September 30, 2017 Saturday
Bedtime Story
What Makes Lambda Calculus so Invaluable
Tonight we shall consider the other two
arguments on what makes lambda calculus, in spite of its simplicity, so
powerful.
The first was its universality in the area
of coding.
[b] The second important point that makes lambda
calculus so fundamental in modern times is that in can be considered as the
basis for all functional programming languages like Haskell, Python, Elixir and
so on.
Functional programming is a programming
paradigm that treats computation as the evaluation of mathematical functions.
It avoids changing-state and mutable data.
This means that the output value of a
function will solely depend in the argument fed into it unlike say in the case
of Turing machine concept where the state of the machine has a crucial role in
deciding the output.
Programming paradigm is a way of
classifying programming languages depending upon its style, structure and
elements.
Lambda calculus despite being a
mathematical abstraction forms the basis of almost all functional programming
languages used today.
It is said that the origin of functional
programming lies in the lambda calculus which was originally developed to study
computability of a given function, Entscheidungsproblem, function definition,
functional application and recursion.
Lambda calculus provides a theoretical
framework for describing functions and their evaluations.
[c] The third important aspect of lambda
calculus is that it is now present in most major programming languages.
Earlier this was not the case bit it is
today.
Programming languages such as Java, C# (C
Sharp), Visual Basic, F# (F Sharp) and so on, they all either encode lambda
calculus or have it as their fundamental component.
Hence it becomes a subject of great
importance for computer scientists.
The odd thing is visibly lambda calculus is
profoundly simple and has nothing much in it.
It lacks numbers, logical values, recursion
and other such elements.
Yet with such simplicity can arise great
complexity.
Just like few simple atoms of elements can
form very complex biological molecules and these not co-complex molecules can
form chain which can ultimately encode life itself.
Same it is with lambda calculus; simple as
it may be yet everything including numbers, logical values, recursion and so on
can be encoded into it.
In fact they actively have to be encoded
into lambda calculus.
So let us see how one can encode logical
values True and False into lambda calculus.
We shall consider this encoding in the
nights to come.
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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