Using custom std::set comparator

You are using a function where as you should use a functor (a class that overloads the () operator so it can be called like a function).

struct lex_compare {
    bool operator() (const int64_t& lhs, const int64_t& rhs) const {
        stringstream s1, s2;
        s1 << lhs;
        s2 << rhs;
        return s1.str() < s2.str();
    }
};

You then use the class name as the type parameter

set<int64_t, lex_compare> s;

If you want to avoid the functor boilerplate code you can also use a function pointer (assuming lex_compare is a function).

set<int64_t, bool(*)(const int64_t& lhs, const int64_t& rhs)> s(&lex_compare);

1. Modern C++20 solution

auto cmp = [](int a, int b) { return ... };
std::set<int, decltype(cmp)> s;

We use lambda function as comparator. As usual, comparator should return boolean value, indicating whether the element passed as first argument is considered to go before the second in the specific strict weak ordering it defines.

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2. Modern C++11 solution

auto cmp = [](int a, int b) { return ... };
std::set<int, decltype(cmp)> s(cmp);

Before C++20 we need to pass lambda as argument to set constructor

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3. Similar to first solution, but with function instead of lambda

Make comparator as usual boolean function

bool cmp(int a, int b) {
    return ...;
}

Then use it, either this way:

std::set<int, decltype(cmp)*> s(cmp);

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or this way:

std::set<int, decltype(&cmp)> s(&cmp);

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4. Old solution using struct with () operator

struct cmp {
    bool operator() (int a, int b) const {
        return ...
    }
};

// ...
// later
std::set<int, cmp> s;

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5. Alternative solution: create struct from boolean function

Take boolean function

bool cmp(int a, int b) {
    return ...;
}

And make struct from it using std::integral_constant

#include <type_traits>
using Cmp = std::integral_constant<decltype(&cmp), &cmp>;

Finally, use the struct as comparator

std::set<X, Cmp> set;

Online demo

Yacoby's answer inspires me to write an adaptor for encapsulating the functor boilerplate.

template< class T, bool (*comp)( T const &, T const & ) >
class set_funcomp {
    struct ftor {
        bool operator()( T const &l, T const &r )
            { return comp( l, r ); }
    };
public:
    typedef std::set< T, ftor > t;
};

// usage

bool my_comparison( foo const &l, foo const &r );
set_funcomp< foo, my_comparison >::t boo; // just the way you want it!

Wow, I think that was worth the trouble!