How to redraw a previous arrow?

Question

I'm trying to write a macro \mappingto which, basically, called after an arrow has been drawn, should add another one below clarifying what elements are mapped to.

e.g. in an easy situation, I'd like

\xymatrix{%
    A \ar[rr]^{f}
      \mappingto{x}{f(x)}
    && B}

to expand to

\xymatrix{%
    A \ar[rr]^{f}
      \ar@{|->}[]!/:a(-90) 3ex/*{x};[rr]!/:a(-90) 3ex/*{f(x)}
    && B}

The main problem I have is how to get the source and target of the previous arrow? I naively thought that

\newcommand{\mappingto}[2]{%
    \POS c="target"
    \POS p="source"
    \ar@{|->}"source"!/:a(-90) 3ex/*{#1};"target"!/:a(-90) 3ex/*{#2}
}

would do the trick, but it obviously doesn't : both items get typeset at the same place, namely below A. I tried all switching of c and p, including c=..., c=... and p=..., p=..., in case the <coord>=<"Id"> does update c and p, but none did change anything.

I'm pretty convinced now, even though I couldn't find confirmation in the reference manual, that arrows and paths save the xy state before being drawn, and restore it afterwards.

So here is my question : is there any way to recover the target of the last drawn arrow? (Since c is always the source, recovering the source isn't a problem)

I also have considered the following solutions :

• pass the direction again as a parameter : it would work, but I don't really like it, in the idea of logical coding
• pass the direction as a parameter and make the \mappingto macro draw both macros : I'd like to be able to use the \mappingto macro with any specific shape, label, position for the "regular" arrow, so it would need a lot of more parameters
• pass the code of the previous arrow as a parameter : Just calling it and saving c and p before or after wouldn't do the trick, because I can already do that. I could actually do something with the code of the macro : extract the direction : from "\ar[rr]^{f}", get "rr". I can almost do it using xstring, but it seems xy-pic can't expand macros inside [ ], so I'm back to step one.

Do you guys see any solution? (preferably in a logical programming mood, aka if I could have a way not forcing me to pass direction or previous arrow to the macro, it would be even nicer ^^)

Thanks in advance

Minimal example for those who want to experiment:

\documentclass{article}
\usepackage[all]{xy}
\usepackage{xstring}

 % Clean code version
\newcommand{\mappingtoI}[2]{%
    \POS c="target"
    \POS p="source"
    \ar@{|->}"source"!/:a(-90) 3ex/*{#1};"target"!/:a(-90) 3ex/*{#2}
}

 % Dirty version
\newcommand{\mappingtoII}[3]{% % First argument is now the first arrow
    \StrBetween{#1}{[}{]}[\direction]
    % Now \direction expands to the direction of the arrow
    #1%     % We draw the first arrow...
    \ar@{|->}[]!/:a(-90) 3ex/*{#2};[\direction]!/:a(-90) 3ex/*{#3}
            % ... and then we try to draw the second one.
}

\begin{document}

% % Uncomment this part to see the expected output.    
% Expected output :
% \xymatrix{%
%    A \ar[rr]^{f}
%      \ar@{|->}[]!/:a(-90) 3ex/*{x};[rr]!/:a(-90) 3ex/*{f(x)}
%    && B
% }

What the basic macro gives :
\xymatrix{%
    A \ar[rr]^{f}
      \mappingtoI{x}{f(x)}
    && B
}

What the "string processing" macro gives : 
 % Won't compile, comment this matrix out if you are trying to get an output!
\xymatrix{%
    A \mappingtoII{\ar[rr]^{f}}
                  {x}{f(x)}
    && B
}        

\end{document}

Edit :

It seems I was wrong stating that xy-pic couldn't expand the macros inside direction definition. Now I think xy-pic tries to evaluate \ar inside macros arguments. :/

Actually, the following macro

\newcommand{\mappingtoTest}[3]{%
    \StrBetween[1]{#1}{[}{]}[\direction]
    \direction
}

which should just print the direction of the entered macro, returns an error message

!Argument of \next has an extra }.

Funny enough, the following macro doesn't return an error :

\newcommand{\mappingtoTest}[3]{}

Adding \protect before \ar doesn't help, and I tried to play with xstring options, finally getting to this macro, which is the most likely to work at the moment, but still doesn't :

\newcommand{\mappingtoTest}[3]{% % First argument is now the first arrow
    \noexpandarg
     \StrBetween{#1}{[}{]}[\direction]
     % Now \direction expands to the direction of the arrow
    \fullexpandarg
    #1%     % We draw the first arrow...
    \ar@{|->}[]!/:a(-90) 3ex/*{#2};[\direction]!/:a(-90) 3ex/*{#3}
            % ... and then we try to draw the second one.
}

The noexpandarg makes a difference though, because

\newcommand{\mappingtoTest}[3]{% % First argument is now the first arrow
    \noexpandarg
     \StrBetween{#1}{[}{]}[\direction]}

does compile, while the same without noexpandarg didn't. If I try to print \direction, I get an obscure xy error again, though. :/

Answer 1

Looks like an expansion problem.

\documentclass{article}
\usepackage[all]{xy}
\usepackage{xstring}

 % Clean code version
\newcommand{\mappingtoI}[2]{%
    \POS c="target"
    \POS p="source"
    \ar@{|->}"source"!/:a(-90) 3ex/*{#1};"target"!/:a(-90) 3ex/*{#2}
}

 % Dirty version
\newcommand{\mappingtoII}[3]{% % First argument is now the first arrow
    {\noexpandarg\StrBetween{#1}{[}{]}[\direction]
    % Now \direction expands to the direction of the arrow
    #1% We draw the first arrow...
    \edef\temp{\noexpand\ar@{|->}[]!/:a(-90) 3ex/*{#2};[\direction]!/:a(-90) 3ex/*{#3}}\temp
            % ... and then we try to draw the second one.
    }
}

\begin{document}
% Expected output :
 \xymatrix{%
    A \ar[rr]^{f}
      \ar@{|->}[]!/:a(-90) 3ex/*{x};[rr]!/:a(-90) 3ex/*{f(x)}
    && B
 }

What the basic macro gives :

\xymatrix{%
    A \ar[rr]^{f}
      \mappingtoI{x}{f(x)}
    && B
}

What the "string processing" macro gives : 


\xymatrix{%
    A \mappingtoII{\ar[rr]^{f}}{x}{f(x)}
    && B
}        

\end{document}