4 ms·

You have something similar in mathematics. Recurrence relations. Since we are dealing with a sort of time difference inside a computer, something like "x = x +

by vlasev 9y ago

You have something similar in mathematics. Recurrence relations. Since we are dealing with a sort of time difference inside a computer, something like "x = x + 1" can be interpreted as "the value of x at the next time unit is the value of x at the previous time unit plus one". That is "x[n+1] = x[n] + 1" and this is a recurrence relation. My guess is that early programmers were deeply aware of this time difference, so "x = x + 1" made perfect sense.

rocqua 9y ago
The way these recurrence relations are taught at university is to distinguish the new value from the old value by using a ' pronounced prime. Here, you would write x' = x + 1 to give the recurrence relation x[n+1] = x[n] + 1. Or, more generally x' = f(x) for x[n+1] = f(x[n]). The reason for this is because in mathematics x = x + 1 is absurd (ignoring modulo arithmetic).
- Izkata 9y ago
  In highschool, we used numeric subscripts for that. Ticks(apostrophes) were kept for derivatives.
  - ascar 9y ago
    Though it's neither a tick nor apostroph, but as the parent said a prime: https://en.wikipedia.org/wiki/Prime_(symbol) https://en.wikipedia.org/wiki/Prime_(symbol)
  - rocqua 9y ago
    If only there were enough notation that every notation could be unique.
jcranberry 9y ago
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.

by vlasev 9y ago

rocqua 9y ago

The way these recurrence relations are taught at university is to distinguish the new value from the old value by using a ' pronounced prime. Here, you would write x' = x + 1 to give the recurrence relation x[n+1] = x[n] + 1. Or, more generally x' = f(x) for x[n+1] = f(x[n]). The reason for this is because in mathematics x = x + 1 is absurd (ignoring modulo arithmetic).

Izkata 9y ago
In highschool, we used numeric subscripts for that. Ticks(apostrophes) were kept for derivatives.
- ascar 9y ago
  Though it's neither a tick nor apostroph, but as the parent said a prime: https://en.wikipedia.org/wiki/Prime_(symbol) https://en.wikipedia.org/wiki/Prime_(symbol)
- rocqua 9y ago
  If only there were enough notation that every notation could be unique.

jcranberry 9y ago

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.