properties ensuring its theoretical soundness.

Contribution

It extends existing calculi by integrating data types and control operators into a call-by-value setting with formal correctness proofs.

Findings

System satisfies subject reduction and progress

System is confluent for untyped terms

Well-typed terms are strongly normalizing

Abstract

Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also include data types. As a step into that direction, this paper defines a simply typed call-by-value lambda calculus with the control operators catch and throw, a data type of lists, and an operator for primitive recursion (a la Goedel's T). We prove that our system satisfies subject reduction, progress, confluence for untyped terms, and strong normalization for well-typed terms.