This article presents the theorem prover Arend (arXiv:2610.27264v2) developed at JetBrains Research. The Arend language is designed to facilitate the formalization of mathematics within the univalent foundations framework, with an emphasis on constructive mathematics. It is built on a variant of homotopy type theory equipped with cubical syntax that aligns closely with Martin‑Löf Type Theory (MLTT) while retaining some practical computational properties.
One of the most notable features of Arend is its powerful system of classes and records, which supports subsumptive subtyping, partial implementations, and anonymous extensions, offering extensive flexibility for building hierarchical definitions.
Formalization is streamlined by the IntelliJ Arend plugin, which turns IntelliJ IDEA into a full‑featured integrated development environment (IDE) for Arend, providing syntax highlighting, code completion, and interactive checking.
The main Arend library, arend‑lib, contains formalizations in constructive algebra, topology, and synthetic homotopy theory, illustrating the language’s applicability to real mathematical research.
Review