Unit-Testing Deep-Equality in C#

In the suite of redux-style applications we are building in C#, we are making extensive use of value-types, which implies that a value compares as equal exactly if all of its contents are equal also known as “deep equality”, as opposed to “reference equality” or “shallow equality”. Both of those imply deep equality, but the other way around is not true. The same object is of course equal to itself, not matter how deep you look. And an object that references the same data as another object also has equal content. But a simple object that contains different lists with equal content will be unequal under shallow comparison, but equal under deep comparison.

Though init-only records already provide a per-member comparison as Equals be default, this fails for collection types such as ImmutableList<> that, against all intuition but in accordance to , only provide reference-equality. For us, this means that we have to override Equals for any value type that contains a collection. And this is were the trouble starts. Once Equals is overridden, it’s extremely easy to forget to also adapt Equals when adding a new property. Since our redux-style machinery relies on a proper “unequal”, this would manifest in the application as a sporadically missing UI update.

So we devised a testing strategy for those types, using a little bit of reflection:

  1. Create a sample instance of the value type with no member retaining its default value
  2. Test, by going over all properties and comparing to the same property in a default instance, if indeed all members in the sample are non-default
  3. For each property, run Equals the sample instance to a modified sample instance with that property set to the value from a default instance.

If step 2 fails, it means there’s a member that’s still at its default value in the sample instance, e.g. the test wasn’t updated after a new property was added. If step 3 fails, the sample was updated, but the new property is not considered in Equals – and it can even tell which property is missing.

The same problems of course arise with GetHashCode, but are usually less severe. Forgetting to add a property just makes collisions more likely. It can be tested much in the same way, but can potentially lead to false positives: collisions can occur even if all properties are correctly considered in the function. In that case, however, the sample can usually be altered to remove the collision – and it is really unlikely. In fact, we never had a false positive.

Improving my C++ time queue

Another code snippet that can be found in a few of my projects is the “time queue”, which is a simple ‘priority queue’ style data structure that I use to defer actions to a later time.

With this specific data structure, I have multiple implementations that clearly came from the same source. One indicator for that is a snarky comment in both about how std::list is clearly not the best choice for the underlying data structure. They have diverged a bit since then though.

Requirements

In my use case not use time points, but only durations in standard-library nomenclature. This is a pretty restrictive requirement, because otherwise any priority queue (e.g. from boost or even from the standard library) can be used quite well. On the other hand, it allows me to use floating-point durations with predictable accuracy. The queue has two important functions:

  1. insert to insert a timeout duration and a payload.
  2. tick is called with a specific duration and then reports the payloads that have timed out since their insertions.

Typically tick is called a lot more frequently than insert, and it should be fast. The payload is typically something like a std::function or an id for a state-machine that needs to be pulsed.

The basic idea is to only keep the duration difference to the previous item in the list. Only the first item keeps its total timeout. This way, when tick is called, usually only the first item needs to be updated. tick only has to touch more items when they time out.

Simple Implementation

One of the implementations for void insert(TimeType timeout, PayloadType payload) looks like this:

if (tick_active_)
{
  deferred_.push_back({ .remaining = after, .payload = std::move(payload) });
  return;
}

auto i = queue_.begin();
for (; i != queue_.end() && timeout > i->remaining; ++i)
  timeout -= i->remaining;

if (i != queue_.end())
  i->remaining -= timeout;

queue_.insert(i, { .remaining = after, .payload = std::move(payload) });

There is a special case there that guards against inserting into queue_ (which is still a very bad std::list) by instead inserting into deferred_ (which is a std::vector, phew). We will see why this is useful in the implementation for template void tick(TimeType delta, Executor execute):

tick_active_ = true;
auto i = queue_.begin();
for (; i != queue_.end() && delta >= i->remaining; ++i)
{
  delta -= i->remaining;
  execute(i->payload);
}

if (i != queue_.end())
  i->remaining -= delta;

queue_.erase(queue_.begin(), i);
tick_active_ = false;

while (!deferred_.empty())
{
  auto& entry = deferred_.back();
  insert(entry.remaining, std::move(entry.payload));
  deferred_.pop_back();
}

The timed out items are reported via a callback that is supplied as Executor execute. Of course, these can do anything, including inserting new items, which can invalidate the iterator. This is a common use case, in fact, as many deferred actions will naturally want follow ups (let’s ignore for the moment that the implementation is nowhere near exception safe…). The items that were deferred to deferred_ in insert get added to queue_ after the iteration is complete.

This worked well enough to ship, but the other implementation had another good idea. Instead of reporting the timed-out items to a callback, it just returned them in a vector. The whole tick_active_ guard becomes unnecessary, as any processing on the returned items is naturally deferred until after the iteration:

std::vector<PayloadType> tick(TimeType delta)
{
  std::vector<PayloadType> result;
  auto i = queue_.begin();
  for (; i != queue_.end() && delta >= i->remaining; ++i)
  {
    delta -= i->remaining;
    result.push_back(i->payload);
  }

  if (i != queue_.end())
    i->remaining -= delta;

  queue_.erase(queue_.begin(), i);
  return result;
}

This solves the insert-while-tick problem, and lets us use the result neatly in a range-based for-loop like this: for (auto const& payload : queue.tick(delta)) {}. Which I personally always find a little bit nicer than inversion-of-control. However, the cost is at least one extra allocation for timed-out items. This might be acceptable, but maybe we can do better for very little extra complexity.

Return of the second list

Edit: The previous version of this article tried to keep the timed-out items at the beginning of the vector before returning them as a std::span. As commenter Steffen pointed out, this again prevents us from inserting while iterating on the result, as any insert might invalidate the backing-vector.

We can get rid of the allocation for most of the tick calls, even if they return a non-empty list. Remember that a std::vector does not deallocate its capacity even when it’s cleared unless that is explicitly requested, e.g. via shrink_to_fit. So instead of returning a new vector each time, we’re keeping one around for the timed out items and return a const-ref to it from tick:

std::vector<PayloadType> const& tick(TimeType delta)
{
  timed_out_.clear();
  auto i = queue_.begin();
  for (; i != queue_.end() && delta >= i->remaining; ++i)
  {
    delta -= i->remaining;
    timed_out_.push_back(std::move(i->payload));
  }

  if (i != queue_.end())
    i->remaining -= delta;

  queue_.erase(queue_.begin(), i);
  return timed_out_;
}

This solution is pretty similar to the deferred list from the first version, but instead of ‘locking’ the main list while iterating, we’re now separating the items we’re iterating on.

Simple abstractions are good abstractions

I think that a lot of accidental complexity in software is produced by not picking the simplest abstraction for the job. Let me lead with an example: Consider this code from a code generator that generates C++ code:

std::ostringstream extra_properties;
if (!attribute.unit.empty())
{
  extra_properties << fmt::format("\n      properties.set_unit(\"{0}\");", attribute.unit);
}
if (!attribute.min_value.empty())
{
  extra_properties << fmt::format("\n      properties.set_min_value(\"{0}\");", attribute.min_value);
}
if (!attribute.max_value.empty())
{
  extra_properties << fmt::format("\n      properties.set_max_value(\"{0}\");", attribute.max_value);
}

It has a lot of ugly duplication: basically everything but the method names and values. So, how do we get rid of the duplication? Just a couple of years ago, I would probably have used a function for that:

void property_snippet(std::ostringstream& str, std::string const& method_name, std::string const& value)
{
  if (value.empty())
    return;
  str << fmt::format("\n      properties.{0}(\"{1}\");", method_name, value);
}

And then turn the call site code into:

property_snippet(extra_properties, "set_unit", attribute.unit);
property_snippet(extra_properties, "set_min_value", attribute.min_value);
property_snippet(extra_properties, "set_max_value", attribute.max_value);

Back then, I would have said that this is a definite improvement, but nowadays I am not so sure anymore. The call-site is a lot more concise, but we still have about half its code duplicated: the first half of each line. The additional function adds lots of complexity that is not necesarily offset by the gain at the call-site: the declaration with all the parameters. And the code gets separated, which is only really good if the function does a little bit more than this one.

This variant can, however, be made simpler with lambdas that capture extra_properties instead of passing it each time. While that is a better solution, I would argue that function objects and capturing are not necessarily simple either, so this only makes second place.

Nowdays, my first go-to abstraction is an in-place list and a loop:

std::tuple<char const*, std::string> methods_and_values[] = {
  {"set_unit", attribute.unit},
  {"set_min_value", attribute.min_value},
  {"set_max_value", attribute.max_value},
};

for (auto [method_name, value] : methods_and_values)
{
  if (value.empty())
    continue;
  extra_properties << fmt::format("\n      properties.{0}(\"{1}\");", method_name, value);
}

For me, this has the added benefit that is clearly separates the ‘inert’ data part of the code and the ‘active’ transformation. While this example is C++, this works in almost languages that I know of, even such arcane beasts as Xbase++.

Writing windows daemons in C++20

One little snippet I’ve found myself reusing surprisingly often is how to write a daemon program with graceful shutdown in windows. To recap, a daemon is a program that sits and does ‘background work’ until it is explicitly shut down by the user. For my purposes, it is also a console program. Like this one:

int main(int argn, char** argv)
{
  while (true)
  {
    std::cout << "ping!" << std::endl;
    std::this_thread::sleep_for(100ms);
  }
  std::cout << "shutdown!" << std::endl;
  return EXIT_SUCCESS;
}

If you run this program, it will, of course, continuously print “ping!”. And you can kill it by entering ctrl+C on the console. But the shutdown will not be graceful: “shutdown!” will not be printed. It’ll just look like this:

ping!
ping!
ping!
^C

C++20 introduced std::stop_source and std::stop_token, which help to implement a graceful shutdown. We’ll use the following code:

'namespace
{
static std::stop_source exit_source;
static std::atomic<bool> main_exited = false;
static bool already_registered = false;

static void atexit_handler()
{
  main_exited = true;
}

BOOL control_handler(DWORD Type)
{
  switch (Type)
  {
  case CTRL_C_EVENT:
  case CTRL_CLOSE_EVENT:
    exit_source.request_stop();

    while (!main_exited)
      Sleep(10);

    return TRUE;
    // Pass other signals to the next handler.
  default:
    return FALSE;
  }
}
} // namespace

std::stop_token register_exit_signal()
{
  if (!already_registered)
  {
    if (!SetConsoleCtrlHandler((PHANDLER_ROUTINE)control_handler, TRUE))
      throw std::runtime_error("Unable to register control handler");

    atexit(&atexit_handler);
    already_registered = true;
  }
  return exit_source.get_token();
}'namespace
{
static std::stop_source exit_source;
static std::atomic<bool> main_exited = false;
static bool already_registered = false;

static void atexit_handler()
{
  main_exited = true;
}

BOOL control_handler(DWORD Type)
{
  switch (Type)
  {
  case CTRL_C_EVENT:
  case CTRL_CLOSE_EVENT:
    exit_source.request_stop();

    while (!main_exited)
      Sleep(10);

    return TRUE;
    // Pass other signals to the next handler.
  default:
    return FALSE;
  }
}
} // namespace

std::stop_token register_exit_signal()
{
  if (!already_registered)
  {
    if (!SetConsoleCtrlHandler((PHANDLER_ROUTINE)control_handler, TRUE))
      throw std::runtime_error("Unable to register control handler");

    atexit(&atexit_handler);
    already_registered = true;
  }
  return exit_source.get_token();
}

You’re going to have to include both <stop_token> and <Window.h> for this. Now we can adapt our daemon loop slightly:

int main(int argn, char** argv)
{
  auto token = register_exit_signal(); // <-- register the exit signal here
  while (!token.stop_requested()) // ... and test the current state here
  {
    std::cout << "ping!" << std::endl;
    std::this_thread::sleep_for(100ms);
  }
  std::cout << "shutdown!" << std::endl;
  return EXIT_SUCCESS;
}

Note that this requires cooperatively handling the shutdown. But now the output correctly prints “shutdown” when killed with ctrl+C.

ping!
ping!
shutdown!

There’s linux/macOS code for this same interface too. It works by handling SIGINT/SIGTERM. But that information is somewhat easier to come by, so I’ll leave it out for brevity. Feel free to comment if you think that’d be interesting as well.

Automated instance construction in C++

I’m currently mostly switching back and forth between C# and C++ projects. One of the things that I’m missing most when switching to C++ is a nice dependency-injection (DI) library. After checking out what was already available, I finally decided I wanted to try to build my own slim type-indexed variant. I quickly started by registering factories and instances in a map on std::type_index, making it possible to both have the DI retain ownership (with std::unique_ptr) or just make a type available via a bare pointer. So I was able to do things like:

// Register an instance
di.insert_unique(std::make_unique<foo_service>());
// Register a factory
di.insert_unique([] {return std::make_unique<bar_service>());
// Register an existing bare pointer
di.insert_bare(my_bare_thingy);

// ... and retrieve them
auto& foo = di.get<foo_service>();

One of the most powerful aspects of a DI library is the ability to transitively setup dependencies. I like constructor injection the most, so I implemented a very naive way like this:

di.insert_unique([](auto& p) { return std::make_unique<complex_service>(
  p.get<base_service1>(), p.get<base_service2>(), p.get<base_service3>());
});

This is pretty verbose and we basically have to repeat all the constructor parameter types. But it’s easy to implement. We can do a little bit better by using a templated type-conversion operator and using it to call the get:

class service_provider
{
  struct inferred_locator
  {
    service_provider const* provider;
    template <class T> operator T&() const
    {
      return provider->get<std::remove_const_t<T>>();
    }
  };
  
  inferred_locator get() const
  {
    return { .provider = this };
  }
  
  /** typed get implementations here... */
};

Now we can reduce the previous registration to:

di.insert_unique([](auto& p) { 
  return std::make_unique<complex_service>(p.get(), p.get(), p.get());
});

That is basically only the number of constructor parameters in a verbose way. We could write a small template that takes the number, creates an std::index_sequence from it and then unpacks each index into an invokation of service_provider::get. But then we would still have to update registrations when adding (or removing) a new dependency to a services’s constructor. With a litte more work, we can actually get this instead:

di.insert_unique<complex_service>();

This partly inspired by Antony Polukhin’s C++ reflection talks, and combines std::index_sequence based unpacking, SFINEA and the templated type-conversion operator:

template <class T, std::size_t Head, std::size_t... Rest>
constexpr auto make_unique_impl(provider_wrapper const& p,
    std::index_sequence<Head, Rest...>,
    decltype(T{ mimic{ Head }, mimic{ Rest }... }) * = nullptr) -> std::unique_ptr<T>
{
    // This next requirement is so we do not accidentally recurse into the copy/move-ctors
    static_assert(sizeof...(Rest) + 1 > 1, "Can only deduce constructors with two or more parameters.");
    return std::make_unique<T>(p(Head), p(Rest)...);
}

template <class T, std::size_t... Rest>
constexpr auto make_unique_impl(provider_wrapper const& p, std::index_sequence<Rest...>) -> std::unique_ptr<T>
{
    // This next requirement is so we do not accidentally recurse into the copy/move-ctors
    static_assert(sizeof...(Rest) > 1, "Can only deduce constructors with two or more parameters.");
    return make_unique_impl<T>(p, std::make_index_sequence<sizeof...(Rest) - 1>{});
}

template <class T, std::size_t Max = 8> auto make_unique(service_provider const& p)
{
    return make_unique_impl<T>(provider_wrapper{ &p }, std::make_index_sequence<Max>{});
}

This uses two new types: mimic, which is only used for SFINEA, takes std::size_t on construction (for the unpacking from the std::index_sequence) and converts to anything (templated type conversion again) and the provider_wrapper, which is a simple adaptor around service_provider that takes an unused std::size_t argument (again, for unpacking). The first overload of make_unique_impl is slightly more specialized (because it has Head and Rest), so the compiler tries it first. If it works, it returns a new instance of the service we want. Otherwise, it will fail without an error due to SFINEA in the unused and defaulted third parameter. The compiler will then try the second overload, which will recurse to a variant with fewer parameters. The outermost make_unique starts this recursion with 8 parameters, because that should be enough for any sane service. I stop this recursion at one constructor parameter, even though that is a useful configuration. This is because I have not yet found a way to avoid calling the copy or move constructors accidentally. If anyone knows how to do that, I’d be very happy to hear how. My workaround right now is to explicitly register a factory in that case.

Reading a conanfile.txt from a conanfile.py

I am currently working on a project that embeds another library into its own source tree via git submodules. This is currently convenient because the library’s development is very much tied to the host project and having them both in the same CMake project cuts down dramatically on iteration times. Yet, that library already has its own conan dependencies in a conanfile.txt. Because I did not want to duplicate the dependency information from the library, I decided to pull those into my host projects requirements programmatically using a conanfile.py.

Luckily, you can use conan’s own tools for that:

from conans.client.loader import ConanFileTextLoader

def load_library_conan(recipe_folder):
    text = Path(os.path.join(recipe_folder, "libary_folder", "conanfile.txt")).read_text()
    return ConanFileTextLoader(text)

You can then use that in your stage methods, e.g.:

    def config_options(self):
        for line in load_library_conan(self.recipe_folder).options.splitlines():
            (key, value) = line.split("=", 2)
            (library, option) = key.split(":", 2)
            setattr(self.options[library], option, value)

    def requirements(self):
        for x in load_library_conan(self.recipe_folder).requirements:
            self.requires(x)

I realize this is a niche application, but it helped me very much. It would be cool if conan could delegate into subfolders natively, but I did not find a better way to do this.

Metal in C++ with SDL2

Metal, Cupertino’s own graphics API, is sort of a middle-ground in complexity between OpenGL and Vulkan. I’ve wanted to try it for a while, but the somewhat tight integration into Apple’s ecosystem (ObjectiveC/Swift and XCode) has so far prevented that. My graphics projects are usually using C++ and CMake, so I wanted a solution that worked with that. Apple released Metal-cpp last year and newer SDL2 versions (since 2.0.14) can create a window that supports drawing to it with metal. Here’s how to weld that together (with minimal ObjectiveC).

metal-cpp

I get the metal-cpp code from the linked website (the download is at step 1). I add a library in CMake that builds a single source file that compiles the metal-cpp implementation with the ??_PRIVATE_IMPLEMENTATION macros as described on the page (see step 3). That target also exports the includes to be used later.

SDL window and view

Next, I use conan to install SDL2. After SDL_Init, I call SDL_CreateWindow to create my window. I do not specify SDL_WINDOW_OPENGL (or in the SDL_CreateWindow‘s flags, or next step will fail. After that, I use SDL_Metal_CreateView from SDL_metal.h to create a metal view. This is where things get a little bit icky. I create a metal device using MTL::CreateSystemDefaultDevice(); but I still need to assign it to the view I just created. I’m doing that in ObjectiveC++. In a new .mm file I add a small function to do that:

void assign_device(void* layer, MTL::Device* device)
{
  CAMetalLayer* metalLayer = (CAMetalLayer*) layer;
  metalLayer.device = (__bridge id<MTLDevice>)(device);
}

I use a small .h file to expose this function to my C++ code like any other free function. There’s another helper I create in the .mm file:

CA::MetalDrawable* next_drawable(void* layer)
{
  CAMetalLayer* metalLayer = (CAMetalLayer*) layer;
  id <CAMetalDrawable> metalDrawable = [metalLayer nextDrawable];
  CA::MetalDrawable* pMetalCppDrawable = ( __bridge CA::MetalDrawable*) metalDrawable;
  return pMetalCppDrawable;
}

At the beginning of each frame, I use that together with SDL_Metal_GetLayer to get a texture to render to:

auto surface = next_drawable(SDL_Metal_GetLayer(view));

Next I create a render pass descriptor that starts by clearing that drawable with our fancy red:

MTL::ClearColor clear_color(152.0/255.0, 23.0/255.0, 42.0/255.0, 1.0);
auto pass_descriptor = MTL::RenderPassDescriptor::alloc()->init();
auto attachment = pass_descriptor->colorAttachments()->object(0);
attachment->setClearColor(clear_color);
attachment->setLoadAction(MTL::LoadActionClear);
attachment->setTexture(surface->texture());

And fire that off to the GPU using a command buffer and render encoder:

auto buffer = queue->commandBuffer();
auto encoder = buffer->renderCommandEncoder(pass_descriptor);
encoder->endEncoding();
buffer->presentDrawable(surface);
buffer->commit();

There you have it, a minimal running metal application. Still a long ways from the traditional “Hello Triangle”, but most metal examples that show how to do that can easily be translated to the C++ API. Note that you probably have to take some extra steps to compile metal shaders (aka MSL). You can either load them from source or precompile them using the command line tools.

My favorite C++20 feature

As I evolved my programming style away from mutating long-lived “big” objects and structures and towards are more functional and data-oriented style based mainly on pure functions, I also find myself needing a lot more structs. These naturally occur as return types for functions with ‘richer’ output if you do not want to use std::tuple or other ad-hoc types everywhere. If you see a program as a sequence of data-transformations, I guess the structs are the immediate representations encoded in the type system.

Let my first clarify what I mean by structs, as opposed to what the language says: A type that has all public data members, obeys the rule of zero, and is valid in any configuration. A typical struct v3 { float x{},y{},z{};}; 3d vector is a struct, std::vector is not.

These types are great. You can copy them around, use them with structured binding, they correctly propagate constness, and they are a great fit to pass them through layers of functions calls. And, when used as function parameters, they are great for evolving your program over time, because you can just change the single struct, as opposed to every function call that uses this parameter combination. Or you can easily batch, or otherwise ‘delay’, calls by recording the function parameters. Just throw the parameters into a container and execute the code later.

And with C++20, they got even better, because now you can use them with my favorite new feature: designated initializers, which allows you to use the member names at the initialization site and use RAII. E.g., for a struct that symbolizes an http request: struct http_request { http_method method; std::string url; std::vector<header_entry> headers; }; You can now initialize it like this:

auto request = http_request{
  .method = http_method::get,
  .uri = "localhost:7634",
  .headers = { { .name = "Authorization", .value = "Bearer TOKEN" } },
};

You can even use this directly as a parameter without repeating the type name, de facto giving your named parameters for a pair of extra curlys:

run_request({
    .method = http_method::get,
    .uri = "localhost:7634",
    .headers = { { .name = "Authorization", .value = "Bearer TOKEN" } },
});

You can, of course, combine this named-parameter style-struct with other function parameters in your API, but like with lambdas, I think they are most readable as the last parameter. Hence, also like with lambdas, you probably never want to have more than one at each call-site. I’m very happy with this new feature and it’s already making the code using my APIs a lot more readable.

The boy scout rule and git in practice

There’s a dichotomy when applying the boy scout rule to programming: cleaning up code that you happen to come across ‘pollutes’ your merge-/pull-requests, making it harder to review and therefor more unlikely to be accepted.

One way to cope with this is to submit the ‘clean up’ and the feature/task related changes separately, and merge them back into upstream in separate steps. But often times, it is much easier to just fix a small problem right away instead of switching back to your main branch and doing it there. In fact, it might prevent the developer from doing the improvement, which I want to avoid. Quite the opposite, I want to encourage my fellow developers to do improvements.

So one thing that we do about this is to mark the changes that are unrelated (or tangentially related) to the task with their own commit and a special prefix in the commit message like:

BSR: More consistent function signatures

As you might have guessed, BSR stands for boy scout rule. This does not solve the fact that the diffs get larger than necessary, but it makes it possible to ‘filter out’ the pure refactorings. In some cases, these commits can later be cherry-picked onto the main branch before doing the review. Of course, this only works for small refactorings, but this is where the boy scout rule applies.

Composition of C# iterator methods

Iterator methods in C# or one of my favorite features of that language. I do not use it all that often, but it is nice to know it is there. If you are not sure what they are, here’s a little example:

public IEnumerable<int> Iota(int from, int count)
{
  for (int offset = 0; offset < count; ++offset)
    yield return from + offset;
}

They allow you to lazily generate any sequence directly in code. For example, I like to use them when generating a list of errors on a complex input (think compiler errors). The presence of the yield contextual keyword transforms the function body into a state machine, allowing you to pause it until you need the next value.

However, this makes it a little more difficult to compose such iterator methods, and in reverse, refactor a complex iterator method into several smaller ones. It was not obvious to me right away how to do it at all in a ‘this always works’ manner, so I am sharing how I do it here. Consider this slightly more complex iterator method:

public IEnumerable<int> IotaAndBack(int from, int count)
{
  for (int offset = 0; offset < count; ++offset)
    yield return from + offset;

  for (int offset = 0; offset < count; ++offset)
    yield return from + count - offset - 1;
}

Now we want to extract both loops into their own functions. My one-size-fits-all solution is this:

public IEnumerable<int> AndBack(int from, int count)
{
  for (int offset = 0; offset < count; ++offset)
    yield return from + count - offset - 1;
}

public IEnumerable<int> IotaAndBack(int from, int count)
{
  foreach (var x in Iota(from, count))
     yield return x;

  foreach (var x in AndBack(from, count))
     yield return x;
}

As you can see, a little ‘foreach harness’ is needed to compose the parts into the outer function. Of course, in a simple case like this, the LINQ version Iota(from, count).Concat(AndBack(from, count)) also works. But that only works when the outer function is sufficiently simple.