[Accepted at the November, 2020 meeting as part of paper P1787R6 and moved to DR at the February, 2021 meeting.]

Nicolai Josuttis sent me an example like the following:

    template <typename RET, typename T1, typename T2>
    const RET& min (const T1& a, const T2& b)
    {
	return (a < b ? a : b);
    }
    template const int& min<int>(const int&,const int&);  // #1
    template const int& min(const int&,const int&);       // #2

Among the questions was whether explicit instantiation #2 is valid, where deduction is required to determine the type of RET.

The first thing I realized when researching this is that the standard does not really spell out the rules for deduction in declarative contexts (friend declarations, explicit specializations, and explicit instantiations). For explicit instantiations, 13.9.3 [temp.explicit] paragraph 2 does mention deduction, but it doesn't say which set of deduction rules from 13.10.3 [temp.deduct] should be applied.

Second, Nicolai pointed out that 13.9.3 [temp.explicit] paragraph 6 says

A trailing template-argument can be left unspecified in an explicit instantiation provided it can be deduced from the type of a function parameter (13.10.3 [temp.deduct]).

This prohibits cases like #2, but I believe this was not considered in the wording as there is no reason not to include the return type in the deduction process.

I think there may have been some confusion because the return type is excluded when doing deduction on a function call. But there are contexts where the return type is included in deduction, for example, when taking the address of a function template specialization.

Suggested resolution:

1. Update 13.10.3 [temp.deduct] to include a section "Deducing template arguments from a declaration" that describes how deduction is done when finding a template that matches a declaration. This should, I believe, include the return type.
2. Update 13.9.3 [temp.explicit] to make reference to the new rules in 13.10.3 [temp.deduct] and remove the description of the deduction details from 13.9.3 [temp.explicit] paragraph 6.