4 ms·

What you have there is a sequence. Recursively defined or not, taking the indices out of a sequence takes away the only thing that makes it a sequence (the mapp

What you have there is a sequence. Recursively defined or not, taking the indices out of a sequence takes away the only thing that makes it a sequence (the mapping from the natural numbers) and would be a horrible abuse of notation. I think language designers were certainly consciously aware that they were designing something well defined, and chose to use this kind of syntax because its simpler, rather than an implicit mapping to the natural numbers via something like CPU cycles.

mpweiher 9y ago
> What you have there is a sequence. See Lucid[1] >takes away the only thing that makes it a sequence Unless everything is a sequence[1] [1] http://www.cse.unsw.edu.au/~plaice/archive/WWW/1985/B-AP85-LucidDataflow.pdf http://www.cse.unsw.edu.au/~plaice/archive/WWW/1985/B-AP85-L...
rocqua 9y ago
There is a really simple mapping between recurrent sequences and functions. Simply, given a function $f: A -> A$ that is, a function that outputs from the set it gets input from. We then have the sequence $x_n+1 = f(x_n)$. Often, when dealing with incremental algorithms, the notation x' = f(x) is used. Here x' (pronounced x prime) stands for "the next value of x". It's a nice balance between the correctness of using indices and the conciseness of leaving them out. Going to a higher level, the sequence x' = f(x) is essentially trying to find a fixed point of the function f. To look at this in an actual for or while loop, you need to consider the stopping condition of the loop as part of the function.