Hello Jan!
Thanks for replying.

My reading is that it's not a requirement.

NaN seems to be supported indeed, and that's possibly the motivation.

Right, the semantic requirements of std::equality_comparable concept
are written in such a way that one might conclude that reflexivity in not
required,
and thus floating point types (float, double, etc.) do model std::
equality_comparable.

In that case, I would argue that the name of the concept is wrong /
misleading,
because it intends to represent types providing operator ==, which
implements partial equality,
that is, it should have been named std::partially_equality_comparable, not
std::equality_comparable.

The Wikipedia article describing partial equivalence relation
<https://en.wikipedia.org/wiki/Partial_equivalence_relation> explicitly
states this fact:

> *In mathematics, a partial equivalence relation is a homogeneous binary
> relation that is symmetric and transitive.*

*If the relation is also reflexive, then the relation is an equivalence
> relation.*


This article also points out that equality of IEEE floating point values
<https://en.wikipedia.org/wiki/Partial_equivalence_relation#Equality_of_IEEE_floating_point_values>
is a partial equality, due to NaN:

> *The IEEE 754:2008 standard for floating-point numbers defines an "EQ"
> relation for floating point values. *

*This predicate is symmetric and transitive, but is not reflexive because
> of the presence of NaN values that are not EQ to themselves.*


Thank you, Mateusz Zych

On Wed, Jul 30, 2025 at 8:51 AM Jan Schultke <janschultke_at_[hidden]>
wrote:

> Correction: I've misremembered something.
>
> x != x
>
> is true for NaN, so NaN seems to be supported indeed, and that's
> possibly the motivation.
>
> On Wed, 30 Jul 2025 at 07:48, Jan Schultke <janschultke_at_[hidden]>
> wrote:
> >
> > > This got me wondering whether reflexivity
> > > is a semantic requirement of std::equality_comparable or not?
> >
> > My reading is that it's not a requirement.
> > To model weakly-equality-comparable-with<T,U>,
> > with lvalues t and u of types T and U,
> > the following requirement has to be met:
> >
> > > bool(t != u) == !bool(t == u).
> >
> > See https://eel.is/c++draft/concept.equalitycomparable
> >
> > For a value such as NaN, this is "false == true" because all
> > comparisons are false. If a value was equal to all other values but
> > not to itself, then equality wouldn't be transitive, so that also
> > wouldn't work. HOWEVER, if == always yields false and != always yields
> > true, then it seems like all the requirements are met.
> >
> > I don't know what the motivation is, seeing that NaN is not supported,
> > but I suppose it's a slightly more minimalistic requirement if we
> > allow values that are equal to nothing, not even themselves, even
> > though I cannot think of a good use case.
>