Functional programming

Imperative

vs

Declarative programming

U = IR

What language is functional?

Main things

Function is a first-class and higher-order citizen
Pure functions
Recurtion
Algebraic data types
Strict versus non-strict evaluation (nice to have)

main = map (\x -> 3 * x + 1) [1, 2, 3, 4, 5]

const fn = arr => (prop, asc) => arr.slice().sort((a, b) => {
    return asc * (a[prop] > b[prop] ? 1 : (a[prop] === b[prop] ? 0 : -1));
});

const sorter = fn([{a: 1}, {a: 2}, {a: 3}]);

// a lot of lines after
sorter("a", 1);

// a few more lines of code
sorter("a", -1);

Pure functions

function fn (a, b) {
    console.log(a, b);
    return a + b;
}

Math.random()

Date.now()

main = let a = 3
           b = 1
        in map (\x -> a * x + b) [1, 2, 3, 4, 5]

const fn = arr => (prop, asc) => arr.slice().sort((a, b) => {
    return asc * (a[prop] > b[prop] ? 1 : (a[prop] === b[prop] ? 0 : -1));
});

function () {
    let hash = {
        // some data
    };

    return function (item) {
        return hash[item.id];
    } 
}

function () {
    let hash = {
        // some data
    };

    return function (item) {
        if (!hash[item.id]) {
            hash[item.id] = item;
        }
        return hash[item.id];
    } 
}

Recurtion

There are no loops

function factorial(x) {
    if (x <= 0) {
        return 1;
    } else {
        return x * factorial(x-1); // (A)
    }
}

factorial(100000);

Tail call optimizations

function id(x) {
    return x; // (A)
}
function f(a) {
    let b = a + 1;
    return id(b); // (B)
}
console.log(f(2)); // (C)

Tail call

function id(x) {
    return x; // (A)
}
function f(a) {
    let b = a + 1;
    return id(b); // (B)
}
console.log(f(2)); // (C)

What can be optimized?

const a = x => x ? f() : g();

const a = () => f() || g();

const a = () => f() && g();

const a = () => (f() , g());

function foo() {
    bar();
}

function foo() {
    bar();
    return undefined;
}

function factorial(x) {
    if (x <= 0) {
        return 1;
    } else {
        return x * factorial(x-1); // (A)
    }
}

function factorial(n) {
    return facRec(n, 1);
}
function facRec(x, acc) {
    if (x <= 1) {
        return acc;
    } else {
        return facRec(x-1, x*acc); // (A)
    }
}

Support in browsers

Why?

function a() { return b() }
function b() { return c() }
function c() { console.trace() ..// would not include b()!

Algebraic data types

Types are also functions

data Bool = False | True

data List a = Nil 
              | Cons a (List a)

data Type :: * -> * where
    Char :: Type Char
    Int :: Type Int
    List :: Type a -> Type [a]

sum :: Type a -> a -> Int
sum Char _ = 0
sum Int n = n
sum (List a) xs = foldr (+) 0 (map (sum a) xs)

f :: Int -> Int
f 0 = 1
f 1 = 5
f 2 = 2
f _ = -1

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

hello :: Pet -> String
hello x = 
  case x of
    Cat -> "meeow"
    Dog -> "woof"
    Fish -> "bubble"

Strict versus non-strict evaluation

print length([2+1, 3*2, 1/0, 5-4])

How we can do?

Immutable data structures

Presentation

Category theory

Functor

data Maybe a = Nothing | Just a

Функтор — это класс типов.

> fmap (+3) (Just 2)
Just 5

instance Functor Maybe where  
    fmap func (Just val) = Just (func val)
    fmap func Nothing = Nothing

post = Post.find_by_id(1)
if post
  return post.title
else
  return nil
end

getPostTitle <$> (findPost 1)

Example of Functor?

what if?

fmap (+3) (+1)

> import Control.Applicative
> let foo = fmap (+3) (+2)
> foo 10
15

Applicatives

Just (+3) <*> Just 2 == Just 5

> (+) <$> (Just 5)
Just (+5)
> Just (+5) <$> (Just 4)

> (+) <$> (Just 5)
Just (+5)
> Just (+5) <*> (Just 3)
Just 8

> (*) <$> Just 5 <*> Just 3
Just 15

Monads

half x = if even x
     then Just (x `div` 2)
     else Nothing

Monad — ещё один класс типов

class Monad m where    
    (>>=) :: m a -> (a -> m b) -> m b

instance Monad Maybe where
    Nothing >>= func = Nothing
    Just val >>= func  = func val

> Just 20 >>= half >>= half >>= half
Nothing

IO монада

getLine >>= readFile >>= putStrLn

Questions?