Implementing Dependent Type Theory Inhabitation and Unification
🤖 AI Summary
This work addresses the undecidability of inhabitation and unification in dependent type theory by proposing and implementing a solver named Canonical-min. Built upon a mere 185 lines of Lean code, the solver leverages a monadic transformation framework to refactor a type checker into an efficient solver, achieving both soundness and completeness despite its minimal implementation. The contributions include the first realization of a sound and complete inhabitation and unification solver within such a compact codebase, as well as the creation of DTTBench—the first benchmark suite specifically designed for evaluating dependent type inhabitation solvers—thereby establishing a standardized foundation for future research in this area.
Application Category
📝 Abstract
Dependent type theory is the foundation of many modern proof assistants. Inhabitation and unification are undecidable problems that are useful for theorem proving and program synthesis. We introduce Canonical-min, a sound and complete solver for inhabitation and unification in dependent type theory, implemented in 185 lines of Lean code. This paper describes a novel implementation of dependent type theory and a monadic framework to transform the type checker into a performant solver. Finally, we introduce DTTBench, a benchmark for type inhabitation in dependent type theory.
Problem
Research questions and friction points this paper is trying to address.
dependent type theory
inhabitation
unification
theorem proving
program synthesis
Innovation
Methods, ideas, or system contributions that make the work stand out.
dependent type theory
inhabitation
unification
monadic framework
DTTBench
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