![]() ![]() 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? 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. We'll extract the variables from each of them using used and merge them together using merge.I have recently become very interested in functional programming - using pure functional languages such as Haskell, as well as functional programming in JavaScript. This case will go quite quickly using the same idea as above. It might look a bit silly to use merge to merge a singleton list into another list, but we need to keep the result ordered and merge is the hammer we have so we turned this problem into a nail. It's the function we're currently defining: used! So we can write this case as: used (Lambda var term) = merge (used term) For term we need a way to turn a Term into a variable or a list of variables. For var we can do the same thing as in the Variable case. If we knew all of those variables we could put those results together with merge. So some variables appear in var and some variables appear in term. Maybe that's why we used those variable names ). So again checking the type declaration of Term we see that var is a Var and term is a Term. The Lambda case used (Lambda var term) =. Thus, really the only option for the implementation is: used (Varable var) = Checking the declaration of Term and the Variable case, we see that var must be a Var. So the right hand side here has to be a list of Var. ![]() The Variable case: used (Variable var) =. Most of that isn't captured in the type of used. While we do so let's keep in mind that used is meant to return an ordered list of Var without repeats. Let's go over how to fill in all the right hand sides of these cases. Finally note that we haven't actually written any of the bodies of the cases for used. Also note that variables in Haskell must start with lowercase characters. Note the parenthesis around each set of data constructor and arguments. It should look like the following: used :: Term -> Next lets look at the syntax of pattern matching. In particular being an empty list ( ) is not a way to be a Term, so that case should be removed. Looking at the definition of Term we see there are 3 ways to be a Term: by being a variable, a lambda, or an apply. And so to write used in a pattern matching style, we'll need to make a case for each of the different ways to be a Term. ![]() How do I collect the variable names and add them to a list? If pattern matching and wild cards are not correct, please can you suggest how I could go about this? I'll use this function to merge two ordered lists together: I think I could achieve this using pattern matching and wild cards, is this possible? import Data.CharĮxample = Lambda "a" (Lambda "x" (Apply (Apply (Lambda "y" (Variable "a")) I want to return them in an ordered list. I want to write a function that will collect the variable names that have been used in a lambda calculus term, both as a Variable and in a Lambda abstraction.įor example in the code I would get the following output: *Main> used example ![]()
0 Comments
Leave a Reply. |