Very True. it has been so troublesome to me, but now its so clear. thank

Agreed: I'm only 2m21s into the video, and he has clarified so much of the syntax that I'm very impressed (and regretful at all the time I lost to other "explanations"!)

Sorry to be so offtopic but does someone know of a trick to log back into an Instagram account?? I somehow lost my account password. I appreciate any tips you can offer me

@Otis Chance instablaster ;)

@Fabian Jax thanks for your reply. I found the site on google and Im waiting for the hacking stuff now. I see it takes a while so I will reply here later when my account password hopefully is recovered.

Top quality is not for everyone, unfortunately

This comment is almost on par with the video!

Welll, good luck!

Not a genius, just had a lot of fun reading up on what other people figured out before me! What you DON'T see here is all the time and effort it took to untangle those ideas, practice them, and examine them from different angles before it made sense to ME. Once I did that, I really wanted to make the subject easier to understand for people like me… by coming up with explanations which I think might have helped. Thanks for the kind words regardless! :-)

Gabriel Lebec please make videos like this! I guarantee you’ll get a lot of exposure

Thanks for the timestamps!

Thanks for you work!

Good one thanks

Yes ;-)

I thought the same! And then when he said "boolean equivalence" I felt both stupid/wrong and smart/correct

Right. I thought of it as 'if and only if'

This is exactly how I feel as well!

FullStack is amazing man!

This is correct and can be verified quickly by a truth table.

Sorry about that! I didn't realize the bottom-left corner was going to be such prime real estate. Slides are linked in the description - I know it's not as good as seeing them live in the video, but I hope they help fill in any gaps regardless! :-)

@@glebec I managed to guess covered parts :-) Thanks for the video!

Hahah, you are the third person to tell me I look like Joel McHale. I don't really see it but I'll take it. 😂

Thanks!

It honestly took me a lot of reading, thinking, and practicing, and I have a degree in math. But like everything in math, with enough time it becomes much easier. I tried to make it easier than when I learned it! :-)

Florian Wicher I absolutely agree.

Thank you for the kind feedback. Glad you enjoyed it.

Thanks for this excellent question! Looking back on this talk, I feel I probably spoke too cavalierly about the M* function, especially as I think I may have subsequently seen definitions for "once removed" functions which differ from my example. Jargon aside, however, we can still talk about the logic. You asked: A) does LC draw a line between lambda statements vs expressions? B) Since (0/0*) yield extensionally equivalent functions (1/1*), and thus any sequential applications of them will yield the same (extensional) results - is it fair to say that extensional equivalence is "backwards propagatable" in general? Hm, interesting question. Certainly LC distinguishes between these at the level of the *grammar* (formal definition of the symbols in the language and how they may be arranged). In the LC grammar, an Expression is either a Value, Application, or Lambda abstraction. Clearly, (1) is an application whereas (1*) is an abstraction. And yet, as we can demonstrate via 2/2*, they are extensionally equal from the perspective of _application behavior_. I think what this comes down to is the notion of "equality" is contextual; we can define extensional equality in terms of application results (which 1/1* uphold), or we can talk about equality in terms of sentences in the grammar (which 1/1* obviously fail to pass). More practically, this sort of thing DOES have profound implications from the perspective of e.g. laziness or evaluation strategies. "Wrapping" some expression E in a "useless" abstraction like `λx.E x` is called "eta expansion". In an eager language like JavaScript, if E is itself an application like `a(a)`, then what you've done is prevented the evaluation of that expression by putting it inside a function body. The evaluation will therefore never be attempted if the function isn't invoked. This technique (eta expansion) is key to representing the Y combinator in JS; the Y combinator unfortunately cannot be used directly in JS because it would trigger infinite recursion. However, the Z combinator uses eta expansion to make part of the evaluation "thunked" or delayed. From LC we know that eta-expanding an expression is extensionally equal to the original expression, so we haven't changed the meaning of the combinator, but we HAVE changed its use case in the context of an engine which evaluates functions "eagerly". (BTW, eager evaluation means arguments to functions are evaluated before being substituted into the function body.) I didn't go much into this in the presentation, but it's a fact that "normal order" evaluation (leftmost outermost) will always find an answer if the expression doesn't diverge; JS doesn't use "normal order" however. Eta expansion can be carried out ad infinitum: `E` becomes `λa.E a` becomes `λb. (λa.E a) b` which becomes `λc. (λb. (λa.E a) b) c` and so on. All are extensionally equal as we have determined, but different evaluation strategies could result in different intensional representations, and some evaluation strategies could in theory fail to terminate. I suppose this implies that our definition of extensional equality only *really* holds for normal order evaluation! I have to think on this more. Thanks again for the stimulating thoughts, -G.

@@glebec What is normal order evaluation? (leftmost outermost)?

@@joseville Normal order evaluation is as follows: when multiple parts of an expression could be beta-reduced (i.e. simplified), choose to beta-reduce the leftmost, outermost expression first. For example, in `foo (bar 8) (qux 9)`, the definition for `foo _ _` will be substituted in before `bar 8` is computed and before `qux 9` is computed.