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MeTTa (Meta Type Talk) is a novel programming language created for use in theOpenCog Hyperon AGI system. It is designed as a meta-language with very basicand general facilities for handling symbols, groundings, variables, types,substitutions and pattern matching. Primitives exist for creating new typesystems and associated DSLs. IInformally, MeTTa is Hyperon's lowest-level"language of thought" -- the meta-language in which algorithms for learningmore particular knowledge representations, will operate, and in which thesealgorithms themselves may be represented. Here we explain how one might goabout formalizing the MeTTa language as a system of metagraph rewrite rules, anapproach that fits in naturally to the Hyperon framework given that thelatter's core component is a distributed metagraph knowledge store (theAtomspace). The metagraph rewrite rules constituting MeTTa programs can also berepresented as metagraphs, giving a natural model for MeTTa reflection andself-modifying code. Considering MeTTa programs that compute equivalencesbetween execution traces of other MeTTa programs allows us to model spaces ofMeTTa execution traces using Homotopy Type Theory. Considering the limit ofMeTTa programs mapping between execution traces of MeTTa programs that mapbetween execution traces of MeTTa programs that ..., we find that a given MeTTacodebase is effectively modeled as an infinity-groupoid, and the space of allMeTTa codebases as an (infinity,1)-topis This topos is basically the same asthe so-called "Ruliad" previously derived from rewrite rules on hypergraphs, ina discrete physics context. The formalization of MeTTA as metagraph rewriterules may also provide a useful framework for structuring the implementation ofefficient methods for pattern matching and equality inference within the MeTTainterpreter.

Reflective Metagraph Rewriting as a Foundation for an AGI "Language of Thought"