Research ArticleOpen accessIn the keywordsFormalizing Relations in Type TheoryFarida KachapovaTypetheory 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 … …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 29 Oct 2022 · 5,778 accessesView PDFCite
Research ArticleOpen accessIn the keywordsFormalizing Probability Concepts in a Type TheoryFarida KachapovaIn this paper we formalize some fundamental concepts of probability theory such as the axiomatic definition of probability space, random variables and their characteristics, in the Calculus of Inductive Constructions, which is a variant of type theory and the foundation for the proof assistant COQ. In a type theory every term and proposition should have a type, so in our … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 12 Nov 2018 · 8,547 accessesView PDFCite