Idris - pure functional programming language with dependent types
idris-lang.org
idris-lang.org
* http://hackage.haskell.org/package/vector-static
* http://hackage.haskell.org/package/hmatrix-static
A nice next step would be to optimize out additional runtime bounds checks.
I mean, using an "element from a finite set" to index a vector? Back home, we use natural numbers for that. Idris also has natural numbers, but somehow we still have to, essentially, use the "finite set of values we don't care about, but that we can order if we want to since, after all, the set has a finite number of elements" concept for what's essentially an array lookup.
Why can't there be a type of "natural numbers under N"?
Or am I all misunderstanding things, and is the "finite set" exactly that type, just explained in a very not straight forward way?
Also, impressively, the author claims it has C-style speed. Does that mean that looking up a value in a vector by means of an element in a finite set is actually translated to a single *(vect+index)? (in C-terms)
There'd also be nothing wrong to use a natural number, along with a proof that it's bounded by the length, to index the vector.
I don't think I've claimed it has C-style speed anywhere. At least, not in general - we have observed it in some cases though, and it is a goal to make it as efficient as possible. Dependent types plus partial evaluation gives you some nice opportunities for optimisation. Early days yet...
Ah, right! I must admit that it feels like an odd definition to me indeed. I see how "the first n natural numbers" is a finite set of n elements, but I don't see how the reverse is true. I mean, look here, a finite set of n elements: {1, 1, 1, 1}. 4 elements, and they're all valued 1. They're also not ordered. So your concept of taking an element from a finite set (in this case, let's say, 1, or maybe 1 instead) to uniquely identify an element in a vector sounds a bit odd to me :-)
Clearly, I'm the noob here, and maybe in this stage Idris just isn't meant for people not on Lambda the Ultimate, but if not, it's good that you intend do something about it :-)
Cause once again, I love the concept, and I'd love to program with this.
I'm an idiot!
And that only 3 years out of university :-(
As for compiling to that pointer access: from what I know of Idris, yes it will. Since you know statically that the array access cannot be out of bounds, you can omit the usual out-of-bounds checks.
Vect a n = vector of a with known length n
(n ** Vect a n) = vector of a with unknown length n
You don't normally need to write each vector function both ways. If you can statically know the length (which you normally do in practice, at least in my experience) then you can write down a more precise type. filter serves as an example of what you might do when you need to compute an index dynamically.