Andrei Alexandrescu wrote:
I've updated my code and documentation to include series (as in math) in the form of infinite ranges. Also series in closed form (given n can compute the nth value without iterating) are supported as random-access ranges.
I've been thinking a little about the concepts involved in range endpoints. Most important ranges are homomorphic to ints; that is, given [x..y], there is some finite number n of elements in the range. And there is an ordering: successor(successor(x)) repeated n times will return y. As well as ints and many data structures, fixed-point and built-in floating-point arithmetic obey these properties. Interestingly this even applies to an "infinite" range: [1..real.infinity] has a limited number of elements.
However, some other ranges do NOT behave this way. Mathematical real numbers defined symbollically, for example. More realistically, arbitrary-precision fractions. For these types of ranges, there is no successor function. Thus, they are not even input ranges; but they have some properties of random-access ranges. There are many algorithms which work on these non-quantised ranges.
Now consider the range 5.0L..real.max, on a system where real is 128 bits. Is it a random-access range? Sort of. You can't provide an opIndex(), even with ulong as an index, because there are just too many entries. But there are many operations you can still do. predecessor and successor are nextDown(), nextUp(). My root-finding algorithm in std.numeric uses these functions as well as an approximate-midpoint-in-representation-space function.
In any case, I think it would be good to come up with some standard names for the predecessor and successor functions.
