![]() The equivalent to the above JavaScript function f, when written with lambda calculus, is: In lambda calculus, the process of applying concrete arguments to an abstraction, and reducing the resulting expression is known as beta reduction. Here, f takes 2 arguments - a function x and a value y, and calls x with y as an argument. In JavaScript when we invoke a (pure) function with its arguments, the function gets evaluated and it returns the evaluated result: const f = (x, y) => x(y) The above process is known as beta reduction, which I will talk more about now. In the above, the \(\) syntax indicates that we are going to substitute all instances of \(x\) in the function with \(3\). apply the function to a concrete argument, we use the following syntax: \(\lambda x\) is the head of the abstraction.We can write the same function using lambda calculus as follows: In JavaScript we can easily define and execute this function: const identity = x => x ![]() The following function is known as the identity function, it takes a value and returns that same value. Rather than working from first principles every time we need them, we can choose to use numbers and basic arithmetic operators for convenience. Numbers and arithmetic operations can be defined in terms of lambda calculus via Church Encoding (which is outside the scope of this article). 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. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |