Just Type It in Isabelle! AI Agents Drafting, Mechanizing, and Generalizing from Human Hints

2026-04-17

AI Summary

This work addresses the problem of generating complete and minimal type annotations for rank-one polymorphic λ-calculus terms in Isabelle, ensuring semantic consistency under reparsing and type inference. We propose a human–AI collaborative workflow that integrates handcrafted proofs by human experts with large language model (LLM)-driven automated formalization, guided by human-provided prompts to steer AI-based optimization and generalization. This approach constitutes the first systematic integration of human intuition and AI-powered formal reasoning, enabling a metatheoretic analysis, a complete specification, and machine-verified correctness of the type annotation problem within Isabelle/HOL. The methodology substantially enhances both the efficiency and generalizability of formal proofs.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Type annotations are essential when printing terms in a way that preserves their meaning under reparsing and type inference. We study the problem of complete and minimal type annotations for rank-one polymorphic $λ$-calculus terms, as used in Isabelle. Building on prior work by Smolka, Blanchette et al., we give a metatheoretical account of the problem, with a full formal specification and proofs, and formalize it in Isabelle/HOL. Our development is a series of experiments featuring human-driven and AI-driven formalization workflows: a human and an LLM-powered AI agent independently produce pen-and-paper proofs, and the AI agent autoformalizes both in Isabelle, with further human-hinted AI interventions refining and generalizing the development.

Problem

• type annotations
• rank-one polymorphism
• λ-calculus
• Isabelle
• type inference

Innovation

• type annotations
• Isabelle/HOL
• AI-driven formalization
• rank-one polymorphism
• autoformalization