September 27, 2017 Wednesday
Bedtime Story
Consider Lambda Calculus as a Black Box
As I said last night, whatever little I do
know on these subjects (mathematics, formal logic and computer science) is
largely inspired by mon ami’s fascination for these subjects and my fascination
for his fascination.
Hence there is an element of recursion in
my interest on these subjects.
Yet even for an average ape lambda calculus
in principle is not a very difficult idea to grasp.
Church was studying notion of a function
from computational perspective.
From the way Church considered function,
pictorially you can consider function as a black box.
This black box is so black that you are not
allowed to look what is going on inside.
You may wonder what this box does.
Well, the box acts like a function.
It takes in an input, processes it and
gives an output.
This is all that a function does.
For instance, it can take as input any
variable x, process it and give an output of say x + 10.
This is a simple function that adds 10 to
any number that goes as input.
So in this case, we have a single input and
a single output.
Consider this second case where there are
two inputs x and y.
The black box takes in two inputs,
processes them and gives the output as x + y which just means the function is
summing of the two inputs.
There are two important things about this
box that Church considered it worth noting:
(a) The Box is black, really black in the
sense that it is opaque.
You are not allowed to see what’s going on
inside which essentially means you have no idea how the black box is processing
the data that is being fed as inputs.
(b) The function is pure.
Now what do I mean by pure?
Here the word “pure” comes in a highly
technical sense wherein a comparison is being made with Turing machine concept.
The so called purity in this case is that
this box has no internal state, a concept that was of critical importance in
Turing machine that contains a state register which stores the state of the
Turing machine.
We will come to that later.
So suffice to say that the black box of
lambda calculus has no internal state; it is a pure mathematical function.
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.
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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:
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