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A library of abstract interfaces for mathematical structures in Coq.
Coq Other
branch: master
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categories patch by Jason for case sensitive file systems
functors patch by Jason for case sensitive file systems
implementations patch by Jason for case sensitive file systems
interfaces
misc
orders patch by Jason for case sensitive file systems
quote
site_scons/site_tools SCons build system added back
theory patch by Jason for case sensitive file systems
varieties patch by Jason for case sensitive file systems
.gitignore Merge branch 'master' of https://github.com/math-classes/math-classes
LICENSE Add papers and talks.
Make.in
README.md
SConscript
SConstruct SCons build system added back
configure.sh

README.md

Compilation

Known to compile with Coq 8.4.pl3.

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.

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