# Study Notes: Functional Programming with C++

I have been enthused with functional programming recently. As C++ is my favourite language (or most familiar language), I have also tried to implement in C++ some of the techniques I learnt. And this blog serves to record my learning experience. It is my sincere hope that it will be useful to other people that come to functional programming with an imperative programming background.

Without further ado, let me describe first what I wanted to implement:

• Map
• Reduce
• Pipeline

If you are not familiar with these concepts, do not worry, as I will show you the code in both C++ and some ‘more functional’ languages. The functional language implementations are always easy to understand, even if you do not know the languages!

### Map

The concept of the `map` function is quite simple: it applies the function parameter to each item in a list parameter, and return the result as a list. The following examples shows the application of the successor function to a list of numbers (in Haskell):

```> print (map succ [1,2,3,4])
[2,3,4,5]
```

Map is normally a built-in function in a functional language, but implementing it is trivial too. The Haskell implementation might be the most succinct:

```map f [] = []
map f (x:xs) = f x : map f xs
```

It does the work recursively: apply f to the head of the list (x), and concatenate the result with that of `map f` applied to the rest of the list (xs) until the list is empty. The procedure may be more explicit in the Scheme code below:

```(define (map f l)
(cond
((null? l) l)
(else (cons (f (car l)) (map f (car l))))))
```

So how do we implement it in C++?

Actually C++98[1] already has something quite close: the `std::transform` [2] function template. The problem is it is not as composable as the functional equivalent, and you cannot just take the return result and print. The equivalent code for the Haskell example above is as follows (in C++11[3] style):

```#include <algorithm>
#include <iostream>
#include <iterator>
#include <vector>

using namespace std;

template <typename Type>
ostream& operator<<(ostream& os, const vector<Type>& v)
{
os << "[ ";
copy(v.begin(), v.end(),
ostream_iterator<Type>(os, " "));
os << "]";
return os;
}

int main()
{
auto const succ = [](int x) { return x + 1; };
vector<int> v1{1, 2, 3, 4};
vector<int> v2;
transform(v1.begin(), v1.end(), back_inserter(v2), succ);
cout << v2 << endl;
}
```

The programmer has to define the return variable first, and something like `back_inserter`[4] needs to be explicitly used. The flexibility is there, but the programmer needs to take extra burdens.

Of course, the C++ language provides enough facilities to define an alternative function. It is actually pretty simple[5] (though the C++ syntax is intimidating indeed for people newly coming into the template world):

```template <template <typename,typename> class OutCont=vector,
template <typename> class Alloc = allocator,
typename Fn, class Cont>
OutCont<typename Cont::value_type,
Alloc<typename Cont::value_type>>
map(Fn mapfn, const Cont& inputs)
{
OutCont<typename Cont::value_type,
Alloc<typename Cont::value_type>> result;
for (auto& item : inputs)
result.push_back(mapfn(item));
return result;
}
```

With this function template, you can now write

```    cout << map(succ, v1) << endl;
```

or even

```    cout << map(succ, vector<int>{1, 2, 3, 4}) << endl;
```

### Reduce

The `reduce` function, also called `fold`, reduces a list to single value. Its usage can be powerfully demonstrated in the following Haskell example:

```> foldl (+) 0 [1..100]
5050```

The implementation of `foldl` (called thus as there is also a `foldr` function) should be like follows:

```foldl f z []     = z
foldl f z (x:xs) = foldl f (f z x) xs
```

I.e., this function applies the two-argument function f recursively over the list items, and the parameter z is used as the initial value. I will show immediately my C++ code for comparison:

```template <typename Fn, class Cont>
typename Cont::value_type
reduce(Fn reducefn, const Cont& inputs,
typename Cont::value_type initval =
typename Cont::value_type())
{
auto result = initval;
for (auto& item : inputs)
result = reducefn(result, item);
return result;
}
```

One can use the template like the code below:

```    cout << reduce(plus<int>(), vector<int>{1, 2, 3, 4, 5})
<< endl;
```

It needs to be mentioned that C++ has a `std::accumulate`[6] function template, which is similar to `reduce`, but it suffers from the similar problem like `std::transform`. I will not elaborate the details here.

### Pipeline

Pipelining is about composing functions to form a new function. Haskell supports composition directly in the language with the operator ‘`.`’. In order to calculate sqrt(x + 1), one only needs to define a new function like follows:

```plus_1_sqrt = sqrt . succ
```

The following is something similar in Python using the `reduce` function:

```def pipeline_func(data, fns):
return reduce(lambda a, x: x(a),
fns,
data)
```

One could use the function like follows:

```def plus_1(x):
return x + 1

pipeline_func(3, [plus_1, math.sqrt])  # result is 2.0
```

I actually was frustrated at this point about how to implement it in C++. I simply did not have a clue. After some googling, and especially after finding the insightful blogs of Bartosz Milewski[7], I had better ideas. Specifically, the blog ‘What Does Haskell Have to Do with C++?’[8] enlightened me. I quickly came up with this solution[9]:

```template <typename Tp>
auto apply(Tp&& data)
{
return forward<Tp>(data);
}

template <typename Tp, typename Fn, typename... Fargs>
auto apply(Tp&& data, Fn fn, Fargs... args)
{
return apply(fn(forward<Tp>(data)), args...);
}
```

In order to make type inference work (which depends on the input and return types of the passed function arguments), a C++14[10] compiler is needed. Using Clang 3.4+ or GCC 4.9 (-std=c++1y needs to be specified on the command line), the following code will print the correct result 55:

```    auto const sqr = [](int x) { return x * x; };
auto const square_list =
[=](const vector<int>& data) {
return map(sqr, data);
};
auto const sum_list =
[=](const vector<int>& data) {
return reduce(plus<int>(), data);
};
cout << apply(vector<int>{1, 2, 3, 4, 5},
square_list,
sum_list)
<< endl;
```

There is a minor problem, though. In Haskell, the result of composition is a function that can be passed around (with type inference); in Python, the function list can be passed  around (no type inference, due to its dynamic nature). In my implementation of `apply`, the programmer has to specify the function list exactly at the point of calling in order to make type inference work. This significantly limits its usefulness.

I realized the solution only a few weeks later. The key issue was that Haskell is a lazy language[11], but C++ is an eager language. Actually the answer was always in front of me, but I just failed to see it for a long time. All I needed was an extra layer of indirection, which lambda expressions fit nicely. After learning that, everything seems simple:

```template <typename Tp>
auto compose()
{
return apply<Tp>;
}

template <typename Tp, typename Fn, typename... Fargs>
auto compose(Fn fn, Fargs... args)
{
return [=](Tp&& x)
{
return fn(compose<Tp>(args...)(forward<Tp>(x)));
};
}
```

You can see that it is very much like the `apply` implementation, but the additional lambda expression makes lazy evaluation possible. Incidentally, `compose()` with no argument returns the identity function (`id` in Haskell).

The following code demonstrates its use:

```    auto const squared_sum =
compose<const vector<int>&>(sum_list, square_list);
cout << squared_sum(vector<int>{1, 2, 3, 4, 5}) << endl;
```

(Please be aware that `apply` and `compose` take function arguments in the opposite order—the latter takes arguments like the Haskell ‘`.`’ operator.)

### Ranges

During the search for functional programming information, I encountered Eric Niebler’s blog ‘Range Comprehensions’[12], which is simply amazing. If you have read thus far and are interested in functional programming with C++, definitely have a look at his blog. He provided a comprehensive library with many Haskell-like features, and the C++ standard committee liked it too! Hopefully we will see it in some production libraries soon.

### Summary

As C++ evolves, more features are added to the language to enable a more functional style for programming. This is a good thing, as it allows people to be more productive, while keeping easy interaction with the traditional C/C++ code. I am learning, and wish my learning experience could be useful to others too.

May Imperative and Functional live happily together ever after!

### Footnotes

1. C++03
2. transform – C++ Reference
3. C++11
4. back_inserter – C++ Reference
5. There are ways to optimize the code for efficiency (and make the code more complicated). You may want to check out a more complete implementation here.
6. accumulate – C++ Reference
7. Bartosz Milewski’s Programming Cafe
8. What Does Haskell Have to Do with C++?
9. To be honest, perfect forwarding was added later. Worse, I did not make it right. See Type Deduction and My Reference Mistakes for my updated code.
10. C++14
11. Lazy evaluation
12. Range Comprehensions