It is worth noting the absence of any of the constructs of basic arithmetic, such as numbers, addition, subtraction, multiplication, division etc - these are not within the basic axioms of lambda calculus. This is all we get in lambda calculus! It is quite amazing that using these 3 lambda terms we calculate pretty much anything! In addition, parentheses are used in lambda calculus to indicate the order of evaluation. The head is a lambda followed by a variable name.Īn expression is a variable, an abstraction, an application, or any combination of these.Variable - a named token used in a function, which will be replaced by concrete arguments when the function is applied.Ībstraction - a function, made up of a head and a body separated by a ‘\(.\)’ It is made up of just 3 basic components, or lambda terms: Lambda calculus is very minimalistic in its rules/axioms. That is to say, lambda calculus can be used to solve any problem that can be computed using a Turing machine (so anything that anyone has ever programmed with a computer)! Lambda calculus basics any problem that can by solved using a Turing machine can be solved using lambda calculus, and vice versa. While lambda calculus is rather different to the Turing machine in its approach to computation, the two are formally equivalent - ie. The computational model most of us are familiar with is the Turing machine.
By that, I mean that it is a system which can be used to encode and compute algorithmic problems. Lambda calculus was invented by the mathematician Alonzo Church in the 1930s, and is what is known as a ‘computational model’. Lambda calculus is an interesting area of mathematics, and is relatively accessible to those with a minimal maths background. Many concepts from lambda calculus are applicable to general purpose languages such as JavaScript.Ĭoncepts such as pure functions, unary functions and currying are used in many general purpose programming languages, and are often used in functional JavaScript. Understanding lambda calculus will help you to understand these languages. The internals of many functional programming languages such as Haskell, are heavily based on lambda calculus It embodies some of the most important concepts of functional programmingįor example, pure functions, unary functions, currying. There are a few reasons to learn lambda calculus, the main ones I can think of are: If after reading this you are interested in learning more about functional programming in JavaScript, I recommend this Udemy course (affiliate link):įunctional Programming For Beginners With JavaScript Why should I learn lambda calculus?
#Alpha reduction in lambda calculus code#
In this article I want to look at what lambda calculus is, why you might want to learn about it, and explain the key concepts and the terminology of lambda calculus using both lambda syntax and ‘equivalent’ JavaScript code snippets. One of the main areas of study that is often cited as significant for functional programmers is lambda calculus. I have recently become very interested in functional programming - using pure functional languages such as Haskell, as well as functional programming in JavaScript.
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