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Preorder
s are rarely Symmetric
, unless they arise already from instances of Setoid
/IsEquivalence
.
So... why in the name of all that is holy do we declare them with a field name _∼_
which is (notationally/syntactically/formally) symmetric.
Consequences:
- the converse (treated in
Relation.Binary.Properties.Preorder
) can't have a 'flipped' notation, so we have to make do with the (semantically)flip
ped definition of the converse relation; - the (underlying relation of the) converse of a
Poset
is declared inRelation.Binary.Properties.Poset
, when that could simply be a renaming of the converse fromRelation.Binary.Properties.Preorder
, were that to be able to have a notation (qua definition, or else assyntax
declaration); - my head exploded while working on Add
_≮_
and_≰_
to bundles in the binary relation hierarchy. #1214 / [fixes #1214] Add negated ordering relation symbols systematically toRelation.Binary.*
#2095 as a result...
Refactoring PROPOSAL: that we rename (and appropriately deprecate, groan) the infix symbol/definition _∼_
to be _≲_
, which becomes _≤_
in Poset
, etc... and whose Relation.Binary.Properties.Preorder.InducedEquivalence
be given by @laMudri 's Relation.Binary.Construct.Interior.Symmetric
from #2071 applied to _≲_
...
Just sayin'.
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