Lambda Calculus Examples (2009) [pdf]

#1

Post by alphanumeric0 » Sun, Jun 27, 2021, 5:32 AM UTC

Lambda Calculus Examples (2009) [pdf]
ics.uci.edu

Re: Lambda Calculus Examples (2009) [pdf]

#2

Post by benrbray » Mon, Jun 28, 2021, 11:01 AM UTC

Another good reference, that also introduces some PLT notation, is Loh 2001, "Introduction to the Dependently-Typed Lambda Calculus" [1], as well as the textbook by Pierce [2], which has a formally-verified spiritual successor [3].

[1] http://www.cs.ru.nl/~wouters/Publications/Tutorial.pdf [2] https://www.cis.upenn.edu/~bcpierce/tapl/ [3] https://softwarefoundations.cis.upenn.edu/plf-current/index....

Re: Lambda Calculus Examples (2009) [pdf]

#3

Post by dgb23 » Mon, Jun 28, 2021, 11:27 AM UTC

Re: Lambda Calculus Examples (2009) [pdf]

#4

Post by louthy » Mon, Jun 28, 2021, 11:43 AM UTC

dgb23 wrote: post #3

related: https://en.wikipedia.org/wiki/To_Mock_a_Mockingbird

And the obligatory: https://dkeenan.com/Lambda/

Re: Lambda Calculus Examples (2009) [pdf]

#5

Post by heinrichhartman » Mon, Jun 28, 2021, 11:43 AM UTC

Ha! This paper contains the definition of Y-Combinator:

> Y combinator: Y = λt. (λx. t (x x)) (λx. t (x x))

#TIL!

Re: Lambda Calculus Examples (2009) [pdf]

#6

Post by louthy » Mon, Jun 28, 2021, 11:47 AM UTC

heinrichhartman wrote: post #5

Ha! This paper contains the definition of Y-Combinator: > Y combinator: Y = λt. (λx. t (x x)) (λx. t (x x)) #TIL!

Which enables recursion

Re: Lambda Calculus Examples (2009) [pdf]

#7

Post by elric » Mon, Jun 28, 2021, 12:18 PM UTC

What's a good way for someone without much of a background in maths to start grokking this? I've had had several encounters with the lambda calculus over the years (including a coworker who is absolutely in love with it), but it's never really clicked for me in any meaningful way.

Re: Lambda Calculus Examples (2009) [pdf]

#8

Post by panzerklein » Mon, Jun 28, 2021, 1:08 PM UTC

elric wrote: post #7

What's a good way for someone without much of a background in maths to start grokking this? I've had had several encounters with the lambda calculus over the years (including a coworker who is absolutely in love with it), but it's never really clicked for me in any meaningful way.

Here's one great introduction - A Flock of Functions: Lambda Calculus and Combinatory Logic in JavaScript | Gabriel Lebec @ DevTalks

https://www.youtube.com/watch?v=6BnVo7EHO_8

Re: Lambda Calculus Examples (2009) [pdf]

#9

Post by globular-toast » Mon, Jun 28, 2021, 1:21 PM UTC

For someone fluent in Python, David Beazley gives a brilliant introduction to lambda calculus here: https://www.youtube.com/watch?v=pkCLMl0e_0k This is great fun to follow through on a rainy afternoon!

Re: Lambda Calculus Examples (2009) [pdf]

#10

Post by lisper » Mon, Jun 28, 2021, 1:37 PM UTC

Factorials in pure lambda calculus:

https://flownet.com/ron/lambda-calculus.html