How to pass a template function in a template argument list

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I suspect the answer is “you cannot do this”.

Yes, that is the case, you cannot pass a function template as a template argument. From 14.3.3:

A template-argument for a template template-parameter shall be the
name of a class template or an alias template, expressed as
id-expression.

The template function needs to be instantiated before you pass it to the other template. One possible solution is to pass a class type that holds a static produce_5_function like so:

template<typename T>
struct Workaround {
  static T produce_5_functor() { return T(5); }
};
template<template<typename>class F>
struct client_template {
  int operator()() const { return F<int>::produce_5_functor(); }
};
int five = client_template<Workaround>()();

Using alias templates, I could get a little closer:

template <typename T>
T produce_5_functor() { return T(5); }

template <typename R>
using prod_func = R();

template<template<typename>class F>
struct client_template {
  int operator()(F<int> f) const { return f(); }
};

int five = client_template<prod_func>()(produce_5_functor);

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