This document provides an introduction to functional programming concepts like currying, functions as parameters, and accumulators. It discusses features of pure functional programming languages like Haskell and ML, including their lack of side effects and strong type systems. Advanced examples demonstrated include recursive functions, higher-order functions, and functional data structures.

1. A brief introduction to functional programming
Sebastian Wild
Stylight GmbH
October 31, 2012

2. Functional programming languages
Some programming concepts
Variables and Functions
Currying
Functions as parameters
Accumulators
Advanced examples
Summary

3. And that language is fast. I mean, really astoundingly
fast, which is why it is so evil. It’s like that psychotic
girlfriend that was amazing in bed. You keep trying to
break up with her, but she seduces you right back into
that abusive relationship.
from brool.com
Article: The Genius of Python, The Agony of OCaml

4. Functional programming languages
Pure
Haskell, Charity, Clean, Curry, Hope, Miranda
Impure
Erlang, F#, Lisp, ML (Standard ML, OCaml), Scala,
Spreadsheets

5. First program
# p r i n t s t r i n g ” H e l l o , World ! ” ; ;
H e l l o , World : u n i t = ( )

6. Variables and Functions
# let a = 5;;
val a : int = 5
# let a = 5 + 3;;
val a : int = 8
(∗ ! ! A t t e n t i o n ! ! Strong type system ∗)
# let a = 5 + 3.0;;

7. Variables and Functions
# l e t a = (5 , () , ” Hello ” ) ; ;
v a l a : i n t ∗ u n i t ∗ s t r i n g = (5 , ( ) , ” H e l l o ”)
# let f x = x ∗ x ;;
v a l f : i n t −> i n t = <fun>

8. Currying
# let f (x , y) = x ∗ y ; ;
v a l f : i n t ∗ i n t −> i n t = <fun>

9. Currying
# let f x y = x ∗ y ;;
v a l f : i n t −> i n t −> i n t = <fun>
( ∗ Types a r e r i g h t b r a c k e t e d ∗ )
i n t −> ( i n t −> i n t )

10. Currying
# let f x y = x ∗ y ;;
# let a = f 5;;
v a l a : i n t −> i n t = <fun>
# let b = a 6;;
v a l b : i n t = 30
(∗ Function c a l l s are l e f t b r a c k e t e d ∗)
# v a l b = ( f 5) 6 ; ;
v a l b : i n t = 30

11. Functions as parameters
# let a = [1;2;3;4];;
val a : int l i s t = [ 1 ; 2; 3; 4]
# l e t r e c map f s =
match s w i t h
[ ] −> [ ]
| x : : x s −> ( f x ) : : ( map f x s ) ; ;
v a l map : ( ’ a −> ’ b ) −> ’ a l i s t −> ’ b l i s t = <fun>
# l e t b = map ( f u n v −> 2 ∗ v ) a ; ;
val b : int l i s t = [ 2 ; 4; 6; 8]

12. Functions as parameters
L i s t . f o l d l e f t : ( ’ a −> ’ b −> ’ a ) −> ’ a −> ’ b l i s t −
L i s t . f o l d l e f t f a [ b1 ; . . . ; bn ]
f ( . . . ( f ( f a b1 ) b2 ) . . . )
# L i s t . f o l d l e f t (+) 0 [ 1 ; 2 ; 3 ; 4 ; 5 ; 6 ] ; ;
− : i n t = 21

13. Accumulators
Faculty of n:
# l e t rec fac n =
i f n <= 0 t h e n 1
else n ∗ fac (n − 1 ) ; ;
v a l f a c : i n t −> i n t = <fun>

14. Accumulator
Tail recursive:
# l e t fac n =
l e t r e c fac ’ acc n =
i f n <= 0 t h e n a c c
e l s e f a c ’ ( n∗ a c c ) ( n−1) i n
fac ’ 1 n ; ;
v a l f a c : i n t −> i n t = <fun>

15. Advanced examples
http://www.ffconsultancy.com/ocaml/bunny/index.html
http://www.ffconsultancy.com/ocaml/ray tracer/index.html

16. Summary
No side effects
Strong type system
Mathematical functions can be expressed very easily
Steep learning curve
https://github.com/wildsebastian/AlgorithmsDataStructures