Point-free style programming

Point-free style programing(or tacit programming) is a style where the arguments to the function are not explicity defined. Rather, the function is defined as the composition of other functions where function adaptors manipulate the function arguments. The advantage of using point-free style in C++ is the template machinery involved with function arguments can be avoided.

Variadic print

For example, if we want to write a variadic print function that prints each argument, like this:

print("Hello", "World");

We would write something like the following, which would recursively iterate over the arguments using varidiac templates:

// Base case
void print()

template<class T, class... Ts>
void print(const T& x, const Ts&... xs)
    std::cout << x;

Instead with point-free style, we can write this using the by adaptor, which calls a function on each arguments. Of course, std::cout is not a function, but we can make it one by using FIT_LIFT:

FIT_STATIC_FUNCTION(simple_print) = FIT_LIFT(std::ref(std::cout) << _);

This uses the placeholders to create a function that prints to std::cout. Then we can pass simple_print to the by adaptor:

FIT_STATIC_FUNCTION(print) = by(simple_print);

As the by adaptor calls the function for each argument passed in, b(f)(x, y) is the equivalent of calling f(x) and then f(y). In this case, it will call simple_print(x) and then simple_print(y):

print("Hello", "World");

Which prints out:


Of course, this puts all the output together, but we can further extend this to print a new line for each item by composing it:

FIT_STATIC_FUNCTION(print_lines) = by(flow(simple_print, _ << std::integral_constant<char, '\n'>{}));

The flow adaptor does function composition but the functions are called from left-to-right. That is flow(f, g)(x) is equivalent to g(f(x)). So in this case, it will call simple_print on the argument which returns std::cout and then pass that to the next function which calls the stream with the newline character. In the above, we write std::integral_constant<char, '\n'>{} instead of just '\n' because the function is statically defined, so all values must be defined statically.

So now calling print_lines:

print_lines("Hello", "World");

It will print out:


With each argument on its own line.

Variadic sum

Another example, say we would like to write a varidiac version of max. We could implement it like this:

// Base case
template<class T>
T max(const T& x)
    return x;

template<class T, class... Ts>
T max(const T& x, const T& y, const Ts&... xs)
    return std::max(x, max(y, xs...));

With point-free style programming, we can recognize this is a fold, and write it using the compress adaptor, which will do a fold over the variadic parameters:

FIT_STATIC_FUNCTION(max) = compress(FIT_LIFT(std::max));

FIT_LIFT is used to grab the entire overload set of std::max function, which is needed since std::max is templated and we want the variadic std::max function to handle any types as well. So now it can be called like this:

auto n = max(1, 2, 4, 3); // Returns 4
auto m = max(0.1, 0.2, 0.5, 0.4); // Returns 0.5

By using compress, max(1, 2, 4, 3) will call std::max like std::max(std::max(std::max(1, 2), 4), 3) and max(0.1, 0.2, 0.5, 0.4) will be called like std::max(std::max(std::max(0.1, 0.2), 0.5), 0.4).