27440 total geeks with 3535 solutions
Recent challengers:
 Welcome, you are an anonymous user! [register] [login] Get a yourname@osix.net email address 

Articles

GEEK

User's box
Username:
Password:

Forgot password?
New account

Shoutbox
MaxMouse
It's Friday... That's good enough for me!
CodeX
non stop lolz here but thats soon to end thanks to uni, surely the rest of the world is going good?
stabat
how things are going guys? Here... boring...
CodeX
I must be going wrong on the password lengths then, as long as it was done on ECB
MaxMouse
lol... the key is in hex (MD5: of the string "doit" without the "'s) and is in lower case. Maybe i should have submitted this as a challenge!

Donate
Donate and help us fund new challenges
Donate!
Due Date: Mar 31
March Goal: $35.00
Gross: $0.00
Net Balance: $0.00
Left to go: $35.00
Contributors


News Feeds
The Register
Forum chat is like
Clarkson punching
you repeatedly in
the face
To baldly go where
no one has gone
before: NASA "naut
twin to spend YEAR
IN SPAACE
Hotel Wi-Fi not
only hideously
expensive ? it"s
horribly insecure
Chip rumor-gasm:
Intel to buy
Altera! Samsung to
buy AMD! ... or not
FCC supremo slams
big cable in
gridiron Robin Hood
metaphor mash-up
Flak for Slack
chaps in yak app
hack flap: User
database whacked
Appeal court
bombshell: Google
must face British
justice for "Safari
spying"
Did we just wake up
in an alternate
universe?
BlackBerry turns a
profit
In-depth:
Supermicro"s
youngest Twin is a
real silent ice
maiden
The injected
JavaScript used to
smash anti-Great
Firewall of China
GitHub projects
of
Slashdot
UK Licensing Site
Requires MSIE
Emulation, But
Won"t Work With
MSIE
New Screenshots
Detail Spartan Web
Browser For Windows
10 Smartphones
Iowa"s Governor
Terry Branstad
Thinks He Doesn"t
Use E-mail
Notel Media Player
Helps North Koreans
Skirt Censorship
Ellen Pao Loses
Silicon Valley
Gender Bias Case
Against Kleiner
Perkins
Dark Matter Is Even
More of a Mystery
Than Expected
Toshiba Announces
3D Flash With 48
Layers
Hoax-Detecting
Software Spots Fake
Papers
Google Loses Ruling
In Safari Tracking
Case
Amazon Requires
Non-Compete
Agreements.. For
Warehouse Workers
Article viewer

Simple Recursion in Scheme



Written by:rae
Published by:SAJChurchey
Published on:2008-11-21 06:07:51
Topic:Common Lisp
Search OSI about Common Lisp.More articles by rae.
 viewed 15262 times send this article printer friendly

Digg this!
    Rate this article :
Understanding recursion and how to implement it to solve problems using classical examples in functional programming.

Recursion is a term used to describe a function calling itself. It is an important concept in programming and doubly so in Lisp and its dialects. To understand recursion, we turn to Scheme - a minimalistic dialect of Lisp. Since this article assumes basic familiarity with Lisp/Scheme syntax, we'll directly jump into looking at our first code.

(define (sum-of-list my-list)
  (cond
    [(empty? my-list) 0]
    [else (+ (first my-list) (sum-of-list (rest my-list)))]))


The above function sum-of-list consumes a list of numbers and produces an output which is the sum of all numbers in the list. Thus,

(sum-of-list '(1 34 5)) => 40


Note that in the above call, we use list abbreviations using the quoted syntax instead of using the cons syntax.

Dissecting sum-of-list we see that it defines a conditional where the output of an empty list, i.e. '() would evaluate to 0. This makes sense because giving it an input of a list with no elements would mean that the sum of the numbers of this list would be 0.

The interesting part comes in the else part of the conditional. If the list is non-empty like in our case of (1 34 5), the list is broken up into two - an atomic value consisting of the first element of the list extracted by the first operator, and the second part is again a list consisting of everything but the first element of the list in question. This is done using the rest operator.

Note that the first and rest operators are the Scheme equivalents of car and cdr of Lisp.

The operation that is being carried out here is addition since we want the sum of the elements of the list. The first atomic element is to be added to the resultant of (sum-of-list (rest my-list)) which is by our definition a recursive call. Note that the same procedure is being called again without the first element. So, after the first pass, the operation which will be called will be



(sum-of-list '(34 5))




This function call will then in turn go through the same process, each time splitting the list into its first element and the rest of the list till it splits the list into its last element and an empty list, thereby satisfying the first conditional and returning 0. These results are then added up starting from 0 to the first element of the list in reverse order. This process in the end would return us the summation of the list in question, i.e. 40.


We now look at another problem which is commonly solved by recursion - computing the factorial of a number. Here is a recursive Scheme program for the same using the lambda procedure.



(define factorial
  (lambda (n)
  (if (= n 0) 1
  (* n (factorial (- n 1))))))



In this example, using recursion we're reducing the problem to a simpler one by recursively calculating the factorial of n - 1. For the case where n equals to 0, we have a base case condition where the problem cannot be simplified further and the recursion stops. This is the same as the case of an empty list in the first example we saw while calculating the sum of a list of numbers.

Since Scheme and other purely functional languages don't give us classical iterative approaches like looping, the most natural way to solve such classes of problems boils down to recursion, where a problem is simplified into smaller pieces and a simple operation like addition or multiplication (the above two examples respectively) and a base case is identified. This base case then has a trivial solution which allows us to build a solution to the problem at hand bottom-up.

For further reference on recursion in Scheme, How to Design Programs by Felleisen et al and Concrete Abstractions: An introduction to computer science using Scheme by Hailperin et al are excellent books.

Written by Rae

Did you like this article? There are hundreds more.

Comments:
Anonymous
2011-06-07 16:48:31
You forgot to mention that even if a procedure is recursive, its generated process might be iterative (tail calls).
Anonymously add a comment: (or register here)
(registration is really fast and we send you no spam)
BB Code is enabled.
Captcha Number:



     
Your Ad Here
 
Copyright Open Source Institute, 2006