CPU-less parallel execution of lambda calculus in digital logic

Abstract: 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.