@opensdh, any thoughts here?

I’m the one who suggested filing the issue, but I don’t have much of an opinion: whether enough people are confused by it to make it worth changing is an empirical matter. Nor am I sure about “direct search”, since “direct” sounds a bit like an intensifier rather than a restriction, although the parallel with members could be helpful.

The meaning of the phrase "single search" might be read out from the following rule:

A search in a scope X for a name N from a program point P is a single search in X for N from P unless X is the scope of a class or class template T, in which case the following steps define the result of the search.

In my opinion, the purpose of defining "single search" is almost used to state how to search the namespace's scope, which is different from the scope of a class, the latter should undergo a search in its base classes if the declarations are not yet found.

Well, in truth it's unambiguous that [basic.lookup.general]/3 defines "single search" (per the index and everything). The question is not what defines it, but how to clarify this situation.

Well, in truth it's unambiguous that [basic.lookup.general]/3 defines "single search" (per the index and everything). The question is not what defines it, but how to clarify this situation.

I also think we should clarify what the t and F are in this bullet.

If N is a non-dependent conversion-function-id, conversion function templates that are members of T are considered. For each such template F, the lookup set S(t,T) is constructed, considering a function template declaration to have the name t only if it corresponds to a declaration of F ([basic.scope.scope]). The members of the declaration set of each such lookup set, which shall not be an invalid set, are included in the result.

Frankly, I am not understanding this bullet. Does it try to construct a hypothetical name t in order to make S(t,T) work here? But, what's the characteristic of the template F here? In the initial, the bullet says "For each such template F", which are members of T, For this sentence "considering a function template declaration...only if it corresponds to a declaration of F" Isn't it the declaration of F does correspond to it by itself? I don't know what's the meaning here. it seems a bit obscure.
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This bit about [class.member.lookup]/7 seems like a very separate issue. Yes, t is a hypothetical name; F is clearly one of the conversion function templates being considered. F certainly corresponds to itself, but other function templates (in other base classes) might do so as well.

This bit about [class.member.lookup]/7 seems like a very separate issue. Yes, t is a hypothetical name; F is clearly one of the conversion function templates being considered. F certainly corresponds to itself, but other function templates (in other base classes) might do so as well.

The bullet says conversion function templates that are members of T are considered." and [class.derived#general-2] says

Members of a base class are also members of the derived class.

That means the set of this consideration only contains "conversion function templates" from T and its base classes and of one of them. We get two pieces of information here, the set only contains "conversion function templates" and they are all from T or its base classes. Every template F in this set certainly does correspond to itself, so, I don't know what's the necessity of this condition here.

Folks, can you please discuss that in a separate issue, the reflector or std-discussion. I feel like this is absolutely the wrong place.

Sorry about the derailment! We definitely appreciate the issue, and welcome a concrete rewording suggestion! Maybe we can find new terms for the current "search" and "single search" that are not overlapping in this confusing way.