Introduction to Functional Programming with Haskell and JavaScript

Introduction to Functional
Programming
with Haskell and JavaScript
Will Kurt

Will Kurt, Creative Commons Attribution-ShareAlike 3.0

"A language that doesn't effect
how you think about
programming is not worth
learning"
--Alan Perlis

So what is Functional Programming?

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What does this mean?

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No Side Effects!

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Haskell!

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JavaScript!!!

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Lists!!!

first [1,2,3,4] -> 1 (aka: car, head)

rest [1,2,3,4] -> [2,3,4] (aka: cdr, tail)

empty [1,2,3,4] -> false (aka: null?, nil? empty?,[])

empty [] -> true

build 1 , [2,3,4] -> [1,2,3,4] (aka: cons, ':' )

build [1] , [2,3,4] -> [[1],2,3,4]

First class functions

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First Class Functions (Haskell)
add2 x = 2 + x
add3 x = 3 + x

> add2 5
7

> add3 5
8

First Class Functions (Haskell)
argIs2 func = (func) 2
argIs3 func = (func) 3

> argIs2(add2)
4
> argIs2(add3)
5
> argIs3(add2)
5
> argIs3(add3)
6

First Class Functions (JavaScript)

function argIs2(func){
return func(2);
}
function argIs3(func){
return func(3);
}

Lambda Functions

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Lambda Function (Haskell)

add4 = (x -> 4+x)

>argIs2((x -> 4+x))
6

Lambda Function (JavaScript)

var add4 = function(x){
return x+2;
}

var example = argIs2(function(x){return x+2});

var exampple2 = argIs2(function(x){return x+1000});

Lambda Function (JavaScript)

$.ajax({ url: "test.html", context: document.body, success: function()
{
$(this).addClass("done");
}});

$("#exec").click(function(){
$("#results").prepend("<li>Normal Handler</li>");
});

Closures

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Closures (Haskell)

add5 = (+5)
makeAdder val = (+val)
makeAdderWithLambda val = (x->x+val)

add6 = makeAdder 6
add7 = makeAdderWithLambda 7

> add5 5
10
> add6 5
11
> add7 5
12

Closures (JavaScript)

var makeAdder = function(val){
return(
function(x){
return val+x;
}
);
};

>var add6 = makeAdder(6);
>add6(5);
11
>add6(8);
14

Higher Order Functions


Map

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Map (Haskell)
doubleAll xs = map (*2) xs
squareAll xs = map (^2) xs
squareAndAdd xs = map (x->x*x+x) xs
upperCase s = map toUpper s

> doubleAll [1,2,3,4]
[2,4,6,8]
> squareAll [1,2,3,4]
[1,4,9,16]
> squareAndAdd [1,2,3,4]
[2,6,12,20]
> upperCase "doggie"
"DOGGIE"

Map (Haskell)
doubleAllv2 = map (*2)
squareAllv2 = map (^2)
squareAndAddv2 = map (x->x*x+x)

Map (JavaScript) 'The Spolsky Map'

function spolsky_map(fn, a)
{
for (i = 0; i < a.length; i++)
{
a[i] = fn(a[i]);
}
}

note the side effects

Map (JavaScript) Purely functional version

var map = function (func,xs) {
return (
empty(xs) ? [] :
build(func(first(xs)),
map(func,rest(xs))));

};

note: xs and the returned list are distinct

Filter (Haskell)

evenList xs = filter even xs
mod17list xs = filter (== (`mod` 17) 0) xs
doubleEvens xs = (doubleAll . evenList) xs

> evenList [1,2,3,4,5,6]
[2,4,6]
> mod17list [1..100]
[17,34,51,68,85]
> doubleEvens [0,3..27]
[0,12,24,36,48]

Filter (JavaScript)

var filter = function (test,xs) {
return (
empty(xs) ? []:
test(first(xs)) ? build(first(xs),
filter(test,rest(xs))) :
filter(test,rest(xs)));
};

Foldl (Reduce)

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Foldl (Haskell)

mySum xs = foldl (+) 0 xs
myReverse xs = foldl (x y -> y:x) [] xs
sumOfSquares xs = foldl (+) 0 (map (^2) xs)
sumOfSquaresv2 = (mySum . squareAll)

> mySum [1..2000000]
2000001000000
> myReverse [4,16..200]
[196,184,172,160,148,136,124,112,
100,88,76,64,52,40,28,16,4]
> sumOfSquares [1..10]
385
> sumOfSquaresv2 [1..10]
385

Foldl (Haskell)

myReverse xs = foldl (x y -> y:x) [] xs
myReverse [1,2,3]

foldl (x y -> y:x) [] [1,2,3]

.. ([] 1 -> 1:[]) .. => [1]

foldl (x y -> y:x) [1] [2,3]

.. ([1] 2 -> 2:[1]) .. => [2,1]

The Spolsky Reduce (foldl)

function spolsky_reduce(fn, a, init)
{
var s = init;
for (i = 0; i < a.length; i++)
s = fn( s, a[i] );
return s;
}

Foldl (JavaScript) Purely Functional

var foldl = function (fn, init, xs) {
return(
empty(xs) ? init:
foldl(fn,
fn(init, first(xs)),
rest(xs))
);
};

Currying (Haskell)

myAdd x y = x + y
add8 = myAdd 8
add9 = (+9)

> myAdd 8 9
17
> add8 9
17
> add9 8
17

Currying (JavaScript)

var curry = function (f,a) {
return(
function(){
var args = Array.prototype.slice.call(arguments);
args.unshift(a);
return f.apply(this, args);
}
);
};

Currying (JavaScript) purely functional

var curry = function (f,a) {
return(
function(){
return(
(function(args){
return f.apply(this, build(a,args));
})
(Array.prototype.slice.call(arguments))
);
}
);
};

Currying (JavaScript)

var add_three = function(a,b,c){
return a+b+c;
};

>f1 = curry(add_three,1);
>f1(2,3)
6

>f2 = curry(curry(add_three,1),2);
>f2(3)
6

Standard Deviation
1. calculate the arithmetic mean of the list

2. subtract the mean from all the numbers in the list
3. square the number in that list
4. calculate the sum of the list
5. divide the sum by length of list by 1
6. get the square root of this number

Standard Deviation
1. calculate the arithmetic mean of the list
mean xs = sum xs / fromIntegral(length xs)
2. subtract the mean from all the numbers in the list
deviations xs = map (x -> x - m ) xs
where m = mean xs
3. square the numbers in that list
squareDeviations xs = map(^2) devs
where devs = deviations xs
4. calculate the sum of the list
sumSquareDeviations xs = (sum .
squareDeviations) xs
5. divide the sum by length of list by 1
6. get the square root of this number
sd xs = sqrt $ sumSqDev / lsub1
where sumSqDev = sumSquareDeviations xs
lsub1 = fromIntegral $ ((-1+) . length)xs

Standard Deviation (JavaScript)

var mean = function (xs){
return(sum(xs)/flength(xs));
};

var deviations = function (xs) {
var m = mean(xs);//we can remove this
return map(function(x){return x-m;},xs);
};

var squareDeviations = function(xs){
return map(square,deviations(xs));
};

Standard Deviation (JavaScript)

var sumSqDeviations = compose(sum,squareDeviations);

var sd = function(xs){
return Math.sqrt( (sumSqDeviations(xs)/(flength(xs)-1)));
};

Standard Deviation
Haskell
> sd [1,4,5,9,2,10]
3.65604522218567

JavaScript
> sd([1,4,5,9,2,10]);
3.65604522218567

Who actually uses this stuff?

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Introduction to Functional Programming with Haskell and JavaScript

more @ http://www.scala-lang.org/node/1658

... continued

more @ http://haskell.org/haskellwiki/Haskell_in_industry

Questions?

email: wkurt@unr.edu

twitter: willkurt

Introduction to Functional Programming with Haskell and JavaScript

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