Hey Pentti, We Did It!: A Fully Vector-Symbolic Lisp
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918164570308608 |
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| author | Tomkins-Flanagan, Eilene Kelly, Mary A. |
| author_facet | Tomkins-Flanagan, Eilene Kelly, Mary A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hey Pentti, We Did It!: A Fully Vector-Symbolic Lisp Tomkins-Flanagan, Eilene Kelly, Mary A. Programming Languages Artificial Intelligence 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. |
| title | Hey Pentti, We Did It!: A Fully Vector-Symbolic Lisp |
| topic | Programming Languages Artificial Intelligence |
| url | https://arxiv.org/abs/2510.17889 |