用向量符号架构实现了一个完整的、可计算的Lisp语言
Hey Pentti, We Did It!: A Fully Vector-Symbolic Lisp
- 用全向量符号表示五种基础函数和lambda表达式
- 基于霍格兰德表示法，实现近最小但图灵完备的Lisp系统
- 首次显式引入清理记忆模块，支持复杂符号运算
Kanerva（2014）曾提出，可基于向量符号架构构建完整的Lisp。本文给出了符合Lisp 1.5规范（McCarthy, 1960）的五种基本函数、lambda表达式及其他辅助函数的向量符号表示形式，该形式近似最小且具备图灵完备性。具体实现采用霍格兰德还原表示（Holographic Reduced Representations, HRR）并引入查表式清理记忆模块。由于所有图灵完备语言本质上是笛卡尔闭范畴，而Lisp在结构上最贴近数学抽象，因此本工作展示了向量符号架构具备笛卡尔闭性。我们还讨论了这一性质的数学意义、设计目的，以及在架构规范中明确包含清理记忆的重要性。
原文摘要 · Abstract (English)
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.
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