Maksym Sokhatskyi

Maksym Sokhatskyi
National Technical University of Ukraine Kyiv Polytechnic Institute ·  Department of Applied Mathematics

Master of Science
Groupoid Infinity

About

17
Publications
1,242
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3
Citations
Citations since 2017
17 Research Items
3 Citations
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Introduction
My current research interests focus on cubical type checkers and formalization of mathematics. I do love code in cubicaltt, but respect other HoTT provers, like yacctt, Arend, Agda, Lean, redtt, RedPRL. Also, I love to create programming languages. I received MSc with «Business Process Engine: Theory and Implementation». My BSc was «PL/1: The Language Design and Implementation». All my academic works are done under the supervision of Pavlo Maslianko.
Additional affiliations
January 2014 - May 2018
National Technical University of Ukraine Kyiv Polytechnic Institute
Position
  • PhD Student
Education
September 2016 - February 2022
September 1998 - May 2005

Publications

Publications (17)
Preprint
Full-text available
1 Нацiональний технiчний унiверситет України iм. Iгоря Сiкорського 11 грудня 2019 р. Анотацiя Ця стаття презентує диайн мови програмування PTS ∞ , iмплiмен-тацiї її типового верифiкатора, а також екстрактор байткоду для вiр-туальної машини Erlang вiд Ericsson. PTS ∞ це мова промiжного рiвня заснована на так званiй чистiй системi типiв, або системi...
Preprint
Full-text available
Background. The long road from pure type systems of AUTOMATH by de Bruijn to type checkers with homotopical core was made. This article touches only the formal Martin-Löf Type Theory (MLTT) core type system with Π and Σ types (that correspond to ∀ and ∃ quantifiers for mathematical reasoning) and identity type. Expressing the MLTT embedding in a ho...
Presentation
Full-text available
The HTS language proposed by Voevodsky exposes two different presheaf models of type theory: the inner one is homotopy type system presheaf that models HoTT and the outer one is traditional Martin-Löf type system presheaf that models set theory with UIP. The motivation behind this doubling is to have an ability to express semisemplicial types. Theo...
Thesis
Full-text available
Where FORMAL stands for system of formal languages up to homotopy type systems for doing formal math research, SYSTEM stands for runtime environment [which consists of CPS interpreter with AVX/GPU vectorization and SMP process calculus with intercore protocol] for mathematical/physical simulations and general purpose programming, and ONE stands for...
Presentation
Full-text available
Introduction to Formal Languages, its Design and Implementations. Three practial modern pure languages will be disclosed: Plutus (Haskell), Morte (Erlang), Formality (Rust).
Preprint
Full-text available
Each language implementation needs to be checked. The one of possible test cases for type checkers is the direct embedding of type theory model into the language of type checker. As types in Martin-Löf Type Theory are formulated by using 5 types of rules, we construct aliases for host language primitives and use type checker to prove theorems about...
Chapter
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This paper represents the very small part of the developed base library for homotopical prover based on Cubical Type Theory (CTT) announced in 2017. We demonstrate the usage of this library by showing how to build a constructive proof of heterogeneous equality, the simple and elegant formulation of the equality problem, that was impossible to achie...
Preprint
Full-text available
The purpose of this work is to clarify all topos definitions using type theory. Not much efforts was done to give all the examples, but one example, a topos on category of sets, is constructively presented at the finale. As this cricial example definition is used in presheaf definition, the construction of category of sets is a mandatory excercise...
Preprint
Full-text available
This paper presents the design of the Om language and an implementation of its type checker and bytecode extractor to Erlang. Om is an intermediate language based on a pure type system with the infinite number of universes, so it is known to be consistent in dependent type theory. This Om language is a core part of the language family for verificat...
Preprint
Full-text available
Here is presented destinctive points of Homotopy Type Theory as an extension of Martin-Löf Type Theory but without higher inductive types which will be given in the next issue. The fibrational (geometric) interpretation of equivalence type is introduced with following univalence releation between equivalence and Path equality. Groupoid (categorical...
Presentation
Full-text available
Homotopy Type Theory (HoTT) is the most advanced programming language in the domain of intersection of several theories: algebraic topology, homological algebra, higher category theory, mathematical logic, and theoretical computer science. That is why it can be considered as a language of space, as it can encode any existent mathematics. Speaker:...
Conference Paper
Full-text available
This paper represents the very small part of the developed base library for homotopical prover based on Cubical Type Theory (CTT) announced in 2017. We demonstrate the usage of this library by showing how to build a constructive proof of heterogeneous equality, the simple and elegant formulation of the equality problem, that was impossible to achie...
Conference Paper
Full-text available
This paper presents the design of the Om language and an implementation of its type checker and bytecode extractor to Erlang. Om is an intermediate language based on a pure type system with the infinite number of universes, so it is known to be consistent in dependent type theory. This Om language is a core part of the language family for verificat...

Network

Projects

Project (1)
Project
Systems Engineering of Functional Languages PTS, MLTT, CCHM, HTS and Base Libraries for Theorem Proving and Program Extraction in Total Dependent Type Theory.