Symbolic Informalization: Fluent, Productive, Multilingual

2026-06-15

AI Summary

This work addresses the challenge of reliably translating formalized mathematics into natural language that is both precise and readable. It proposes a symbol-to-text framework based on an intermediate language architecture, extending conventional syntactic sugar mechanisms to support general mathematical expressions. By unifying formal systems such as Agda, Lean, and Rocq through Dedukti and integrating Grammatical Framework (GF), the approach ensures grammatical correctness and expressive diversity across multiple languages. The resulting system, Informath, generates fluent, accurate, and multilingual mathematical narratives at relatively low development cost, effectively rendering AI-generated or automatically formalized proofs into comprehensible expository text.

Abstract

Symbolic informalization enables a reliable conversion of formal mathematics to natural language. It has the potential to make machine-checked content human-readable without loss of precision. In a traditional proof system usage, symbolic informalization generalizes the limited mechanisms of syntactic sugar into the ordinary language of mathematics. In a setting where proofs are constructed by artificial intelligence and autoformalization, symbolic informalization can explain what precisely has been constructed. This paper outlines the project Informath, which aims to show how symbolic informalization can produce fluent text with a reasonable development effort and address multiple formal and natural languages. Informath is based on an interlingual architecture, where Dedukti works as a hub between different proof systems (Agda, Lean, Rocq) and Grammatical Framework (GF) takes care of linguistic correctness and variation in different natural languages.

Problem

• symbolic informalization
• formal mathematics
• natural language generation
• multilingual
• human-readable proofs

Innovation

• Symbolic Informalization
• Interlingual Architecture
• Dedukti
• Grammatical Framework
• Autoformalization