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Mechanize the Algebra hierarchy #2287

@Taneb

Description

@Taneb

Many of the modules under Algebra (e.g. Algebra.Structures, Algebra.Bundles, Algebra.Morphism.Structures...) are highly structured and repetitive. This makes it a lot of work to add something new, and very easy to miss things. We should come up with a way to mechanize this and generate this portion of the library from a more concise form somehow.

Considerations

  • Concision: we want to be able to generate large amounts of the library's functionality from a small specification
  • Completeness: we want to take care that anything we want in these modules, we can still have in these modules.
  • Ease of understanding: the documentation of this library, such as it is, is in the form of source code listings. We want users of the library to still be able to figure out what we provide
  • Ease of installation: the library is generally installed by copying it verbatim somewhere onto the system. We don't have a way to run, say, a Haskell program at installation time.
  • Extensibility: if we want to add a new form of algebraic structure, we should be able to do so easily. If we want to add a new expression of algebraic structures (e.g. morphism bundles, or finite algebraic structures), we should be able to do that easily also.

Current state of affairs

We have three modules of "structures", containing records of laws for various algebraic structures, parameterized by their equivalence relation and operations. We have three modules of "bundles" containing records bundling the equivalence relation, operations, and the law structure, and three modules of "raw bundles" which omit the law structure. We have three modules of morphism structure, each of which is parameterized on the raw bundle. We have many modules of various properties of structures and morphisms, which may be harder to mechanize.

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