Toward SMT-Based Refinement Types in Agda

TL;DR

This paper explores integrating SMT-based refinement types into Agda to simplify proof development with dependent types, aiming to combine the strengths of both approaches for more efficient theorem proving.

Contribution

It introduces a novel approach to incorporate SMT-based refinement types into Agda, enhancing usability and proof automation in dependently-typed programming.

Findings

Proposed a framework for SMT refinement types in Agda

Demonstrated potential improvements in proof development efficiency

Outlined integration strategies for SMT solvers with Agda

Abstract

Dependent types offer great versatility and power, but developing proofs with them can be tedious and requires considerable human guidance. We propose to integrate Satisfiability Modulo Theories (SMT)-based refinement types into the dependently-typed language Agda in an effort to ease some of the burden of programming with dependent types and combine the strengths of the two approaches to mechanized theorem proving.