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[ add ] Relation.Binary.Properties.PartialSetoid #2678

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@jamesmckinna jamesmckinna commented Mar 17, 2025

This adds the properties of PERs discussed in #2677 .

Issues:

  • naming: p- prefix to signify 'partial'
  • where to add:
    • Properties (as here)
    • Consequences (contra: dependency on PropositionalEquality)
    • or as manifest fields of Relation.Binary.Structures.IsPartialEquivalence (contra: every IsEquivalence gets bloated by the addition)

Downstream:

  • potential refactoring of Relation.Binary.Properties.Setoid to inherit from this?

trans-reflʳ : x ≈ y → y ≡ z → x ≈ z
trans-reflʳ p ≡.refl = p

p-reflˡ : x ≈ y → x ≈ x
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What does p stand for here?

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see above! under "issues: naming" ;-)

@jamesmckinna
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@JacquesCarette any suggestions regarding the names?

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I'm actually fine with the names as they are.

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