Harry Fitchett | Searcharxiv

arXiv2026

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

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.

cs.AR↗

arXiv2026

CPU-less parallel execution of lambda calculus in digital logic

While transistor density is still increasing, clock speeds are not, motivating the search for new parallel architectures. One approach is to completely abandon the concept of CPU -- and thus serial imperative programming -- and instead to specify and execute tasks in parallel, compiling from programming languages to data flow digital logic. It is well-known that pure functional languages are inherently parallel, due to the Church-Rosser theorem, and CPU-based parallel compilers exist for many functional languages. However, these still rely on conventional CPUs and their von Neumann bottlenecks. An alternative is to compile functional languages directly into digital logic to maximize available parallelism. It is difficult to work with complete modern functional languages due to their many features, so we demonstrate a proof-of-concept system using lambda calculus as the source language and compiling to digital logic. We show how functional hardware can be tailored to a simplistic functional language, forming the ground for a new model of CPU-less functional computation. At the algorithmic level, we use a tree-based representation, with data localized within nodes and communicated data passed between them. This is implemented by physical digital logic blocks corresponding to nodes, and buses enabling message passing. Node types and behaviors correspond to lambda grammar forms, and beta-reductions are performed in parallel allowing branches independent from one another to perform transformations simultaneously. As evidence for this approach, we present an implementation, along with simulation results, showcasing successful execution of lambda expressions. This suggests that the approach could be scaled to larger functional languages. Successful execution of a test suite of lambda expressions suggests that the approach could be scaled to larger functional languages.

cs.DC↗