[ refactor ] (Re)define (Is)TightApartness and (Is)HeytingCommutativeRing/(Is)HeytingField
#2588
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| @@ -36,8 +37,19 @@ open SetoidProperties setoid | |||
| ; cotrans = ≉-cotrans | |||
| } | |||
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| ≉-tight : Tight _≈_ _≉_ | |||
| ≉-tight x y = decidable-stable (x ≟ y) | |||
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Missing addition from Changelog.
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yeah, I wasn't sure how to record this... it's a redefinition, rather than an addition, because the definition of Tight has been changed in Relation.Binary.Definitions to drop the redundant second conjunct, which is equivalent to Irreflexive, as noted on the issue.
What's the best way to do this? (See latest commits for one attempt...)
| @@ -17,6 +17,10 @@ Non-backwards compatible changes | |||
| significantly faster. However, its reduction behaviour on open terms may have | |||
| changed. | |||
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| * The definitions of `Algebra.Structures.IsHeyting*` and | |||
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I know this is a draft, but in the final version it would be good to explain broadly what the refactorings actually are here?
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See latest commits, hopefully enough, but not too much, detail now!
… re-exported by `Algebra.Properties.Ring`
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I think this is now ready for review! Many thanks to @MatthewDaggitt for the pre-review, hopefully the latest round of (many!) commits have put things on a more sound footing. As in updated preamble above:
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| x#0y#0→xy#0 : x # 0# → y # 0# → x * y # 0# | ||
| x#0y#0→xy#0 {x} {y} x#0 y#0 = helper (#⇒invertible x#0) (#⇒invertible y#0) |
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@JacquesCarette 's wanting to refactor the proofs (and FTR, largely inherited from the original PR #1968 ...)
It occurs to me that some (all?) of these arguments could be refactored by going via Algebra.Properties.CancellativeCommutativeSemiring, after establishing the relevant structure/bundle?
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Er... no, in fact. Those properties require Decidable _≈_, and maybe could be simplified to consider only Tight _≈_ _≉_, but I'm not going to push my luck...
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Could be. I was thinking of analogs to the elim and cancel reasoning combinators of agda-categories. While at it, I would have ported push/pull (but renamed them) too. Many of these already work on Monoid.
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Indeed: please raise a PR addressing #2288 !
Hopefully the discussion on #2587 clarifies this? |
Fixes #2587
Adds:
Algebra.Apartness.Properties.HeytingField, supersedingAlgebra.Apartness.Properties.HeytingCommutativeRingNB:
Algebra.Properties.Ring(or evenAlgebra.Properties.AbelianGroup...) DONE properties moved; module NOT deprecatedData.Rational.Unnormalised.Propertiesshould be refactored to make use ofRelation.Binary.Properties.DecSetoidfor its(Is)*ApartnessRelationdefinitions DONEIssue:
bugfix of the various APIs involved?) or v3.0 (as a largebreakingchange?)Apartnessvs.TightApartness, etc. but that the fundamental distinction should be between*CommutativeRingand*Field(and yes: perhapsHeytingLocalRingwould have been better, but see also DefineLocalRing#2219 ) in that the latter should have inverses, while the former need not. The existing APIs make the distinction turn on whether the apartness is tight or not, which seems 'wrong'... even to the point of being abug?RFC from @cspollard and @bsaul ...