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Cubical Alternatives
Similar projects and alternatives to cubical
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redtt
"Between the darkness and the dawn, a red cube rises!": a proof assistant for cartesian cubical type theory
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WorkOS
The modern identity platform for B2B SaaS. The APIs are flexible and easy-to-use, supporting authentication, user identity, and complex enterprise features like SSO and SCIM provisioning.
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UniMath
This coq library aims to formalize a substantial body of mathematics using the univalent point of view.
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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
cubical reviews and mentions
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Will Computers Redefine the Roots of Math?
For those interested in formalisation of homotopy type theory, there are several (more or less) active and developed libraries. To mention a few:
UniMath (https://github.com/UniMath/UniMath, mentioned in the article)
Coq-HoTT (https://github.com/HoTT/Coq-HoTT)
agda-unimath (https://unimath.github.io/agda-unimath/)
cubical agda (https://github.com/agda/cubical)
All of these are open to contributions, and there are lots of useful basic things that haven't been done and which I think would make excellent semester projects for a cs/math undergrad (for example).
- Homotopy Type Theory
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Cubical Type Theory?
In the case of transpension, it seems like one of the uses is proving something about a path in inductive types by cases on an abstract point along that path. For instance, right now, the way that you prove that a path in A + B is either a path in A or a path in B is to define a family by cases and then transport like here. But I think transpension might let you just do cases on a formal intermediate point directly, which would be much simpler.
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agda/cubical is an open source project licensed under GNU General Public License v3.0 or later which is an OSI approved license.
The primary programming language of cubical is Agda.