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

arXiv: https://arxiv.org/abs/2510.17889 · HTML: https://mlsanity.com/paper/2510.17889/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 18 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Consciousness in Artificial Intelligence: Insights from the Science of Consciousness](https://mlsanity.com/paper/2308.08708/) (2023)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges](https://mlsanity.com/paper/2112.15424/) (2021)
- [Codebook Features: Sparse and Discrete Interpretability for Neural Networks](https://mlsanity.com/paper/2310.17230/) (2023)
- [Neurocompositional computing: From the Central Paradox of Cognition to a new generation of AI systems](https://mlsanity.com/paper/2205.01128/) (2022)
- [Torchhd: An Open Source Python Library to Support Research on Hyperdimensional Computing and Vector Symbolic Architectures](https://mlsanity.com/paper/2205.09208/) (2022)
- [Maze Learning using a Hyperdimensional Predictive Processing Cognitive Architecture](https://mlsanity.com/paper/2204.00619/) (2022)

## Built on by (most cited first, 2 of 2)

- [Vector Symbolic Algebras for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2511.08747/) (2025)
- [Hey Pentti, We Did (More of) It!: A Vector-Symbolic Lisp With Residue Arithmetic](https://mlsanity.com/paper/2511.08767/) (2025)

## Abstract (arXiv)

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.