Hey Pentti, We Did It!: A Fully Vector-Symbolic Lisp
Eilene Tomkins-Flanagan, Mary A. Kelly
TL;DR
The paper demonstrates that a fully vector-symbolic implementation of Lisp 1.5 is achievable by mapping Lisp primitives and lambda expressions to VSA operations, using HRR-style vectors and explicit cleanup memories to enable retrieval. Grounded in Cartesian closed category theory, it argues that VSAs provide a minimal yet powerful substrate capable of representing arbitrary Lisp programs, thereby achieving Turing-completeness within a distributed representation. It further analyzes cleanup-memory architectures, advocating modern Hopfield networks for their high storage capacity while acknowledging tradeoffs in encoding and interference. By connecting these ideas to broader theories of cognition and general intelligence, the work highlights how memory can encode arbitrary programs and how brain-inspired syntactic manipulation might scale to complex cognitive tasks. Overall, the work advances the integration of symbolic computation with vector-based representations, informing memory-design choices for VSA-based reasoning systems and offering a path toward brain-inspired, programmable neural architectures.
Abstract
Kanerva (2014) suggested that it would be possible to construct a complete Lisp out of a vector-symbolic architecture. We present the general form of a vector-symbolic representation of the five Lisp elementary functions, lambda expressions, and other auxiliary functions, found in the Lisp 1.5 specification McCarthy (1960), which is near minimal and sufficient for Turing-completeness. Our specific implementation uses holographic reduced representations Plate (1995), with a lookup table cleanup memory. Lisp, as all Turing-complete languages, is a Cartesian closed category, unusual in its proximity to the mathematical abstraction. We discuss the mathematics, the purpose, and the significance of demonstrating vector-symbolic architectures' Cartesian-closure, as well as the importance of explicitly including cleanup memories in the specification of the architecture.