![]() The typesetter turned it into (λy.xy) ab, which is visually close enough. In the typed manuscript, he put the roof in front of the head, so it became (⋀y.xy) ab. Initially, Alonzo Church just drew a little roof to mark the head variable, like this: (ŷ xy) ab. The only thing we can do with it is to resolve it.Ī: An accident, perhaps. It is just a kind of expression, with a head and a body. You can rename variables all you want, without changing the expression.Ī: Nothing, really. The only thing that matters is: when two variables have the same name, they are the same. Q: What is the value or meaning of a variable?Ī: None. part of a function is called its head, and the remainder (the expression) is called the body. The λ does not have any complicated meaning: it just says that a function starts here. A function starts always with the λ and a variable, followed by a dot, and then comes an expression. ![]() With λ and the dot, we can write functions. The greek letter λ (pronounced, of course: Lambda), and the dot.Where we don’t have parentheses, we look at expressions simply from left to right. Parentheses can be used to indicate that some part of an expression belongs together (just as the braces around this part of the sentence make it belong together). More generally, we can write any two or more expressions together to get another expression. An expression can be a single letter, or several letters in a row. Single letters (like a, b, c, d…), which are called variables.As you will see, the Lambda Calculus can compute everything that can be computed, just with a very simple cut and paste.Ī line of symbols is called an expression. All it ever does is taking a line of letters (or symbols), and performing a little cut and paste operation on it. Don’t be intimidated by the word “calculus”! It does not have any complicated formulae or operations. The Lambda Calculus has been invented at roughly the same time as the Turing Machine (mid-1930ies), by Alonzo Church. And if you understood it, you might end up with a much better intuition of computation. It might look frighteningly mathematical from a distance (it has a greek letter in it, after all!), so nobody outside of academic computer science tends to look at it, but it is unbelievably easy to understand. The Lambda Calculus does exactly the same thing, but without wheels to cloud your vision. (A Turing Machine, doing more harm than good. Many may have heard of Turing Machines, but these things tend to do more harm than good, because they leave strong intuitions of moving wheels and tapes, instead of what it really does: embodying the nature of computation. Unfortunately, most people outside of programming and computer science don’t know exactly what computation means. If the universe/the mind/the brain/bunnies/God is explicable in a mechanical way, then it is a computer, and vice versa. The term computation does just this: it defines exactly what machines can do, and what not. For millennia, philosophers have struggled when they wanted to express or doubt that the universe can be explained in a mechanical way, because it is so difficult to explain what a machine is, and what it is not. ![]() Why is it so important? Because computationalism is the new mechanism. If there is one highly underrated concept in philosophy today, it is computation. ![]() The Lambda Calculus for Absolute Dummies (like myself) ![]()
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