[ add ] Setoid from PartialSetoid
#2816
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jamesmckinna
added
the
subsets
| @@ -45,3 +53,37 @@ partial-reflexiveˡ p ≡.refl = partial-reflˡ p | |||
| partial-reflexiveʳ : x ≈ y → y ≡ z → y ≈ z | |||
| partial-reflexiveʳ p ≡.refl = partial-reflʳ p | |||
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| ------------------------------------------------------------------------ | |||
| -- Setoids from partial setoids | |||
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My instinct would be to put all of these in a (named) module rather than adding more things to the exported namespace of this module. That would also obviate the need for the awkward names with subscripts.
Also: definitely a construction. In fact, why not build the Setoid bundle directly?
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Are you saying that I 'just' build a value of type Setoid, and not explicitly define all the other fields at top-level?
I'm not quite sure what you mean otherwise, but it would be good to be clear...
Our custom to date seems to be to such structures/bundle explicitly piece-by-piece, but my suggestion in #2391 was that, at least for additional structure, that we could apply a Construct, and then publicly re-open it to expose its subfields. But that's not the same as making a Construct definition from scratch, as here?
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In any case, will move to Relation.Binary.Construct.SetoidFromPartialSetoid, unless a better name is available/recommended?
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Or did you mean to build the relevant Function.Bundles object(s) directly from isRelHomomorphism? That's not possible, precisely because the Function hierarchy is based on Setoids as source and target, ... and we only have the former here!
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Are you saying that I 'just' build a value of type Setoid, and not explicitly define all the other fields at top-level?
Yes. Because the pieces are so trivial.
Having all the pieces exposed in SetoidFromPartialSetoid does make sense. It's just pollution here.
| Carrier = Σ S.Carrier λ x → x S.≈ x | ||
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| _≈_ : Rel Carrier _ | ||
| x≈x@(x , _) ≈ y≈y@(y , _) = x S.≈ y |
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x ≈ y = proj₁ x S.≈ proj₁ y
? Or even
_≈_ = S._≈_ on proj₁
I certainly don't like binding names that are not used on the rhs as you do here.
This tackles one version of how to develop 'subsetoid's via PERs. Cf. #2814
Not necessarily the 'right' way to go, but still functionality which may be useful in the future
UPDATED: to live under
Relation.Binary.Construct