ionfish

6 ms·

1.
by ionfish 12y ago
Here is the cartoon Knuth refers to. http://www.danzigercartoons.com/archive/cmp/2002/danziger141...
2.
by ionfish 14y ago
I wouldn't confuse modules with modularity. Think of it like this: types are the primary API for the program. In fact, I tend to call the modules that perform this function in my code something like 'Core'. Since they're a shared language t
3.
by ionfish 14y ago
It's pretty common in the UK these days.
4.
by ionfish 14y ago
No, the default backend is the native code generator. You need to use the -fllvm flag to enable the LLVM backend. http://www.haskell.org/ghc/docs/7.6.1/html/users_guide/code-... "[The LLVM backend] is an alternative backend that uses the
5.
by ionfish 14y ago
Coming from a set-theoretic perspective, I suppose I've got so used to Tarski's theorem that I consider it intuitive. As far as Tychonoff's theorem goes, you might find this paper interesting: http://matwbn.icm.edu.pl/ksiazki/fm/fm113/fm11
6.
by ionfish 14y ago
Lots. For example, that every set has a cardinality (is bijective with some aleph). That's pretty intuitive, too, as (I think) are the following. * Let X and Y be sets. Then either they have the same cardinality, or one is smaller than the
7.
by ionfish 14y ago
Having written the following, I now wonder whether you meant something more specific by computation than I did, so I'm not certain whether my point is really a response. Could you spell out the details of your comment a bit more, and perhap
8.
by ionfish 14y ago
I don't care that nobody cares. I care that they pretend that they do. Fake friendliness is annoying, and good service is not formulaic.
9.
by ionfish 14y ago
AC is equivalent to a lot of things. There's a collection of them on the Wikipedia page. http://en.wikipedia.org/wiki/Axiom_of_choice#Equivalents Something I find pretty interesting is that some of these equivalences break down in weak sy
10.
by ionfish 14y ago
The history of the proof is a little messy; the Wikipedia page has a decent summary. http://en.wikipedia.org/wiki/Cantor–Bernstein–Schroeder_theo...
11.
by ionfish 14y ago
Yes, it does rely implicitly on Cantor–Schröder–Bernstein. That might be a downside, but I think when working informally (that is to say, when not teaching a set theory course) one can simply assert that if there exist injective functions f
12.
by ionfish 14y ago
I think this becomes much more intuitive once one understands that the cardinality of any nondegenerate closed interval is the same as the cardinality of the continuum.
13.
by ionfish 14y ago
The usual way this is done is by selecting a canonical representation for the reals in the list. It's pretty much the same thing as you said, but I don't think you're putting it in the right terms. The list you're diagonalising (in Cantor's
14.
by ionfish 14y ago
Like I said in my response to pndmnm, in my view if someone "[would] think that the cardinals also formed a set with an (infinite) cardinality of its own" then they haven't really grasped the theorem yet. It's built into it that if we're a
15.
by ionfish 14y ago
I'm not saying it's not interesting—in fact, I think it's fascinating—but all of this is implicit in Cantor's Theorem. "Harder question" to me implies there's something there that goes beyond the fundamental result that the powerset of a se
16.
by ionfish 14y ago
That's a really nice way to show that, thanks. I may borrow it for future use.
17.
by ionfish 14y ago
Why is that a harder question? It's a direct corollary of Cantor's Theorem that there is no largest cardinal number (assuming the powerset axiom, of course).
18.
by ionfish 14y ago
The set of fractions isn't larger than the set of whole numbers, so how good an explanation could it be?
19.
by ionfish 14y ago
I don't think one can ignore that and also focus on practicality. Using these JS dialects is a practical issue. Learning them and remembering how they work imposes a certain amount of overhead, albeit a reasonably small one. Of greater co
20.
by ionfish 14y ago
> having to write Udon.curry everywhere sort of takes away from that cleanliness you are trying to recreate. This is true, and I considered your approach when writing functions like `elem`. There were two reasons for this. Firstly, I wa
21.
by ionfish 14y ago
You probably shouldn't. :)
22.
by ionfish 14y ago
Oh, I think it was mainly trivial stuff. I'm afraid I don't remember the specifics, this was two years ago.
23.
by ionfish 14y ago
Yes, although there is one subtlety here: should `flip` return a curried function, or an uncurried function? This isn't an issue in Haskell since it only has unary functions.
24.
by ionfish 14y ago
Yes, it does. This is true in Haskell too, of course. subtract :: (Int, Int) -> Int subtract (n, m) = n - m fiveMinus = (curry subtract) 5 minusFive = ??? subtract' = \n m -> n - m fiveMinus = \
25.
by ionfish 14y ago
It has a few more functions that operate on lists, but it's missing a lot of the general utility functions that Underscore has. Roy looks interesting, thanks for the link.
26.
by ionfish 14y ago
It seemed unnecessary, yes, although I suppose there are possibly some circumstances where one might want a `first` function—for example if one were folding over a list of lists.
27.
by ionfish 14y ago
That's very cool, although you have to use another dialect of JavaScript if you want to modify the source code, with all the disadvantages that entails.
28.
by ionfish 14y ago
Patches for these would be welcome; I did mean to add them, but I got distracted by other projects, and then by my PhD.
29.
by ionfish 14y ago
To be honest, I completely agree with you. But it wouldn't be a JavaScript functional programming library if it didn't have the curry function. I'm pretty familiar with Underscore, just wasn't happy with a couple of the design decisions, ot
30.
by ionfish 14y ago
Of course it would. Patches which improved the documentation would be very welcome.

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