How to create a "delay expansion" environment?

Question

I don't want to use the following

\begingroup
\edef\next{\endgroup
    \noexpand\const{Xp}{\X(tp)}
    \noexpand\const{Yp}{\Y(tp)}
    \noexpand\const{Xf}{\X(tf)}
    \noexpand\const{Yf}{\Y(tf)}
}\next

and

\begingroup
\edef\next{\endgroup
\noexpand\psparametricplot[algebraic,plotpoints=100]{0}{\tf}{\X(t)|\Y(t)}}\next

because they seem to be cryptic.

Instead I want to create a new environment as follows,

\newenvironment{DelayExpansion}
{\begingroup
\edef\next\bgroup\endgroup\ignorespaces}
{\egroup\next\ignorespacesafterend}

but unfortunately it produces compilation errors that you can see by yourself.

If the errors can be fixed, the environment will be used as follows,

\DelayExpansion
  \noexpand\const{Xp}{\X(tp)}
  \noexpand\const{Yp}{\Y(tp)}
  \noexpand\const{Xf}{\X(tf)}
  \noexpand\const{Yf}{\Y(tf)}
\endDelayExpansion

and

\DelayExpansion
    \noexpand\psparametricplot[algebraic,plotpoints=100]{0}{\tf}{\X(t)|\Y(t)}}
\endDelayExpansion

Or without specifying the \noexpand as follows.

\DelayExpansion
  \const{Xp}{\X(tp)}
  \const{Yp}{\Y(tp)}
  \const{Xf}{\X(tf)}
  \const{Yf}{\Y(tf)}
\endDelayExpansion

and

\DelayExpansion
    \psparametricplot[algebraic,plotpoints=100]{0}{\tf}{\X(t)|\Y(t)}}
\endDelayExpansion

The MWE for the real scenario is given as follows.

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

\addtopsstyle{gridstyle}{gridlabels=0,griddots=0,subgriddiv=5,gridwidth=0.4pt,subgridwidth=0.2pt}

\usepackage[nomessages]{fp}
\newcommand\const[3][3]{%
    \expandafter\FPeval\csname#2\endcsname{round(#3:#1)}%
    \pstVerb{/#2 \csname#2\endcsname\space def}%
}

\const{Vox}{2}
\const{Xo}{1}

\const{Voy}{4}
\const{Yo}{10}

\const{g}{10}

\def\X(#1){Xo+Vox*#1}
\def\Y(#1){Yo+Voy*#1-0.5*g*#1^2}

\const{tp}{Voy/g}
\const{toffset}{0.5}
\const{tf}{2*tp+toffset}

%\newenvironment{DelayExpansion}
%{\begingroup
%\edef\next\bgroup\endgroup\ignorespaces}
%{\egroup\next\ignorespacesafterend}
%
%\DelayExpansion
  %\noexpand\const{Xp}{\X(tp)}
    %\noexpand\const{Yp}{\Y(tp)}
    %\noexpand\const{Xf}{\X(tf)}
    %\noexpand\const{Yf}{\Y(tf)}
%\endDelayExpansion

\begingroup
\edef\next{\endgroup
    \noexpand\const{Xp}{\X(tp)}
    \noexpand\const{Yp}{\Y(tp)}
    \noexpand\const{Xf}{\X(tf)}
    \noexpand\const{Yf}{\Y(tf)}
}\next

\begin{document}
\begin{pspicture}[showgrid](0,\Yp)(\Xf,\Yf)
    \psframe[fillstyle=vlines,fillcolor=gray](0,\Yf)(\Xo,\Yo)
    \psparametricplot[algebraic,plotpoints=100]{0}{\tf}{\X(t)|\Y(t)}
\end{pspicture}
\end{document}

How to create a "delay expansion" environment?

The latest update:

I have tried the solution given by Ryan, but it still produces some errors (please try it by yourself to see the error messages).

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

\usepackage[nomessages]{fp}

% cannot be simplified unless I must break my real scenario

\newcommand\const[3][3]{%
    \expandafter\FPeval\csname#2\endcsname{round(#3:#1)}%
    \pstVerb{/#2 \csname#2\endcsname\space def}%
}

\const{Xo}{1}
\const{Yo}{10}
\const{tp}{0.4}
\const{tf}{2*tp+1.5}

\def\X(#1){Xo+2*#1}
\def\Y(#1){Yo+4*#1-0.5*5*#1^2}


% try this for comparison first
%\begingroup
%\edef\next{\endgroup
    %\noexpand\const{Yp}{\Y(tp)}
%}\next

% Ryan's suggestin
\usepackage{environ}
\NewEnviron{DelayExpansion}{%
  \begingroup
  \edef\next{\endgroup\BODY}%
  \next%
}

% Ryan's suggestion
\begin{DelayExpansion}
    \noexpand\const{Yp}{\Y(tp)}
\end{DelayExpansion}


\begin{document}
\begin{pspicture}(0,6)(6,\Yp)
    \psparametricplot[algebraic,plotpoints=100]{0}{\tf}{\X(t)|\Y(t)}
\end{pspicture}
\end{document}

I will offer 4 bounties of 500 each to a single accepted answer. Does it sound excited?

Answer 1

This kind of thing is what the environ package exists for. Try:

\usepackage{environ}

\NewEnviron{DelayExpansion}{%
  \global\let\xBODY\BODY
}[\aftergroup\expandBODY]

\def\expandBODY{%
  \begingroup
  \edef\next{\endgroup\xBODY}%
  \next
}

It collects the entire environment before applying the \edef to it.

The reason your attempt failed is that \edef (and \def, and \xdef) require not just implicit braces such as \bgroup to set off their contents, but actual braces {. It is not easy to split a \def across several macros for this reason, which is exactly why environ exists to collect the contents of an environment contained between two "start" and "end" macros.

I should also say that it's unlikely that you'll be able to write a version of this environment that works without \noexpand being explicitly specified at the desired places. If you only want to \noexpand the beginning of the lines you can try to make ^^M active before the environment and have it insert \noexpand itself, but that sounds very risky...

Edit: The cause of your errors is that your macro \const is internally making definitions via \def, yet the environ package runs its code inside the environment, where it is protected by a group (by design of environments). Normally you'd just use \gdef or \xdef to circumvent this, but since to do that is to acquiesce to the peculiarities of one's coding environment a more automatic approach is to simply export the \edef outside the group using \aftergroup. I've declared this export in two stages. First, I export \BODY itself via \global\let\BODY\BODY and then, using the optional argument to \NewEnviron (which runs its contents at \end{DelayExpansion}), I export the expansion code.

This doesn't require any trickery (other than \aftergroup, which is pretty tricky) and also doesn't require hacking into the specific code of \end (as in \end{DelayExpansion}, except for knowing that there's a group in it.

Edit 2: Here is a slightly more complex environment that, in imitation of egreg's answer, can automatically preserve specified macros. I'll give an example in a minimal case:

\documentclass{article}
\usepackage{environ,etoolbox}

\NewEnviron{DelayExpansion}[1][]{%
  \global\let\xBODY\BODY
  \global\def\xARGS{{#1}}
}[\aftergroup\expandBODY]

\def\expandBODY{%
  \begingroup
  \def\do##1{\let##1\relax}%
  \expandafter\docsvlist\xARGS
  \edef\next{\endgroup\xBODY}%
  \next
}

\begin{document}

\begin{DelayExpansion}[\macro]
  \def\macro{a}
\end{DelayExpansion}
\macro

\end{document}

(output: a)

Or, in your example,

\begin{DelayExpansion}[\const]
    \const{Yp}{\Y(tp)}
\end{DelayExpansion}

Any macro named in the optional argument is not expanded (the list is comma-separated and may be empty, in which case the environment does nothing).

It doesn't use LaTeX3 but instead etoolbox, which provides some of the same programming conveniences for LaTeX2e.

Answer 2

I wouldn't use an environment, which has the problem of doing its work in a group. Here's a proposal:

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

\usepackage[nomessages]{fp}
\newcommand\const[3][3]{%
    \expandafter\FPeval\csname#2\endcsname{round(#3:#1)}%
    \pstVerb{/#2 \csname#2\endcsname\space def}%
}

\ExplSyntaxOn
\NewDocumentCommand{\DelayExpansion}{mm}
 {
  \group_begin:
  \clist_map_inline:nn { #1 } { \cs_set_eq:NN ##1 \scan_stop: }
  \use:x { \group_end: #2 } 
 }
\ExplSyntaxOff

\const{Vox}{2}
\const{Xo}{1}

\const{Voy}{4}
\const{Yo}{10}

\const{g}{10}

\def\X(#1){Xo+Vox*#1}
\def\Y(#1){Yo+Voy*#1-0.5*g*#1^2}

\const{tp}{Voy/g}
\const{toffset}{0.5}
\const{tf}{2*tp+toffset}

\begin{document}
\DelayExpansion{\const}
 {
  \const{Xp}{\X(tp)}
  \const{Yp}{\Y(tp)}
  \const{Xf}{\X(tf)}
  \const{Yf}{\Y(tf)}
 }

\begin{pspicture}[showgrid](0,\Yp)(\Xf,\Yf)
  \psparametricplot[algebraic,plotpoints=100]{0}{\tp}{\X(t)|\Y(t)}
\end{pspicture}
\end{document}

The \DelayExpansion has two arguments; the first is a list of macros that shouldn't be expanded, the second argument is what will be expanded, except for the macros in the list.

In the example you have to use twice \DelayExpansion, because the macros \Yp, \Xf and \Yf wouldn't be available until they have been defined (by the first \DelayExpansion).

How does \DelayExpansion work?

First of all it makes (in a group) all chosen macros equivalent to \relax (which is \scan_stop: in LaTeX3 parlance). Then the second argument is given as argument to \use:x that fully expands everything (but \scan_stop: is not expandable, so in the first one \const will remain itself).

This is just a wrapper around the well known trick

\begingroup\edef\x{\endgroup<tokens>}\x

which is used also by Ryan. The \group_end: will make \const (or whatever macro is in the first argument) return to its previous value and LaTeX will continue its normal operations.

Answer 3

Building on Ryan's approach, the definitions can be moved out of the group with a bit of expansion trickery:

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

\usepackage[nomessages]{fp}

% cannot be simplified unless I must break my real scenario

\newcommand{\const}[3][3]{%
    \expandafter\FPeval\csname#2\endcsname{round(#3:#1)}%
    \pstVerb{/#2 \csname#2\endcsname\space def}%
}

\const{Xo}{1}
\const{Yo}{10}
\const{tp}{0.4}
\const{tf}{2*tp+1.5}

\def\X(#1){Xo+2*#1}
\def\Y(#1){Yo+4*#1-0.5*5*#1^2}


\usepackage{environ}
\makeatletter
\NewEnviron{DelayExpansion}{%
  \expandafter\endgroup
  \expandafter\begingroup
  \expandafter\edef\expandafter\next\expandafter
    {\expandafter\endgroup\BODY}%
  \next
  \begingroup
    \def\@currenvir{DelayExpansion}%
}
\makeatother

\begin{DelayExpansion}
    \noexpand\const{Yp}{\Y(tp)}
\end{DelayExpansion}


\begin{document}
\begin{pspicture}(0,6)(6,\Yp)
    \begin{DelayExpansion}
        \noexpand\psparametricplot[algebraic,plotpoints=100]{0}{\tf}{\X(t)|\Y(t)}
    \end{DelayExpansion}
\end{pspicture}
\end{document}

Answer 4

Since there are several environment forms posted I think I'll ignore the suggested solution of an environment and offer an alternative. Using an environment for this seems inherently fragile and not at all LaTeX-like.

Just define an \econst variant of your \const macro that expands its second argument. (Such variants are the basis of the whole LaTeX3 xparse stack, but I'll use classic TeX syntax here).

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

\addtopsstyle{gridstyle}{gridlabels=0,griddots=0,subgriddiv=5,gridwidth=0.4pt,subgridwidth=0.2pt}

\usepackage[nomessages]{fp}
\newcommand\const[3][3]{%
    \expandafter\FPeval\csname#2\endcsname{round(#3:#1)}%
    \pstVerb{/#2 \csname#2\endcsname\space def}%
}
\def\econst#1#2{\edef\next##1{\noexpand\const{##1}{#2}}\next{#1}}


\const{Vox}{2}
\const{Xo}{1}

\const{Voy}{4}
\const{Yo}{10}

\const{g}{10}

\def\X(#1){Xo+Vox*#1}
\def\Y(#1){Yo+Voy*#1-0.5*g*#1^2}

\const{tp}{Voy/g}
\const{toffset}{0.5}
\const{tf}{2*tp+toffset}





\econst{Xp}{\X(tp)}
\econst{Yp}{\Y(tp)}
\econst{Xf}{\X(tf)}
\econst{Yf}{\Y(tf)}
\begin{document}
\begin{pspicture}[showgrid](0,\Yp)(\Xf,\Yf)
    \psframe[fillstyle=vlines,fillcolor=gray](0,\Yf)(\Xo,\Yo)
    \psparametricplot[algebraic,plotpoints=100]{0}{\tf}{\X(t)|\Y(t)}
\end{pspicture}
\end{document}

Or if you don't need the unexpanded form and want the expanded form to have an optional argument you could directly define \econst rather than make it a variant of \const.

\newcommand\econst[3][3]{%
    \edef\next{round(#3}%
    \expandafter\FPeval\csname#2\expandafter\endcsname
         \expandafter{\next:#1)}%
    \pstVerb{/#2 \csname#2\endcsname\space def}%
}

Answer 5

Here is a version of Ryan's solution without etoolbox package. \dolist could have been replaced by LaTeX's \@for.

\documentclass{article}
\usepackage{environ}
\begingroup
\catcode`\,=\active
\gdef\dolist#1#2{%
  \begingroup\toks0{}%
  \def,##1{\toks0\expandafter{\the\toks0 #2}}%
  \catcode`\,=\active
  \scantokens{,#1}%
  \expandafter\endgroup\the\toks0 %
}
\endgroup

\NewEnviron{DelayExpansion}[1][]{%
  \global\let\xBODY\BODY
  \gdef\xARGS{#1}%
}[\aftergroup\expandBODY]

\def\expandBODY{%
  \begingroup
  \ifx\xARGS\empty\else
    \expandafter\dolist\expandafter{\xARGS}{\let##1\relax}%
  \fi
  \edef\next{\endgroup\xBODY}\next
}

\begin{document}
\def\xmacro{a}
\begin{DelayExpansion}[\macro,\foo]
  \def\foo##1{##1}%
  \def\macro{\xmacro}
  x
\end{DelayExpansion}
\macro
\end{document}