Get ready for Lambda Calculus

We're assuming you never heard about it in your life. And that is totally normal because there is very little information on the internet about this stuff.

If you are just a beginner in lambda calculus and had experience in programming, then You are in the right place.

### What is Lambda Calculus?

**Lambda(λ) Calculus** can be called the **smallest universal programming language** in the world, and it's not an object-oriented programming language.

The main use of **λ-calculus** is in the field of mathematics, it is a mathematical model for understanding computation based on function abstraction and application using **variable binding**(*when the compiler assigns a variable*) and **substitution**(*assigning a new value of an entity*).

It is a universal model of computation that can be used to simulate any Turing Machine(*changes according to assigned rules*).

You can read What is a model of the lambda calculus? by Albert R.Meyer

##### Who developed Lambda Calculus?

It was developed by **Alonzo Church** (American mathematician and logician) in the 1930s to study computations with functions.

##### Why it is called Lambda?

Lambda(λ) is derived from the Greek language and lambda means binding(*assigning a variable to an entity*).

### 3 Rules of Lambda Calculus

These are the following rules:-

Syntax | Name | Description |
---|---|---|

x | Variable | A character or string representing a parameter or mathematical/logical value. |

(λx.M) | Abstraction | A Function definition (M is a lambda term). The variable x becomes bound in the expression. |

(M N) | Application Applying | A function to an argument. M and N are lambda terms. |

You can checkout **λ Calculus Interpreter** by **Lian Gong**

### Topics in Lambda Calculus

- Lambda terms
- Functions that operate on functions
- Alpha equivalence
- Free and bound variables
- Capture-avoiding substitutions
- Reduction
- Substitutions

And if you want to continue lambda calculus and know more about it we really recommend the book An Introduction to Functional Programming Through Lambda Calculus by **Greg Michaelson**

### Conclusion

This was our first article about lambda calculus And thanks for reading it.

we would love it and it really helps us cover our costs if you can donate some money to our Patreon page.

Donate Us!In the future, we're looking to bring up a big course about lambda calculus and for that, we need some funding and we're still looking for it.