Trying Haskell
chestergrant.posterous.com
chestergrant.posterous.com
For example:
https://github.com/yairchu/red-black-tree/blob/master/AvlTre... -- in lines 13..21, an AVLTree type is defined -- with its invariants encoded in the type system. If there's a mistake in these 9 lines, you may get a wrong program. But the nice thing is that if you get just these 9 lines right -- then the hundreds of lines below it that implement an AVL tree cannot get the AVL invariants wrong.
The same is also true for Red Black Trees: https://github.com/yairchu/red-black-tree/blob/master/RedBla...
Lines 26..36 inclusive encode the RBTree type such that the invariants are enforced by the type-checker.
In case this is unclear: the type-checker enforcing the correctness of the invariants is at compile-time. A running program is a correct program, at least from the invariants' perspective.
To paraphrase: Some people write tricky code and say, "Ah! I will use a comment to make this clear." Now they have two problems.
I didn't write it, by the way.
This encoding is left as an exercise for the reader.
The most useful kind of comments are "why" comments, about why specific design trade-offs were chosen.
To understand code, you need to figure out "why" and "what". Code gives you one, comments give you the other.
If you want to dismiss me as "one of those" people that is anti-commenting, you're reading too much into what I said. You said, "it doesn't have comments!", I said "actually, it does, and they're even checked." The end.
In a more complex program, I'd add comments. How many, and the nature of the comments, depends on whether I was writing in something relatively low-level (like C) or something high-level (like Haskell, Erlang, or K).
In this specific case, it doesn't matter much since compilation takes less than a second on my underpowered netbook. I'm curious whether it's an issue for a program of significant size.
1.
> in lines 13..21, an AVLTree type is defined -- with its invariants encoded in the type system
Its balance invariants are encoded, but its ordering invariants are not.
2. The code for manipulating AVL and red-black trees in GADT form is significantly more complicated that it would be if they were not in GADT form.
3. Sometimes, whether using GADTs or not, one ends up with code like this, from the AVL example:
> Nil -> undefined -- shouldnt happen
Needless to say, this negatively affects the comfort we might receive from the type system.
Having said all that, I think there are cases where GADTs are really worth the extra effort. Sometimes, they even simplify code when the alternative to GADTs is checking things at run-time!
2. The assurances you get in return are probably worth it.
3. I think that piece is unnecessary, and the type system will see that constructor is impossible. If it doesn't, it's a limitation of Haskell GADT's, and can be fixed. I don't think you ever resort to "Nil -> undefined" in Agda.
I don't disagree on any particular point, but this is hardly news (on HN, at least), and is rather lacking in substance.
http://www.haskell.org/ghc/docs/7.0.2/html/libraries/base-4....
I would be impressed if a sort which used the same 3 combined techniques could be faster.
(Of course, there might be better sorts, such as TimSort, but that's a change of algorithm, not language).
It's still short and sweet ;).
http://hackage.haskell.org/package/vector-0.7.0.1
Mutability is attained by using the ST monad. The ST monad uses mutable memory, but since it does not allow other interactions with the outside world, its value can be extracted (unlike the IO monad). When you are done with the modification of the vector, it can be frozen to obtain a pure vector.
The IO monad can also be used, but not if you want to return a pure value.
A good tutorial can be found at:
http://www.haskell.org/haskellwiki/Numeric_Haskell:_A_Vector...
I used mutable vectors in the ST monad in maximum entropy training software, and they are really performant.
I was like, "Wait. Wait. Waaaiiiitt. How does it do that?"
For an extreme example, the best way to write an efficient matrix multiplication in Fortran is to write a naive matrix multiplication. The compiler will recognize the pattern, and transform it.
Obligatory comment about how sorting algorithm speed is far more important when dealing with incredibly large datasets, spanning across multiple machines. Uninsightful (and perhaps glib) point about how Machines Are So Fast These Days that even Bubble Sort appears fast for medium-sized datasets.
Cleverly-worded comment about how Merge Sort is not the sort of sort to let you down in a jam, and how it is particularly suited to distributed computation (where the overhead of allocation is rendered meaningless by the I/O requirements).
#include <algorithm>
#include <iterator>
#include <functional>
using namespace std;
template <typename T>
void sort(T begin, T end) {
if (begin != end) {
T middle = partition (begin, end, bind2nd(less<iterator_traits<T>::value_type>(), *begin));
sort (begin, middle);
sort (max(begin + 1, middle), end);
}
}
The Haskell version also refrains from importing the equivalent Data.List, which would allow us to define `more` and `less` as simply `partition (< x) xs`.