A brief introduction to functional programming

Sebastian Wild

Stylight GmbH

October 31, 2012

Functional programming languages

Some programming conceptsVariables and FunctionsCurryingFunctions as parametersAccumulators

Advanced examples

Summary

And that language is fast. I mean, really astoundinglyfast, which is why it is so evil. It’s like that psychoticgirlfriend that was amazing in bed. You keep trying tobreak up with her, but she seduces you right back intothat abusive relationship.

from brool.comArticle: The Genius of Python, The Agony of OCaml

Functional programming languages

I PureHaskell, Charity, Clean, Curry, Hope, Miranda

I ImpureErlang, F#, Lisp, ML (Standard ML, OCaml), Scala,Spreadsheets

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 = ( )

Variables and Functions

# l e t a = 5 ; ;v a l a : i n t = 5

# l e t a = 5 + 3 ; ;v a l a : i n t = 8

(∗ ! ! A t t e n t i o n ! ! St rong t y p e system ∗)# l e t a = 5 + 3 . 0 ; ;

Variables and Functions

# l e t a = ( 5 , ( ) , ” H e l l o ” ) ; ;v a l a : i n t ∗ u n i t ∗ s t r i n g = ( 5 , ( ) , ” H e l l o ”)

# l e t f x = x ∗ x ; ;v a l f : i n t −> i n t = <fun>

Currying

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

Currying

# l e t 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 )

Currying

# l e t f x y = x ∗ y ; ;

# l e t a = f 5 ; ;v a l a : i n t −> i n t = <fun>

# l e t b = a 6 ; ;v a l b : i n t = 30

(∗ F u n c t i o n c a l l s a r e 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

Functions as parameters

# l e t a = [ 1 ; 2 ; 3 ; 4 ] ; ;v a l a : i n t 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 xs ) ; ;

v a l map : ( ’ a −> ’ b ) −> ’ a l i s t −> ’ b l i s t = <fun>

# l e t b = map ( fun v −> 2 ∗ v ) a ; ;v a l b : i n t l i s t = [ 2 ; 4 ; 6 ; 8 ]

Functions as parameters

L i s t . f o l d l e f t : ( ’ a −> ’ b −> ’ a ) −> ’ a −> ’ b l i s t −> ’ a

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

Accumulators

Faculty of n:

# l e t r e c f a c n =i f n <= 0 then 1e l s e n ∗ f a c ( n − 1 ) ; ;

v a l f a c : i n t −> i n t = <fun>

Accumulator

Tail recursive:

# l e t f a c n =l e t r e c fac ’ acc n =

i f n <= 0 then acce l s e fac ’ ( n∗ acc ) ( n−1) i n

fac ’ 1 n ; ;v a l f a c : i n t −> i n t = <fun>

Advanced examples

http://www.ffconsultancy.com/ocaml/bunny/index.htmlhttp://www.ffconsultancy.com/ocaml/ray tracer/index.html

Summary

I No side effects

I Strong type system

I Mathematical functions can be expressed very easily

I Steep learning curve

https://github.com/wildsebastian/AlgorithmsDataStructures