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INTRODUCTION
What is Lambda Calculus ?
Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic and computer science for expressing computation based on function abstraction and application using variable binding and substitution.It was first formulated by Sir Alonzo Church to formalize the concept of effective computability.
Anurag seems confused..!
Lets explain him what it actually means.
It is nothing but a bridge between a Funcional Language Program and its corresponding Low Level Program
Lamda Calculus
Functional Language Program (1,0)100 Low Level Program
Sayoni has come up with a nice question.
Why we need this bridge ?
Now ,suppose we fix the latter half of the bridge i.e. //
Lamda Calculus (1,0)100 Low Level Program
If any new Functional Language comes up in the future, it can be easily integrated with the latter half of the bridge . Thus making our life a whole lot easier when dealing with a new Function Language.
Why only Lamda Calculus as this bridge ?
- It is very simple . It has very few constructs and very easy semantics, so gettig from Lamda Calculus to Low Level Object Code is very easy
- Powerful enough to express any type of computation. Theoritically, we have Lamda calculus equivalent to Turing Model
\( Turing Model \approx Lamda Calculus\)
Turing Model
:Major model of computation in Computer Science.
Thus all that we can do through a computer can be done through Lamda Calculus
Applied Lamda Calculus
We have discussed about so far.But it was lacking some features, so we switch over to , which filled all the holes present in the raw form of Lamda Calculus. Some of these features are discussed below
- Inbuilt Functions: Basic Functions like +, -, *,|, were not present in the raw form.
- Conditional Operators: IF then ELSE construct was not present in the raw form of Lamda Calculus.
Lamda Expression
When he goes—“Hello World!”
She replies—“Hello dear!”
Ligatures
Questo è strano assai!
Numerals
Old style: 1234567
Lining: 1234567
Vivek Ruparel
created
last updated over 3 years ago