Abstract
Formal libraries, especially large ones, usually employ modularity to build and maintain large theories efficiently. Although the techniques used to achieve modularity vary between systems, most of them can be understood as operations in the category of theories and theory morphisms. This yields a representation of libraries as diagrams in this category, with all theory-forming operations extending the diagram.
However, as libraries grow even bigger, it is starting to become important to build these diagrams modularly as well, i.e., we need languages and tools that support computing entire diagrams at once. A simple example would be to systematically apply the same operation to all theories in a diagram and return both the new diagram and the morphisms that relate the old one to the new one.
In this work, we introduce such diagram combinators as an extension to the MMT language and tool. We provide many important combinators, and our extension allows library developers to define arbitrary new ones. We evaluate our framework by building a library of algebraic theories in an extremely compact way.
The authors were supported by DFG grant RA-18723-1 OAF and EU grant Horizon 2020 ERI 676541 OpenDreamKit.
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The Scala code is available at https://github.com/UniFormal/MMT/blob/devel/src/mmt-lf/src/info/kwarc/mmt/moduleexpressions/Combinators.scala.
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Acknowledgment
We would like to thank Jacques Carette, William Farmer, and Michael Kohlhase for fruitful discussions.
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Rabe, F., Sharoda, Y. (2019). Diagram Combinators in MMT. In: Kaliszyk, C., Brady, E., Kohlhase, A., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2019. Lecture Notes in Computer Science(), vol 11617. Springer, Cham. https://doi.org/10.1007/978-3-030-23250-4_15
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