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

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 (nLab authors, 2024), unusual in its proximity to the mathematical abstraction. We discuss the mathematics, the purpose, and the significance of demonstrating vector-symbolic architectures' Cartesian-closedness, as well as the importance of explicitly including cleanup memories in the specification of the architecture.