[ draft ] add Galois connections and residuated lattices. #1760
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This PR is not ready to be merged. I think the contents are useful, but there are some problems with the organization of the code (what goes into which module etc.) and I need some help/feedback to address these. In particular:
I don't know where the definition and properties of Galois connections should go. They involve both relations/orders and (monotone) functions, so maybe
Relation.Binary
? If so, where exactly? For now, I put them underFunction
.Currently, the definition of Galois connection and their properties are in the same file. Following the rest of the stdlib, the properties should probably go into a separate file, but I'm not sure where (depends on point 1).
There are definitions for (right-)residuated pomonoids and (right-)residuated semilattices. I put them all in the same file, in the
Algebra.Ordered
hierarchy, but maybe the semilattices should go intoRelation.Binary.Lattice
hierarchy?Residuated structures and bundles currently live in the same file. To be consistent with the library, these should be split, but I'm not sure where the resulting modules should live (depends on point 3).
The definitions of the residuated structures are biased in several ways:
In theory, this is sufficient, but it may be nicer to have unbiased versions for symmetry. But I don't know how much symmetry is enough symmetry and where to put the biased versions, etc. (This all depends on points 3 and 4).
Finally, there are properties of the residuated structures, in separate modules, but these may be in the wrong place too (depends on 3).