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The usual convention in math is that the shapes of inf/sup-operators are chosen consistent with the shape of the comparison relation, with typical flavors being:
- rectangular
- round
- triangular
Thus the choice of a rectangular operator symbol in connection with a triangular relation symbol seems unnatural to me:
agda-stdlib/src/Algebra/Construct/NaturalChoice/Min.agda
Lines 29 to 37 in fb1d6f4
_⊓_ : Op₂ A | |
x ⊓ y with total x y | |
... | inj₁ x≤y = x | |
... | inj₂ y≤x = y | |
------------------------------------------------------------------------ | |
-- Properties | |
x≤y⇒x⊓y≈x : ∀ {x y} → x ≤ y → x ⊓ y ≈ x |
Also, isn't the standard style for lattice operations the triangular one?