Mfcttrf

Consider the following code.

%!TEX program = lualatex
documentclass[tikz]standalone 

begindocument

pgfmathsetmacrosumk0

foreach k in 1,2,...,10
 pgfmathsetmacrosumkk+sumk
 directlua print(k,sumk)


enddocument

In this simple example, I want to sum recursively from 1 to 10. This is just done to reproduce my problem: accessing a variable which is set within the loop in next loop iteration, and possibly accessing it also after the loop ended.

My expected output would be (in the log, written with lua print)

1 1.0
2 3.0
3 6.0
4 10.0
5 15.0
6 21.0
7 28.0
8 36.0
9 45.0
10 55.0

However, it is

1 1.0
2 2.0
3 3.0
4 4.0
5 5.0
6 6.0
7 7.0
8 8.0
9 9.0
10 10.0

Can a macro defined within the loop be reused later?

Here is a way:

documentclass[tikz]standalone 

begindocument

defsumk0
deffinsumk0
noindentforeach k in 1,2,...,10%
 pgfmathsetmacrosumkk+finsumk%
 xdeffinsumksumk%
 %directlua print(k,sumk)
 k, finsumk\


enddocument

PS: Add the lua code instead of my simple LaTeX way to print.

Output: Your desired output.

Reason of your failure: Try to change my xdef to def and you will realize that it doesn't work because been lost (gets 0) in every iteration. This is because sumk is a value that expands for one usage inside the code and xdef first expands it and then save it globally.

Actually, TikZ/pgf offers a quite simple solution.
For me, the standard behavior is completely unexpected.

%!TEX program = lualatex
documentclass[tikz]standalone 

begindocument

pgfmathsetmacrosumk0

foreach k [remember=sumk as sumk] in 1,2,...,10
 pgfmathsetmacrosumkk+sumk
 directlua print(k,sumk)


enddocument

It is actually a common behavior of foreach compared to e.g. pgfplotsinvokeforeach provided by pgfplots. You can get more information about this behavior and some examples in pgf-tikz manual § 7 Utilities and pgfplots manual § 8.1 Utility Commands.
I think it is because foreach introduces scopes, while pgfplotsinvokeforeach does not, so the sumk variable is not expanded.

The following example produces the desired output

%!TEX program = lualatex
documentclass[tikz]standalone 
usepackagepgfplots
begindocument

pgfmathsetmacrosumk0

pgfplotsinvokeforeach1,2,...,10
 pgfmathsetmacrosumk#1+sumk
 directlua print(#1,sumk)


enddocument