• Corpus ID: 244117435

Birkhoff's Completeness Theorem for Multi-Sorted Algebras Formalized in Agda

@article{Abel2021BirkhoffsCT,
  title={Birkhoff's Completeness Theorem for Multi-Sorted Algebras Formalized in Agda},
  author={Andreas Abel},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.07936}
}

• Andreas Abel
• Published 15 November 2021
• Mathematics
• ArXiv

This document provides a formal proof of Birkhoff’s completeness theorem for multi-sorted algebras which states that any equational entailment valid in all models is also provable in the equational theory. More precisely, if a certain equation is valid in all models that validate a fixed set of equations, then this equation is derivable from that set using the proof rules for a congruence. The proof has been formalized in Agda version 2.6.2 with the Agda Standard Library version 1.7 and this document reproduces the commented Agda code.