Stepping Lazy Programs

TL;DR

This paper introduces an algebraic program stepper for lazy functional programs, providing a mathematically clear visualization of evaluation that aids understanding, especially for novices, by representing lazy evaluation as parallel rewriting.

Contribution

The paper presents a novel algebraic stepper tool that visualizes lazy evaluation as a mathematical rewriting sequence, bridging existing debugging approaches and enhancing comprehension.

Findings

The algebraic stepper accurately reconstructs standard lazy evaluation sequences.

Lazy semantics as parallel rewriting offers a new perspective on lazy evaluation.

The tool is particularly useful for novice programmers learning lazy evaluation.

Abstract

Debugging lazy functional programs poses serious challenges. In support of the "stop, examine, and resume" debugging style of imperative languages, some debugging tools abandon lazy evaluation. Other debuggers preserve laziness but present it in a way that may confuse programmers because the focus of evaluation jumps around in a seemingly random manner. In this paper, we introduce a supplemental tool, the algebraic program stepper. An algebraic stepper shows computation as a mathematical calculation. Algebraic stepping could be particularly useful for novice programmers or programmers new to lazy programming. Mathematically speaking, an algebraic stepper renders computation as the standard rewriting sequence of a lazy lambda-calculus. Our novel lazy semantics introduces lazy evaluation as a form of parallel program rewriting. It represents a compromise between Launchbury's store-based semantics and a simple, axiomatic description of lazy computation as sharing-via-parameters. Finally, we prove that the stepper's run-time machinery correctly reconstructs the standard rewriting sequence.