How to make parentheses usable as macro delimiters when the macro is passed as a point in RPN notation?

Question

How to make ( and ) usable as macro delimiters when the macro is passed as a point in RPN notation?

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-plot}

\def\f#1{#1 2 exp 1 sub}
\def\g[#1]{#1 2 exp 1 sub}
\def\h(#1){#1 2 exp 1 sub}
\def\i<#1>{#1 2 exp 1 sub}
\def\j|#1|{#1 2 exp 1 sub}

\begin{document}
\begin{pspicture}[showgrid=bottom](-4,-2)(4,4)
    \psplot{-2}{2}{\f x}
    \psdots(!0 \f{0})
    \psdots(!-2 \g[-2])
%   \psdots(!2 \h(2))% <== cannot be compiled!
    \psdots(!1.25 \i<1.25>)
    \psdots(!1.5 \j|1.5|)
\end{pspicture}
\end{document}

Answer 1

that is the default problem with TeX and how it reads tokens. It looks for the first ( and the first ), the reason why you cannot use that kind of notation. It is a similiar problem as the well known [...[...]]. However, you can use the algebraic notation:

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-plot}

\def\f#1{#1 2 exp 1 sub}
\def\g[#1]{#1 2 exp 1 sub}
\def\h(#1){#1^2-1}

\begin{document}
\begin{pspicture}[showgrid=bottom](-4,-2)(4,4)
\psplot{-2}{2}{\f x}
\psdots(!0 \f{0})(!-2 \g[-2])(*2 {\h(x)})(*1 {x^2-1})
\end{pspicture}
\end{document}

as an alternative you can use

\def\h{dup 2 exp 1 sub}
\psdot(!2 \h)

it makes no sense to use an argument for h which is already present on top of the stack. Same for \g. The other way roung is (which also works):

\def\h(#1){#1 dup 2 exp 1 sub}
\psdot(!{\h(2)})

However, if one wants the double parentheses then it can be solved with

\psdot(!2 {\h(2)}/Y ED Y)

Answer 2

As Herbert notes, \psdots takes the first right parenthesis as a delimiter, not the second. This common TeX problem is solved in the xparse package. Here I save the definition of \psdots and redefine it with xparse to take a "required" argument "r" delimited by ( and ). Those delimiters will be paired, so #1 is !2 \h(2) as wanted. I then feed this #1 to the saved \psdots within parentheses: the extra set of braces around #1 ensure that the correct argument is used.

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-plot}

\usepackage{xparse}
\let\savedpsdots\psdots
\RenewDocumentCommand {\psdots} {r()} {\savedpsdots({#1})}

\def\f#1{#1 2 exp 1 sub}
\def\g[#1]{#1 2 exp 1 sub}
\def\h(#1){#1 2 exp 1 sub}
\def\i<#1>{#1 2 exp 1 sub}
\def\j|#1|{#1 2 exp 1 sub}

\begin{document}
\begin{pspicture}[showgrid=bottom](-4,-2)(4,4)
    \psplot{-2}{2}{\f x}
    \psdots(!0 \f{0})
    \psdots(!-2 \g[-2])
    \psdots(!2 \h(2))% <== could be compiled!
    \psdots(!1.25 \i<1.25>)
    \psdots(!1.5 \j|1.5|)
\end{pspicture}
\end{document}

A more general solution would be to redefine \pst@object which seems to underlie a few pst-plot commands.