I get that JavaScript is a popular language, but burying a fundamental concept under a cluttered and confusing syntax like JavaScript, when it's much cleaner to explain the math using sensibly notation.
Ugh. It's nice that Steve is reaching down to his audience, but it would be nice for the audience to step out of their muddy sandbox once in a while.
I have a degree in mathematics from the University of Chicago. Want to talk about self-adjoint algebras of compactly supported continuous functions? I'm your man.
I also think teaching this using mathematical notation would be a mistake. People only learn things when they relate in part to something they already know. The original lambda calculus syntax is not only abstract, it was invented before programmable computers existed.
Unless someone is either already comfortable with mathematical notation or has a background in a programming language with similar concepts (Lisp, Haskell, etc.), it's going to be a stretch to teach someone the lambda calculus -- really teach them -- unless it's framed in terms of a language they already know.
JavaScript is a great language to use for this because it has C-like syntax, which virtually all programmers understand, and first-class functions. You could use Ruby, too, but the syntax would be even more opaque.
The point is not that you can represent it better. The point is that you can actually run it. You can't run the original notation (as such, we know languages that are close, of course).
I agree that the terser notation is better if you're just considering the mathematics in isolation. However, I also think that the true power of this kind of mathematics isn't made evident to people until you actually add some integers and make some lists.... from "nothing"... in a language you already know.
It's the same reason he doesn't use lisp or haskell, which are, obviously, vastly more appropriate. The idea is to illustrate something using something people have readily at hand. Once you have the concrete representation of the idea, you can work backwards to whatever notation you desire and forwards again using that notation, understanding that, yes, it has a basis in reality.
It's the same reason people draw 2d graphs to represent machine learning concepts instead of solely relying upon linear algebra notation. Humans are limited in that way: we have to gain some kind of appropriate intuition, and then we can work with the abstractions after that. No one is going to argue that js is an appropriate way to develop the mathematics -- it's just a way to make it more concrete for people, that's all.
The grouping of expressions is clearer to many readers in the JS example. Unless you've spent a decent amount of time grokking the lambda calculus, the second line could be any of:
(λx. (λf. f)) x
(λx. (λf. f) x)
(λx. (λf. f x))
The lambda calculus notation is weird. Using "." to separate parameter and body is unusual. The scope of the body isn't obvious.
JS is painfully verbose, but it's a verbose syntax many people have already put the time in to internalize.
Not everyone is used to read that math notation. Is like say: "Why put it in JS instead of assembler?". JS is probably the most universal language out there (at least in terms of widespread).
I prefer this stuff in python. Less syntax, more clear. But then, is the same thing: You imagine your (math) syntax is better, I think is python, somebody will complain why not haskell, but js is more practical. Or, is just the one the OP like. That is probably the only and best reason.
> Not everyone is used to read that math notation.
Agreed, but it doesn't take more than a couple of sentences to describe the entire syntax of the λ-calculus. It's not hard to pick it up even if you've never encountered it before.
Contrast that with JavaScript, where even as someone who has written my fair share of it, my eyes tend to glaze over when they hit a string of `});}))());};`. Yet people happily write that sort of thing, then turn around and complain about nested parentheses in Lisp!
Comments
I get that JavaScript is a popular language, but burying a fundamental concept under a cluttered and confusing syntax like JavaScript, when it's much cleaner to explain the math using sensibly notation.
Ugh. It's nice that Steve is reaching down to his audience, but it would be nice for the audience to step out of their muddy sandbox once in a while.
I have a degree in mathematics from the University of Chicago. Want to talk about self-adjoint algebras of compactly supported continuous functions? I'm your man.
I also think teaching this using mathematical notation would be a mistake. People only learn things when they relate in part to something they already know. The original lambda calculus syntax is not only abstract, it was invented before programmable computers existed.
Unless someone is either already comfortable with mathematical notation or has a background in a programming language with similar concepts (Lisp, Haskell, etc.), it's going to be a stretch to teach someone the lambda calculus -- really teach them -- unless it's framed in terms of a language they already know.
JavaScript is a great language to use for this because it has C-like syntax, which virtually all programmers understand, and first-class functions. You could use Ruby, too, but the syntax would be even more opaque.
Here's someone building the lambda calculus using only Procs in Ruby: http://codon.com/programming-with-nothing
Then using Ruby 1.9's "stabbby lambda syntax" you get
Not sure that's any better. The key is explaining it in terms of something the ready already understands well.If they're not already thinking mathematically a straight-forward introduction to the lambda calculus would be ineffective.
Programming with nothing is such an awe-inducing article. There was a conference talk by Jim Weinrich (http://www.confreaks.com/videos/1287-rubyconf2012-y-not-adve...) using the same basic concepts. A nice-to-see for all Ruby/FP enthusiasts out there.
Nice to see a fellow Maroon on here!
The point is not that you can represent it better. The point is that you can actually run it. You can't run the original notation (as such, we know languages that are close, of course).
I agree that the terser notation is better if you're just considering the mathematics in isolation. However, I also think that the true power of this kind of mathematics isn't made evident to people until you actually add some integers and make some lists.... from "nothing"... in a language you already know.
It's the same reason he doesn't use lisp or haskell, which are, obviously, vastly more appropriate. The idea is to illustrate something using something people have readily at hand. Once you have the concrete representation of the idea, you can work backwards to whatever notation you desire and forwards again using that notation, understanding that, yes, it has a basis in reality.
It's the same reason people draw 2d graphs to represent machine learning concepts instead of solely relying upon linear algebra notation. Humans are limited in that way: we have to gain some kind of appropriate intuition, and then we can work with the abstractions after that. No one is going to argue that js is an appropriate way to develop the mathematics -- it's just a way to make it more concrete for people, that's all.
Agreed. I can't understand how something like
can be considered easier to comprehend thanThe grouping of expressions is clearer to many readers in the JS example. Unless you've spent a decent amount of time grokking the lambda calculus, the second line could be any of:
The lambda calculus notation is weird. Using "." to separate parameter and body is unusual. The scope of the body isn't obvious.JS is painfully verbose, but it's a verbose syntax many people have already put the time in to internalize.
Put the brackets in the lambda syntax then. It would be unambiguous and still clearer than the Javascript syntax.
In current Firefox nightlies (and soon everywhere (i.e. Firefox AND Chrome)) it's just:
http://wiki.ecmascript.org/doku.php?id=harmony:arrow_functio...Not everyone is used to read that math notation. Is like say: "Why put it in JS instead of assembler?". JS is probably the most universal language out there (at least in terms of widespread).
I prefer this stuff in python. Less syntax, more clear. But then, is the same thing: You imagine your (math) syntax is better, I think is python, somebody will complain why not haskell, but js is more practical. Or, is just the one the OP like. That is probably the only and best reason.
> Not everyone is used to read that math notation.
Agreed, but it doesn't take more than a couple of sentences to describe the entire syntax of the λ-calculus. It's not hard to pick it up even if you've never encountered it before.
Contrast that with JavaScript, where even as someone who has written my fair share of it, my eyes tend to glaze over when they hit a string of `});}))());};`. Yet people happily write that sort of thing, then turn around and complain about nested parentheses in Lisp!