Work

On the Formal Metatheory of the Pure Type Systems using One-sorted Variable Names and Multiple Substitutions

Year: 2025

Type: article

Abstract: We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions.We then formalize the Pure Type Systems along some fundamental metatheoretic properties: weakening, syntactic validity, closure under alpha-conversion and substitution.Finally, we compare our formalization with others related.The whole development has been machine-checked using the Agda system.Our work demonstrates that the mechanization of dependent type theory by using conventional syntax and without identifying alpha-convertible lambda-terms is feasible.

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.431.2

Author: Sebastián Urciuoli

Institution: Universidad ORT Uruguay

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Agencia Nacional de Investigación e Innovación

OpenAlex ID: W4415102319