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Catlab.jl is a framework for applied and computational category theory, written in the Julia language. Catlab provides a programming library and interactive interface for applications of category theory to scientific and engineering fields. It emphasizes monoidal categories due to their wide applicability but can support any categorical structure that is formalizable as a generalized algebraic theory. First and foremost, Catlab provides data structures, algorithms, and serialization for applied category theory. Macros offer a convenient syntax for specifying categorical doctrines and type-safe symbolic manipulation systems. Wiring diagrams (aka string diagrams) are supported through specialized data structures and can be serialized to and from GraphML (an XML-based format) and JSON.
Features
- Programming library
- Interactive computing environment
- Computer algebra system:
- Catlab can also be used interactively in Jupyter notebooks
- Catlab will serve as a computer algebra system for categorical algebra
- Unlike most computer algebra systems, all expressions are typed using fragment of dependent type theory called generalized algebraic theories
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