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Add Algebra.Bundles.SuccessorSet and related records #2273

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@jamesmckinna

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@jamesmckinna

Previously, on #2264 I raised the following discussion point:
we currently have the following choices for an Algebra with a distinguished point (0#? or ‵zero, because it's a 'quoted' version of Agda.Builtin.Nat.zero?)) and unary operation (suc#, or _+1#, or ‵suc because it's a 'quoted' version of Agda.Builtin.Nat.suc?):

  • PointedUnary? ... the universal algebra way;
  • NNO/NaturalNumber(s)Object? ... the Lawvere/categorical way; may he rest in peace, I've been completely ignoring initiality...
  • SuccessorSet? ... the Dedekind way

Can we agree on 'sensible' choices from this palette?

Originally posted by @jamesmckinna in #2264 (comment)

So this issue to is to offer the following specimen design/implementation, for discussion (and is tantamount to a fully articulated PR, moreover purely mechanically derivable by analogy with all the others). I'd be happy to change any of the names, in the spirit of the above original comment. Against @JacquesCarette I'd hold out for NNO, but

I'll go for SuccessorSet as a reasonable, if still verbose, first choice...

(deleted: previous content, invalid thanks to my stupidity...)

Activity

changed the title [-]Add `Algebra.Bundles.NNO` and related modules[/-] [+]Add `Algebra.Bundles.NNO` and related records[/+] on Feb 3, 2024
added a commit that references this issue on Feb 3, 2024

[fix agda#2273] Add `NNO`-related modules

99bd01e
linked a pull request that will close this issue [fix #2273] Add `NNO`-related modules #2275on Feb 3, 2024
changed the title [-]Add `Algebra.Bundles.NNO` and related records[/-] [+]Add `Algebra.Bundles.SuccessorSet` and related records[/+] on Feb 4, 2024
added a commit that references this issue on Apr 4, 2024

[fixes #2273] Add `SuccessorSet` and associated boilerplate (#2277)

21b7243
added a commit that references this issue on Jul 10, 2024

[fixes #2273] Add `SuccessorSet` and associated boilerplate (#2277)

b7bc4f7
added a commit that references this issue on Sep 7, 2024
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        Add `Algebra.Bundles.SuccessorSet` and related records · Issue #2273 · agda/agda-stdlib