λ Calculus (2013) [pdf]

That's a bit of a strange statement. The Y combinator is an expression in λ calculus. It's like saying French is even more beautiful than the phrase "nouveau départ".

Re: λ Calculus (2013) [pdf]

#7

Post by carlineng » Fri, Aug 18, 2023, 2:21 AM UTC

My favorite discussion of this topic is from David Beazley: https://www.youtube.com/watch?v=5C6sv7-eTKg

He does a wonderful job of taking very dense mathematical notation and explaining it in ways that anyone can understand. He derives the basic concepts of the lambda calculus from the ground up using Python. Super fun to follow along with.

Re: λ Calculus (2013) [pdf]

#8

Post by curryhoward » Fri, Aug 18, 2023, 2:22 AM UTC

cbarrick wrote: post #5

andsoitis wrote: post #2

created by Church and Kleene in the 1930’s! Even more beautiful than the y combinator

They're one and the same. Y = λf.(λx.f (x x)) (λx.f (x x))

The Y combinator is not the same as λ calculus. The Y combinator is an expression in λ calculus.

Re: λ Calculus (2013) [pdf]

#9

Post by mangodrunk » Fri, Aug 18, 2023, 2:23 AM UTC

leetrout wrote: post #4

Mimmy wrote: post #3

any idea what book this chapter is from?

Programming Distributed Computing Systems A Foundational Approach Carlos A. Varela 2013 https://mitpress.mit.edu/9780262018982/programming-distribut...

You beat me to it, this is the link that I found for the book: http://wcl.cs.rpi.edu/pdcs/#chapters

Re: λ Calculus (2013) [pdf]

#10

Post by lmm » Fri, Aug 18, 2023, 2:34 AM UTC

curryhoward wrote: post #8

cbarrick wrote: post #5

Earlier quoted context omitted.

They're one and the same. Y = λf.(λx.f (x x)) (λx.f (x x))

The Y combinator is not the same as λ calculus. The Y combinator is an expression in λ calculus.

The Y combinator is in a sense the heart of the λ calculus; it's a key discovery for understanding that the λ calculus is universal, which is what makes it a useful concept rather than an arbitrary bundle of rules.