## Introduction:

Programming is based on functions which can be primary programming and its called functional programming it is a basic practical approach towards programming and make them easier and problem solving in general into computation. We can say that it play a role of bridge between computer application and formal methods. In every computation, output depends on parameters. So we can say that any functions is best way of a specifying a computation. And Functional programming is depends on computation.

It have a characteristic features, that means any expression which having well defined value, then order which in which computation is processed does not affect evaluation. It means language can be calculated, manipulated just like mathematical expression using some algebraic laws. After this outcome is conceptual framework of programming is processed one time but it is very simple, concise and flexible.

## Characteristics of Functional programming:

- It have no harmful affect and more efficient.
- Assignment statements are absent.
- In maximum case variables are not found.
- It use very concise and small framework.
- Syntaxes are very simple and uniform.
- It can be implemented through interpreters instead of compilers.
- Due to mathematical expression it can be handle easily.

### Importance of Functional programming:

- In original state it allot with notion of assignment it can help in making programming eaiser in written.
- It gives a courage to thinking at higher level of concepts, it means it can support in modification and combining with present programs and therefore, you can do programming
- It is important for development of specification execute, and implementation.

#### Expressions:

Aim of functional programming is increase the advantages of expressions to whole programming languages.

`( x+y )*z`

it is an arithmetic`( x+y)=0`

it is rational`-(x Ñµ y )`

Boolean

Assignment can alter the computations but must be in order for an example

` x:=x*y; y:=y+1`

But expression in order is not harmful and thus it is order dependent. It is called Church-Rosser Theorem

#### Church-Rosser Theorem:

This theorem state that if any expression can be reduce by zero or may be more reduction steps to either M or any be N then may be their other irreducible expression are present, may be normal form in which M and N will be reduced.

`( Æ›x .x+1)4 => 4+1`

This example shows that lambda-calculus contain beta-reduction rule for evaluate the application of lambda concept to an expression. This theorem gives expression of reasoning is easy and also support order independence and fine-grained parallelism.

Some example of functional programming languages:

- First functional programming language is came in about 1958 called LISP
- Haskell and Miranda is two most popular example of pure functional programming language.
- Meta language and standard meta language is more practical but have some side effects.

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