Extending CPU-less parallel execution of lambda calculus in digital logic with lists and arithmetic

TL;DR

This paper explores extending CPU-less digital logic execution of lambda calculus with lists and arithmetic primitives, aiming to improve practicality by reducing execution time and resource usage.

Contribution

It introduces new structures and algorithms for primitive extensions, demonstrating their effectiveness in enhancing CPU-less lambda calculus execution.

Findings

Substantial reductions in execution time

Decreased node usage in digital logic implementation

Successful evaluation of diverse lambda expressions

Abstract

Computer architecture is searching for new ways to make use of increasingly available digital logic without the serial bottlenecks of CPU-based design. Recent work has demonstrated a fully CPU-less approach to executing functional programs, by exploiting their inherent parallelisability to compile them directly into parallel digital logic. This work uses lambda-calculus as a hyper simple functional language to prove the concept, but is impractical for real-world programming due to the well-known inefficiencies of pure lambda$-calculus. It is common in language design to extend basic lambda-calculus with additional primitives to short-cut common tasks such as arithmetic and lists. In this work, we build upon our previous research to examine how such extensions may be applied to CPU-less functional execution in digital logic, with the objective of advancing the approach toward practical implementation. We present a set of structures and algorithms for representing new primitives, describe a systematic process for selecting, implementing, and evaluating them, and demonstrate substantial reductions in execution time and node usage. These improvements are implemented in an open-source system, which is shown to correctly evaluate a range of representative lambda expressions.