Comparative TMP #1: MPL, Mp11, Kvasir, Hana, Metal

I thought it’d be interesting to take some well-known template metaprogramming libraries and show how a simple (but non-trivial) program looks, in each respective style. So here’s my first entry in that vein. I’ve solved the same problem, in roughly the same way, in five different metaprogramming libraries:

  • Boost.MPL (Aleksey Gurtovoy and Dave Abrahams, 2001—)

  • Boost.Mp11 (Peter Dimov, 2015—)

  • Metal (Bruno Dutra, 2015—)

  • Kvasir.MPL (Odin Holmes and Chiel Douwes, 2017—)

  • Boost.Hana (Louis Dionne, 2013—)

MPL, Mp11, and Hana are all part of mainline Boost. Both Boost and Kvasir.MPL are preinstalled on Godbolt Compiler Explorer. Metal is not preinstalled, but since it’s single-header, you can include it like this.

#include <>

Neat, right?!

For a similar qualitative comparison of Kvasir, Mp11, Metal, Meta, and Brigand, see “Tradeoffs of TMP MPL design” (Odin Holmes, March 2017).

If you liked this post, you might also like “Four versions of Eric’s Famous Pythagorean Triples Code” (2019-03-06).

The problem statement

Define an alias template SortedAndFiltered that takes a user-defined typelist, filters out empty classes, and then sorts its input in descending size order. (Here’s the test cases fleshed out in Godbolt.)

template<class...> struct TypeList;  // incomplete
struct Z {};
    SortedAndFiltered<TypeList<int[2], Z, int[1], int[4], int[3], Z>>,
    TypeList<int[4], int[3], int[2], int[1]>
    SortedAndFiltered<TypeList<Z, Z, char, Z, Z, double, Z, Z>>,
    TypeList<double, char>

I’m not terribly concerned with performance (either compile-time or runtime); in this comparison I’m concerned mainly with readability and with trying to showcase code that is “idiomatic” in each style. But be warned: I have essentially zero experience with any of these libraries, so my sense of what is “idiomatic” is likely to be miscalibrated! If you see something that could be expressed more cleanly, please shoot me an email or something.


This hand-rolled solution “cheats” in at least two ways. First of all, it uses a “recursive template” to implement cat, which is going to be pretty slow. (People who took my STL from Scratch course at previous CppCons will remember that we can implement tuple_cat to do all its work at once, non-recursively, which should be a lot faster for large lists.) Secondly, it uses another recursive template to do a selection sort. I initially wrote a “counting sort,” which is non-recursive and slightly shorter in lines-of-code, but it ran the compiler out of memory if you fed it TypeList<int[1], int[1'000'000]>.

template<class... Ts> struct typelist {
    template<template<class...> class Tc>
    using as = Tc<Ts...>;
template<class...> struct cat;
template<> struct cat<> { using type = typelist<>; };
template<class Head, class... Tail>
struct cat<Head, Tail...> {
    template<class... Hs, class... Ts>
    static typelist<Hs..., Ts...> f(typelist<Hs...>, typelist<Ts...>);
    using type = decltype(f(Head{}, typename cat<Tail...>::type{}));
template<bool> struct if_ {
    template<class T> using maybe = typelist<T>;
template<> struct if_<false> {
    template<class T> using maybe = typelist<>;

struct Max {
    int value;
    constexpr Max operator*(Max b) const {
        return Max{value > b.value ? value : b.value};

template<class> struct SortedAndFilteredImpl;
template<template<class...> class Tc>
struct SortedAndFilteredImpl<Tc<>> { using type = Tc<>; };
template<template<class...> class Tc, class... Ts>
struct SortedAndFilteredImpl<Tc<Ts...>> {
    static constexpr int biggest_size = (Max{sizeof(Ts)} * ... * Max{0}).value;

    using big_ones = typename cat<
        typename if_<sizeof(Ts) == biggest_size && !std::is_empty_v<Ts>>::template maybe<Ts> ...
    using small_ones = typename cat<
        typename if_<sizeof(Ts) != biggest_size>::template maybe<Ts> ...

    using type = typename cat<
        typename SortedAndFilteredImpl<small_ones>::type
    >::type::template as<Tc>;

template<class TL>
using SortedAndFiltered = typename SortedAndFilteredImpl<TL>::type;


Boost.MPL is super classical TMP, full of ::types and weird tricks with placeholders such as boost::mpl::_. Notably, it does not seem to have any way to turn an mpl::vector<Ts...> back into a TypeList<Ts...> except through hand-rolled code. Another disadvantage of MPL for blogging purposes is that it has no “all.hpp” header; you have to #include a whole zoo of little headers.

Peter Dimov informs me that my ToTc-in-terms-of-mpl::at is unidiomatic, or at least anachronistic; remember that Boost.MPL was designed for C++03, which has no variadic templates. I’m not sure how to do it “idiomatically” in a way that still passes all my test cases.

#include <boost/mpl/at.hpp>
#include <boost/mpl/greater.hpp>
#include <boost/mpl/int.hpp>
#include <boost/mpl/size.hpp>
#include <boost/mpl/sizeof.hpp>
#include <boost/mpl/sort.hpp>
#include <boost/mpl/remove_if.hpp>
namespace lib = boost::mpl;

template<template<class...> class, class, class> struct ToTcImpl;

template<template<class...> class Tc, class V, size_t... Is>
struct ToTcImpl<Tc, V, std::index_sequence<Is...>> {
    using type = Tc<
        typename lib::at<V, lib::int_<Is>>::type ...

template<template<class...> class Tc, class V>
using ToTc = ToTcImpl<
    Tc, V, std::make_index_sequence<lib::size<V>::value>

template<class> struct SortedAndFilteredImpl;

template<template<class...> class Tc, class... Ts>
struct SortedAndFilteredImpl<Tc<Ts...>> {
    using type = typename ToTc<
        typename lib::sort<
            typename lib::remove_if<
            lib::greater<lib::sizeof_<lib::_1>, lib::sizeof_<lib::_2>>

template<class TL>
using SortedAndFiltered = typename SortedAndFilteredImpl<TL>::type;


Mp11 is perhaps the most portable and battle-tested of the C++11 libraries shown here. It is also one of the most readable, thanks to the way it transparently treats any Tc<Ts...> as a list. Every other solution has to spend at least two lines of code transforming TypeList<Ts...> into lib::something<Ts...> and back again. In Mp11, it just works.

(Thanks to Ilya Popov for improving this code!)

#include <boost/mp11/algorithm.hpp>
#include <boost/mp11/integral.hpp>
namespace lib = boost::mp11;

template<class T1, class T2>
using SizeofGT = lib::mp_bool<(sizeof(T1) > sizeof(T2))>;

template<class TL>
using SortedAndFiltered = lib::mp_sort<
    lib::mp_remove_if<TL, std::is_empty>,


Metal has the best documentation of any of these libraries; see the docs here. It also wins the readability contest, due to its plethora of handy adaptors such as metal::as_lambda and metal::trait: it eliminates almost all of the helper classes that the other solutions needed.

#include <metal/metal.hpp>
namespace lib = metal;

template<class T1, class T2>
using SizeofGT = lib::number<(sizeof(T1) > sizeof(T2))>;

template<class TL>
using SortedAndFiltered = lib::apply<


Kvasir.MPL isn’t super well documented. The best documentation I’ve found is here. Notice Kvasir’s distinctive “continuation” style: to express that we want to unpack and then remove_if, we pass remove_if<...> as the continuation parameter of unpack — and sort<...> as the continuation parameter of remove_if, and so on. This means that the nesting of the primitives appears “reversed” relative to the more traditional MPL/Mp11/Metal.

#include <kvasir/mpl/mpl.hpp>
namespace lib = kvasir::mpl;

template<class T1, class T2>
using SizeofGT = lib::bool_<(sizeof(T1) > sizeof(T2))>;

template<class> struct AsLambda;
template<template<class...> class Tc, class... Ts>
struct AsLambda<Tc<Ts...>> : lib::cfe<Tc> {};

template<class TL>
using SortedAndFiltered = lib::call<


Louis Dionne’s Hana has the most distinctive appearance of any of these libraries. (Docs here.) The helper that we had to out-of-line as SizeofGT in other versions can be done in Hana as a plain old generic lambda.

I doubt that my way of unpacking TL into Ts... is idiomatic; this is the version I most expect to have to update in response to Reddit comments. For the difference between hana::type and hana::basic_type, see “How hana::type<T> disables ADL” (2019-04-09).

#include <boost/hana.hpp>
namespace lib = boost::hana;

template<template<class...> class Tc, class... Ts>
constexpr auto SortAndFilter(lib::basic_type<Tc<Ts...>>) {
    auto filtered = lib::remove_if(
    auto sorted = lib::sort(
        [](auto t1, auto t2) {
            return lib::sizeof_(t1) > lib::sizeof_(t2);
    return lib::unpack(sorted, lib::template_<Tc>);

template<class TL>
using SortedAndFiltered = typename decltype(
Posted 2019-12-28