Hey Pentti, We Did It!: A Fully Vector-Symbolic Lisp

TL;DR

This paper demonstrates a fully vector-symbolic Lisp implementation using holographic reduced representations, showing that such architectures can achieve Turing-completeness and Cartesian-closure, with implications for cognitive modeling.

Contribution

It provides the first complete vector-symbolic Lisp implementation, including elementary functions and lambda expressions, highlighting the mathematical and computational significance.

Findings

Vector-symbolic architectures can implement Turing-complete Lisp functions.

The implementation uses holographic reduced representations with cleanup memory.

Demonstrates Cartesian-closure in vector-symbolic systems.

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.