A library of abstract interfaces for mathematical structures in Coq.
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categories
functors
implementations
interfaces
misc
orders
quote
site_scons/site_tools
theory
varieties
.gitignore
LICENSE
Make
Make.in
Makefile
README.md
SConscript
SConstruct
configure.sh

README.md

Compilation

Known to compile with Coq 8.5.

Directory structure

categories/

Proofs that certain structures form categories.

functors/

interfaces/

Definitions of abstract interfaces/structures.

implementations/

Definitions of concrete data structures and algorithms, and proofs that they are instances of certain structures (i.e. implement certain interfaces).

misc/

Miscellaneous things.

orders/

Theory about orders on different structures.

quote/

Prototype implementation of type class based quoting. To be integrated.

theory/

Proofs of properties of structures.

varieties/

Proofs that certain structures are varieties, and translation to/from type classes dedicated to these structures (defined in interfaces/).

The reason we treat categories and varieties differently from other structures (like groups and rings) is that they are like meta-interfaces whose implementations are not concrete data structures and algorithms but are themselves abstract structures.

To be able to distinguish the various arrows, we recommend using a variable width font.