1. ______ _ _ _
| ____| | | (_) | |
| |__ _ _ _ __ ___| |_ _ ___ _ __ __ _| |
| __| | | | '_ / __| __| |/ _ | '_ / _` | |
| | | |_| | | | | (__| |_| | (_) | | | | (_| | |
|_| __,_|_| |_|___|__|_|___/|_| |_|__,_|_|
_____ _
| __ (_)
| |__) | __ ___ __ _ _ __ __ _ _ __ ___ _ __ ___ _ _ __ __ _
| ___/ '__/ _ / _` | '__/ _` | '_ ` _ | '_ ` _ | | '_ / _` |
| | | | | (_) | (_| | | | (_| | | | | | | | | | | | | | | | (_| |
|_| |_| ___/ __, |_| __,_|_| |_| |_|_| |_| |_|_|_| |_|__, |
__/ | __/ |
|___/ |___/
____ __ __ __ __ __ ____ __ _ _ __ ____ __ ____ __ __ _
( _ / _ ( ) / _ _( )( ) ( / _ ( / ) / ( / _ ( _ / _ ( (
) _ (/ / (_// / ) )( ) D (/ / / ( O )) D (/ ) // / /
(____/_/_/____/_/_/____/(__) (____/_/_/_)(_/ __/(____/_/_/(___)_/_/_)__)

2. http://eli.thegreenplace.net/wp-content/uploads/2008/05/tc_000.png

3. http://sites.google.com/site/andrewsporfotilio/_/rsrc/1226818616654/Home/math_400.jpg

4. Functional Programming is a style whose
underlying model of computation is the
function.
f(x)

5. Referential Transparency
Higher Order functions
Lazy Evaluation
Pattern Matching
http://picasaweb.google.com/damodaran.balaji/DevCampChennaiJuly2010#5493004664487949618

6. Lambda Calculus
Continuations
Monads
Type Inference

7. Referential Transparency
Higher Order functions
Lazy Evaluation
Pattern Matching

8. Referential Transparency
“Equals can be replaced
with equals”
http://2.bp.blogspot.com/_DS3VD3b2euI/TRIcIUzduDI/AAAAAAAAAGA/Xp2E6kPxZCc/s1600/Pascal+the+chameleon+from+tangled+rapunzel+disney+cartoon.jpg

9. Referential Transparency
“Equals can be replaced with equals”
f(x) = g(x) + 5
h(x) = x * f(x)

10. Referential Transparency
“Equals can be replaced with equals”
f(x) = g(x) + 5
h(x) = x * f(x)
h(x) = x * (g(x) + 5)

11. public class ReferentiallyOpaque {
private int x = 0;
static int f(int y) {
return x += y;
}
public static void main(String[] args) {
ReferentiallyOpaque ro = new ReferentiallyOpaque();
System.out.println(ro.f(5));
System.out.println(ro.f(5));
}
}

12. public class ReferentiallyOpaque {
private int x = 0;;
static int f(int y) {
return x += y;
}
public static void main(String[] args) {
ReferentiallyOpaque ro = new ReferentiallyOpaque();
System.out.println(ro.f(5));
System.out.println(ro.f(5));
}
}
5
10

13. public class Example {
public static void main(String[] args) {
StringBuffer buffer = new StringBuffer("Hello World");
System.out.println(buffer.reverse());
System.out.println(buffer.reverse());
}
}

14. public class Example {
public static void main(String[] args) {
StringBuffer buffer = new StringBuffer("Hello World");
System.out.println(buffer.reverse());
System.out.println(buffer.reverse());
}
}
dlroW olleH
Hello World

15. public class Example {
public static void main(String[] args) {
StringBuffer buffer = new StringBuffer("Hello World");
StringBuffer s1 = buffer.reverse();
StringBuffer s2 = buffer.reverse();
System.out.println(s1 + " " + s2);
}
}

16. public class Example {
public static void main(String[] args) {
StringBuffer buffer = new StringBuffer("Hello World");
StringBuffer s1 = buffer.reverse();
StringBuffer s2 = buffer.reverse();
System.out.println(s1 + " " + s2);
}
}
Hello World Hello World

17. Varying Variables
Global State

18. • Looping
• File I/O
• Modify Data
• Do more than one thing?
http://paulafanclub.com/wp-content/uploads/2010/12/confused.jpg

19. Looping
static int factorial(int number) {
int f = 1;
for (int i = number; i > 0; i--)
f = f * i;
return f;
}

20. Looping
Recursion
static int factorial(int number) {
int f = 1;
for (int i = number; i > 0; i--)
f = f * i;
return f;
}
static int factorial(int number) {
return (number == 1) ?
number :
number * factorial(number - 1);
}
http://www.shrink4men.com/wp-content/uploads/2010/11/dog-chasing-its-tail.jpg

21. Modifying data
static List<Integer> addToList(List<Integer> integers, int a) {
integers.add(a);
return integers;
}
Mutable data structures

22. Modifying data
Immutable
static List<Integer> addToList(List<Integer> integers, int a) {
integers.add(a);
return integers;
}
let addToList list a =
list @ [a]
> let g = [1;2;3;];;
val g : int list = [1; 2; 3]
> addToList g 4;;
val it : int list = [1; 2; 3; 4]
> g;;
val it : int list = [1; 2; 3]
>
http://4.bp.blogspot.com/_RpRScqAI8e4/SbNPgumsqPI/AAAAAAAAAK4/ZK8ZsfKJCmQ/s400/wolverine+hugh+jackman.jpg

23. Referential Transparency
Higher Order functions
Lazy Evaluation
Pattern Matching

24. Higher Order functions
“Functions as first class values”
http://www.dreamstime.com/looking-up-to-the-sky-thumb4655038.jpg

25. Higher Order functions
“Functions that can be passed as arguments”
def square(x):
return x * x
def add(function, x):
return function(x) + function(x)
print add(square, 5)

26. Higher Order functions
“Functions that can be returned as results”
function addNumber(x) {
return function(y) {
return x + y
}
}
var add4With = addNumber(4)
var add5With = addNumber(5)
add4with(8)
add5with(8)
12
13

27. Higher Order functions
“Functions that can be returned as results”
function addNumber(x) {
Lambda Functions
return function(y) {
return x + y
}
}
var add4With = addNumber(4)
var add5With = addNumber(5)
add4with(8)
add5with(8)
12
13

28. Higher Order functions
“Functions that can be returned as results”
function addNumber(x) {
Lambda Functions
return function(y) {
return x + y
}
}
var add4With = addNumber(4)
var add5With = addNumber(5)
add4with(8)
Functions stored in
add5with(8)
data structures
12
13

29. Higher Order functions
“Currying”
let add x y =
x + y
val add : int -> int -> int
> let add5 = add 5;;
val add5 : (int -> int)
> add5 4;;
val it : int = 9
>

30. Referential Transparency
Higher Order functions
Lazy Evaluation
Pattern Matching

31. Lazy Evaluation
“Arguments in a function call are evaluated at most once.”
http://www.arngren.dk/image/Wallpaper/Comic/Calvin%20Hobbes/Sleeping1024.jpg

32. Lazy Evaluation
“Ability to invoke expressions only when its value is needed.”
static void Main(string[] args)
{
var lazy = new Lazy<int>(() =>
{
Console.WriteLine("calculating...");
return 6 * 7;
});
Console.WriteLine(lazy.Value);
Console.WriteLine(lazy.Value);
}

33. Lazy Evaluation
“Ability to invoke expressions only when its value is needed.”
static void Main(string[] args)
{
var lazy = new Lazy<int>(() =>
{
Console.WriteLine("calculating...");
return 6 * 7;
});
Console.WriteLine(lazy.Value);
Console.WriteLine(lazy.Value);
}
calculating...
42
42

34. Lazy Evaluation
“Memoization”
function Lazy_Memoized(def) {
var cache = [];
return function(i) {
return (i in cache) ? cache[i] :
(cache[i] = def.call(arguments.callee, i));
};
}
var factorial = new Lazy_Memoized(function(i) {
return i <= 1 ? i : i * this(i - 1);
});
factorial(6)

35. Lazy Evaluation
“Ability to create infinite sequence in data structures”
http://softwarezku.co.cc/wp-content/uploads/2010/09/Visual-Studio-2010-Logo.png

36. Referential Transparency
Higher Order functions
Lazy Evaluation
Pattern Matching

37. Pattern Matching
“Writing several equations defining the same function”
http://softwareandfinance.com/images/vcpp-trig1.jpg

38. Pattern Matching
A typical function definition
f(x) = 1, when x = 0
= 3x + ex, when x > 0

39. Pattern Matching
A typical function definition
fac :: Integer -> Integer
fac 0 = 1
fac n | n > 0 = n * fac(n-1)
let rec factorial = function
| 0 -> 1
| n -> n * factorial(n - 1)

42. References
• Concepts, Evolution and Application of Functional Programming Languages – Paul
Hudak
• http://msdn.microsoft.com/en-us/library/dd547125.aspx - Pattern Matching in
F#
• http://appden.com/javascript/lazy-list-comprehensions-in-javascript-a-lazy-
evalution/
• http://images.google.com
• http://en.wikipedia.org
• http://www.haskell.org/haskellwiki/Haskell
• http://homepages.inf.ed.ac.uk/wadler/