The lambda calculus executes via a substitution model. When you apply arguments to a function, you instantiate the function body, replacing its parameters with the actual arguments that were passed in (like we were doing above). You have to be careful when doing this to avoid name collisions. But in the lambda calculus, names don't really matter.

2014年6月22日 · He developed lambda calculus and its logic specifically to avoid type systems. But this typeless logic lead to a paradox that killed it. The typed lambda calculus was susceptible to an even broader paradox, which killed it (for mathematicians...computer scientists dusted it …

In lambda calculus, booleans are often encoded as functions that take two arguments, x and y, and it gives back the first, x, or the second, y, depending on if the boolean is true or false respectively.

2012年8月10日 · The lambda calculus and the Universal Turing Machine are basically two different ways of proving the same thing. I can't remember which one came first, but I seem to recall that they didn't know about the other's work.

2012年6月16日 · The book uses the lambda calculus and various extensions of it to teach topics in type theory, and is really one of the best computer science books around. While it does assume some knowledge of functional programming, it teaches the lambda calculus from the ground up.

2014年12月23日 · Lambda calculus is elegant and quickly applicable, while Turing machines are a harder pill to swallow. It also "opens the mind" to a different approach to programming and computer science early on.

2015年1月7日 · Lambda calculus is really useful for formalising concepts in programming language theory. The theorem prover Isabelle uses typed lambda calculus, a variant of regular lambda calculus but with types, to prove that mathematical statements and even programs are mathematically correct.

2024年4月2日 · lambda calculus is actually less "provable" than TMs; The fact that lambda calculus terms act as functions on other lambda calculus terms, and even on themselves, led to questions about the semantics of the lambda calculus.

Lambda calculus is what most functional programming languages is built on, and the theory of how lambda calculus works helps drive a lot of modern programming linguistical features. I'd liken it to the programming equivalent of a grammar-diagram for a language which allows you to dissect any sentence completely.

2018年12月3日 · In lambda calculus, there are only two things you can do: define a function and apply a function. A function is something that takes an input, does something to it (possibly nothing), and returns some output.