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* Bruno Le Floch <blflatex@GMAIL.COM> [2012-02-03 15:01:01 -0500]:

: > : All LaTeX3 functions are either fully expandable or engine-protected. In
: > : this case, we are talking about protected functions: these are not
: > : expandable. (In the documentation, expandable functions are marked with
: > : a star.)
: 
: Joseph is right. Regular expression matching is already tough enough
: to not try to do it expandably (besides, that would become
: unreasonably slow, and would break in corner cases). What you seem to
: be trying can be done as follows instead:

Hi again,


I've made some progress with the recurrence equations, but I have a error
that I don't understand. I'd appreciate it if you could have a quick look.

Given the standard (naive) definition of the Fibonacci numbers (f[0]=1,
f[1]=1,f[i]=f[i-1],f[i-2]), my code generates the following artificial
macros:

\f macro:#1->\f:n {#1}
\f:n macro:#1->\exp_args:Nx \recurrence_f_0:x {\int_eval:n {#1}}
\recurrence_f_0:x macro:#1->\int_compare:nTF {#1=0}{1}{\recurrence_f_1:x {#1}}
\recurrence_f_1:x macro:#1->\int_compare:nTF {#1=1}{1}{\recurrence_f_2:x {#1}}
\recurrence_f_2:x macro:#1->\bool_if:nTF {\int_compare_p:n{1=1}}{\f:n{#1-1}+\f:n{#1-2}}{\recurrence_f_3:x {#1}}
\recurrence_f_3:x \long macro:#1->\error {f[ #1 ] undefined.}

The macros \f and \f:n are wrappers. The macros \recurrence_f_0, ...,
\recurrence_f_2 deal with the three different conditions, and
\recurrence_f_3 deals with errors, which cannot occur here, but
in general cases may not be matched.

Computing \f{0} and \f{1} works fine, but evaluating \f{2} doesn't.

The current code I have is packaged as a .tex and a .sty file. If you have
any comments on the problem, or indeed, the source files, then that'd be
much appreciated.

I've tried to keep the code simple. Optimising can be done later.

I'm attaching the source files.

Regards,


Marc van Dongen

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Content-Type: text/x-tex; charset=us-ascii
Content-Disposition: attachment; filename="recurrence.tex"

\documentclass[12pt]{article} 

\usepackage[paper=a4paper,landscape]{geometry}
\usepackage{recurrence} 

\begin{document} 

\section{Start}

%\tracingmacros=1
   \NewRecDef{f[0]=1,
              f[1]=1,
              f[i]=f[i-1]+f[i-2]}


\begin{tt}
\begin{tabular}{ll}
   f   & \meaning\f
\\ f:n & \expandafter\meaning\csname f:n\endcsname
\\ recurrence\_f\_0:x & \expandafter\meaning\csname recurrence_f_0:x\endcsname
\\ recurrence\_f\_1:x & \expandafter\meaning\csname recurrence_f_1:x\endcsname
\\ recurrence\_f\_2:x & \expandafter\meaning\csname recurrence_f_2:x\endcsname
\\ recurrence\_f\_3:x & \expandafter\meaning\csname recurrence_f_3:x\endcsname
\end{tabular}
\end{tt}

% \f{2}

\end{document}

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Content-Type: text/x-tex; charset=us-ascii
Content-Disposition: attachment; filename="recurrence.sty"

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{recurrence}[2012/02/02 Recurrence Equation Support]


%\usepackage{tikz} 
\usepackage{xparse}
\usepackage{expl3}
\usepackage{l3regex}
\usepackage{l3int}
\ExplSyntaxOn

\def\testme#1{[[[#1]]]}

\clist_new:N  \recurrence_csv_list
\tl_new:N     \recurrence_tl_bin
\tl_new:N     \recurrence_tl_temp
\tl_new:N     \recurrence_tl_name
\tl_new:N     \recurrence_tl_index
\tl_new:N     \recurrence_tl_rhs
\tl_new:N     \recurrence_tl_guard
\regex_const:Nn \recurrence_tl_integer_regex { ^[-+]*[0-9]+$ }
\regex_const:Nn \recurrence_tl_true          { true }
\int_new:N    \recurrence_case_count

\cs_new_nopar:Npn \recurrence_prefix: {
    recurrence
}

\cs_new_nopar:Npn \recurrence_is_integer:xTF #1{
    \regex_match:NnTF \recurrence_tl_integer_regex {#1}
}

\cs_new_nopar:Npn \recurrence_is_integer:NTF #1{
    % I don't understand why I need the exp_args:Nx
    \exp_args:Nx
    \recurrence_is_integer:xTF {\tl_use:N #1}
}

\cs_new_nopar:Npn \recurrence_case_name:xx #1#2{
    \recurrence_prefix: _ #1 _ #2:x
}

% #1 is integer token list
\cs_new_nopar:Npn \recurrence_case_name:N #1{
    \recurrence_case_name:xx \recurrence_tl_name {\int_use:N #1}
}

% #1 is integer
\cs_new_nopar:Npn \recurrence_case_name:n #1{
    \recurrence_case_name:xx \recurrence_tl_name {#1}
}


% #1 is index
% #2 is rhs
\cs_new_nopar:Npn \recurrence_define_constant:xx #1#2{%
    \edef\recurrence_current_case_count{\int_use:N \recurrence_case_count}
    \int_incr:N \recurrence_case_count
    \cs_new_nopar:cpx {\recurrence_case_name:n \recurrence_current_case_count} ##1{
        \exp_not:N
        \int_compare:nTF {##1=#1} {#2}
                         {\cs:w \recurrence_case_name:N \recurrence_case_count
                          \cs_end:{##1}}
    }
}

% #1 is guard tl
% #2 is rhs   tl
\cs_new_nopar:Npn \recurrence_case_definition:xx #1#2{
    \edef\recurrence_current_case_count{\int_use:N \recurrence_case_count}
    \int_incr:N \recurrence_case_count
    \cs_new_nopar:cpx {\recurrence_case_name:n \recurrence_current_case_count} ##1{
        \exp_not:N
        \bool_if:nTF {#1} {#2}
                     {\cs:w \recurrence_case_name:N \recurrence_case_count
                      \cs_end:{##1}}
    }
}

% #1 is name  tl
% #2 is index tl
% #3 is rhs   tl
% #4 is guard tl
\cs_new_nopar:Npn \recurrence_case_definition:NNNN #1#2#3#4{
    \exp_args:Nx
    \recurrence_sanitise:nNN {{\tl_use:N #1} {\tl_use:N #2}} #3 #4
    \regex_replace_all:NnN \recurrence_tl_true {\\int_compare_p:n \{ 1 = 1 \}} #4
    \recurrence_case_definition:xx #4 #3
}

\cs_new_nopar:Npn \recurrence_sanitise:nNN #1#2#3{
    \recurrence_sanitise:nnNN #1 #2 #3
}

% #1 is name
% #2 is index
% #3 is rhs   tl
% #4 is guard tl
\cs_new_nopar:Npn \recurrence_sanitise:nnNN #1#2#3#4{
    \recurrence_sanitise:nnN {#1} {#2} #3
    \recurrence_sanitise:nnN {#1} {#2} #4
}

% #1 is name
% #2 is index
% #3 is tl list
\cs_new_nopar:Npn \recurrence_sanitise:nnN #1#2#3{
    \regex_replace_all:nnN {#2} {\#1} #3
    \regex_replace_all:nnN {\b#1\b\[([^\]]+)\]} {\\#1:n\{\1\}} #3
}

\cs_new_nopar:Npn \recurrence_error_definition:{
    \edef\recurrence_current_case_count{\int_use:N \recurrence_case_count}
    \cs_new:cpx {\recurrence_case_name:n \recurrence_current_case_count}##1{
        \exp_not:N
        \error{\tl_use:N \recurrence_tl_name[~##1~]~undefined.}
    }
}


\cs_new_nopar:Npn \recurrence_wrapper_definitions:{
    \edef\recurrence_temp{\tl_use:N \recurrence_tl_name}
    \cs_new_nopar:cpx {\recurrence_temp} ##1{%
        \exp_after:wN \exp_not:N
        \cs:w \recurrence_temp :n \cs_end: {##1}
    }
    \cs_new_nopar:cpx {\recurrence_temp :n} ##1{%
        \noexpand \exp_args:Nx
        \exp_after:wN \exp_not:N
        \cs:w \recurrence_case_name:n 0 \cs_end:
              {\exp_not:N \int_eval:n{##1}}
    }
}

\cs_new_nopar:Npn \NewRecDef:n #1{
    \begingroup
    \clist_set:Nn  \recurrence_csv_list {#1}
    \clist_map_inline:Nn \recurrence_csv_list {
        \regex_extract_once:nnNTF
        { ^(\w+)\[(\w+)\]\=(.+?)\|(.+)\|(.+) } {##1|true||} \recurrence_tl_temp
        {
            % at this stage, \recurrence_tl_temp has 6 items,
            % 0th: a[i]= expression | guard | guard option
            \seq_pop:NN \recurrence_tl_temp \recurrence_tl_bin
            \seq_pop:NN \recurrence_tl_temp \recurrence_tl_name
            \seq_pop:NN \recurrence_tl_temp \recurrence_tl_index
            \seq_pop:NN \recurrence_tl_temp \recurrence_tl_rhs
            \seq_pop:NN \recurrence_tl_temp \recurrence_tl_guard
            \recurrence_is_integer:NTF
                \recurrence_tl_index
                {\recurrence_define_constant:xx \recurrence_tl_index \recurrence_tl_rhs}
                {\recurrence_case_definition:NNNN
                            \recurrence_tl_name \recurrence_tl_index
                            \recurrence_tl_rhs \recurrence_tl_guard}
        } { \recurrence_error }
    }
    \recurrence_error_definition:
    \recurrence_wrapper_definitions:
    \endgroup
}

\DeclareDocumentCommand\NewRecDef{ m }{
    \NewRecDef:n {#1}
}

\ExplSyntaxOff

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