Arend is a new theorem prover that have been developed at JetBrains
for quite some time. We are proud to announce
that the first version of the language was released! To learn more about
Arend, visit our site .
Arend is based on a version of homotopy type theory that includes some of
the cubical features. In particular, it has native higher inductive types,
including higher inductive-inductive types. It also has other features
which are necessary for a theorem prover such as universe polymorphism and
class system. We believe that a theorem prover should be convenient to use.
That is why we also developed a plugin for IntelliJ IDEA
that turns it into a full-fledged IDE for
the Arend language. It implements many standard features such as syntax
highlighting, completion, auto import, and auto formatting. It also has
some language-specific features such as incremental typechecking and
various refactoring tools.
To learn more about Arend, you can check out the documentation
. You can also learn a lot from
studying the standard library . It
implements some basic algebra, including localization of rings, and
homotopy theory, including joins, modalities, and localization of types.
Frequently asked questions (that nobody asked):
- Why do we need another theorem prover? We believe that a theorem
prover should be convenient to use. This means that it should have an IDE
comparable to that of mainstream programming languages. That is why we
implemented IntelliJ Arend
. This also means
that the underlying theory should be powerful and expressive. That is why
Arend is based on homotopy type theory and has features such as an
impredicative type of propositions and a powerful class system.
- Does Arend have tactics? Not yet, but we are working on it.
- Does Arend have the canonicity property, i.e. does it evaluate closed
expressions to their canonical forms? No, but it computes more terms than
ordinary homotopy type theory, which makes it more convenient in many
aspects.
If you want to know about language updates, you can follow us on twitter
. Questions, suggestions, and comments are
welcome at google groups
.
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