October 15, 2017 Sunday
Bedtime Story
Understanding a Combinator
I ended last night with a very complex and
jargon filled definition of combinator.
Tonight I shall try to simplify it for you.
Combinatory logic uses combinators which is
a higher-order function that uses only function application and earlier defined
combinators to define a result from its arguments.
In short, a combinator is a type of
function.
A higher-order function is a function that
will do any of the following:
(i) the argument of this function is one or
more functions – which means that unlike most functions that we know in
mathematics that take in numerical values as inputs, in a combinator what goes
as input is either a function or functions
(ii) the output of this combinator function
is yet another function (instead of some value)
Combinatory logic uses functions without
bound variables.
Let us see how it does so.
This might not be an easy topic specially
coming come from someone who is himself new to it.
Yet there is no harm in giving it a try for
its worth failing than never having tried.
Later we shall see how it is associated
with lambda calculus.
Combinatory logic also known as combinatory
calculus begins with limited set of primitive functions from which other
functions can be built.
The basic constituents of combinatory logic
are the combinatory terms.
The combinatory terms are the following
three:
x which is a variable
P which is a primitive function
(E1E2) are
combinatory terms E1 and E2 that are being applied
P is not only a primitive function but also
a combinatory as it does not contain any free variables
The combinatory terms are combined as E1E2E3E4…En.
Now how can one convert these combinatory
terms into a function?
Here is how.
Consider this.
(P x1 … xn) = E
This pretty becomes a function as several
variables are being fed into the primitive function P.
Now let see some simple example of
combinators that exist in combinatory logic.
We shall look into the various combinators
in the nights to come as this is a heady topic and we should not rush things.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night mon ami and my fellow cousin ape.
Advertisements
Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
No comments:
Post a Comment