Formalizing Relations in Type Theory
- 1 Department of Mathematical Sciences, Auckland University of Technology, New Zealand
Abstract
Typetheory plays an important role in the foundations of mathematics as a frameworkfor formalizing mathematics and a base for proof assistants providingsemi-automatic proof checking and construction. Derivation of each theorem intype theory results in a formal term encapsulating the whole proof process.This study uses a variant of type theory, namely the Calculus of Constructionswith Definitions, to formalize the standardtheory of binary relations. This includes basic operations on relations,criteria for special properties of relations, invariance of these propertiesunder the basic operations, equivalence relation, well-ordering, andtransfinite induction. Definitions and proofs are presented as flag-stylederivations.
DOI: https://doi.org/10.3844/jmssp.2022.148.162
Copyright: © 2022 Farida Kachapova. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Type Theory
- Calculus of Constructions
- Binary Relation
- Transfinite Induction
- Flag-Style Derivation