Emulate a “tuple” data structure (when you are free to choose the syntax)

Question

How can a "tuple" data structure be implemented in LaTeX? The idea is to store several elements (possibly a predefined number) in one macro and then be able to extract each of these elements by index (numeric or otherwise).

\documentclass{article}

% HOW TO IMPLEMENT THIS?
\newcommand{\definetuple}[...]{...}
\newcommand{\extractfromtuple}[...]{...}
% HOW TO IMPLEMENT THIS?

% YOU ARE FREE TO CHANGE SYNTAX HERE
\definetuple{first}{Alice}{Munich}{Germany}
\definetuple{second}{Bob}{London}{United Kingdom}

\begin{document}
  \extractfromtuple{first}{1} lives in \extractfromtuple{first}{2}
  which is located in \extractfromtuple{first}{3};
  this may or may not be true for \extractfromtuple{second}{1}.
\end{document}
% YOU ARE FREE TO CHANGE SYNTAX HERE

I'd like to split the original question so that nice solutions with a new API have a place to live. Should this be community wiki?

Answer 1

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\definetuple}{mmmm}
  {
   \tl_new:c { g_tuple_#1_tl }
   \tl_gset:cn { g_tuple_#1_tl } { {#2} {#3} {#4} }
  }
\DeclareExpandableDocumentCommand{\extractfromtuple}{mm}
  {
   \tl_item:cn { g_tuple_#1_tl } { #2-1 }
  }
\ExplSyntaxOff
\begin{document}
\definetuple{alice}{Alice}{Munich}{Germany}
\definetuple{bob}{Bob}{London}{United Kingdom}

\extractfromtuple{alice}{3}

\extractfromtuple{bob}{1}

\end{document}

In this simple case I've used a token list; for more complex tasks a sequence would be better, perhaps.

Another approach might be with property lists.

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\definetuple}{mmmm}
  {
   \prop_new:c { g_tuple_#1_prop }
   \prop_gput:cnn { g_tuple_#1_prop } { name }    {#2}
   \prop_gput:cnn { g_tuple_#1_prop } { town }    {#3}
   \prop_gput:cnn { g_tuple_#1_prop } { country } {#4}
  }
\DeclareExpandableDocumentCommand{\extractfromtuple}{mm}
  {
   \prop_get:cn { g_tuple_#1_prop } { #2 }
  }
\ExplSyntaxOff
\begin{document}
\definetuple{alice}{Alice}{Munich}{Germany}
\definetuple{bob}{Bob}{London}{United Kingdom}

\extractfromtuple{alice}{country}

\extractfromtuple{bob}{name}

\end{document}

Here the available keys are name, town and country. I'd prefer this approach for more complicated tasks, where, for example, data are added one piece of information at a time; for example one could define

\NewDocumentCommand{\addtotuple}{mmm}
  {
   \prop_gput:cnn { g_tuple_#1_prop } { #2 } { #3 }
  }

and \addtotuple{alice}{town}{Berlin} would move Alice to the north.

Answer 2

Here is a generalized solution similar to Python's tuples in six lines of TeX code.

\documentclass{article}
\makeatletter
\def\tuple#1=(#2 #3 #4){%
    \expandafter\def\csname#1@1\endcsname{#2}
    \expandafter\def\csname#1@2\endcsname{#3}
    \expandafter\def\csname#1@3\endcsname{#4}
}
\def\xtuple#1#2{%
    \csname#1@#2\endcsname
}
\makeatother
\begin{document}
% example add
\tuple firstauthor=(Alice Munich Germany)
\tuple secondauthor=(Bob London United Kingdom)
% example print
\xtuple{firstauthor}{1}
\xtuple{secondauthor}{3}
\end{document}

Like in Python spaces are significant:) You add a triplet (your structure is made of triplets, as you indicated not tuples) as:

  \tuple firstauthor=(Alice Munich Germany)

You access the n-element as:

  \xtuple{firstauthor}{1} 
  \xtuple{secondauthor}{3}

It is easier to understand the structure if we define a triplet for color,

  \tuple red=(255 0 0)
  \xtuple{red}{1}

More operations can be added fairly easily.