How to create a conditional which checks if one or another condition is true in plain TeX?

Question

I need to make a conditional like this:

IF #1 > \variable OR #1 = 0
THEN
   PRINT "True"
ELSE
   PRINT "False"

If #1 is greater than \variable or is equal to 0, then it it true. The value only contains integers of 0 or greater. There are never any decimals.

I have this conditional in plain TeX, which checks if #1 is greater than \variable, but I do not know how to add the #1 = 0 part.

\ifnum0#1>\variable
    True
\else
    False
\fi

How can I create a conditional that checks if at least one of these conditionals is true?

Answer 1

\if\ifnum#1>\variable T\else\ifnum#1=0 T\else F\fi\fi T%
  TRUE
\else
  FALSE
\fi

\if expands tokens until two non-expandable tokens remain. If one of the conditions is true, then the expansion is T, otherwise F. This is compared with the last T in the line.

• Advantage: TRUE is not duplicated as in

  \ifnum#1>\variable
    TRUE
  \else
    \ifnum#1=0 %
      TRUE
    \else
      FALSE
    \fi
  \fi
  

• Advantage: All number parsings are stopped by well defined tokens. Example: The token T stops the scanning of the number \variable. If the TRUE part starts with a number 123abc and \variable is defined as 5

  \def\variable{5}
  \ifnum#1>\variable
    123abc
  \fi
  

  Then #1 must be greater than 5123!

  Depending on the definition of \variable the evaluation of \variable as number might skip a first space of the TRUE part.

• Advantage: The conditionals are well matched, thus this construct can also be used inside other conditionals. If TeX skips a conditional branch it only checks the command tokens for real \if... primitives, \else, \fi, and \or (for \ifcase).

  For example with a macro \ifOR the following is not well matched:

  \ifOR{\ifnum#1>\variable}{\ifnum#1=0}
    TRUE
  \else
    FALSE
  \fi
  

  \ifOR does not count as macro, but there are two \ifnum, but only one \fi.

• Disadvantage: The \if condition is not easy to read.

Answer 2

Here is one way, where the first macros are essentially from lambda.sty by Alan Jeffrey:

\def\True#1#2{#1}
\def\False#1#2{#2}
\def\Or#1#2{#1\True{#2}}
\def\gobblefalse\else\gobbletrue\fi#1#2{\fi#1}
\def\gobbletrue\fi#1#2{\fi#2}
\def\TeXif#1{#1\gobblefalse\else\gobbletrue\fi}

\def\Morethan#1#2{\TeXif{\ifnum#1>#2 }}
\def\Equals#1#2{\TeXif{\ifnum#1=#2 }}

\def\Test#1{%
  \Or
    {\Morethan{#1}\variable}
    {\Equals{#1}0}
  {True}
  {False}}

\newcount\variable
\variable=5

\Test{2} \Test{5} \Test{10} \Test{0}

\variable=2
\Test{2} \Test{5} \Test{0} \Test{1}
\bye

I have a feeling there is a possibility for a higher level abstraction in the spirit of Schemesque cond here somewhere...

Answer 3

You can use

\def\variable{5}
\def\test#1{%
  \ifnum0#1>\variable
    True
  \else
    \ifnum0#1=0
      True
    \else
      False
    \fi
  \fi
}
\test{6} \par
\test{5} \par
\test{4} \par
\test{3} \par
\test{2} \par
\test{1} \par
\test{0}

which outputs

True
False
False
False
False
False
True

Note that this would only work for positive integers.

Answer 4

My solution(s) has the some idea as Werner's answer but extend this a little:

\def\variable{5}

% Solution 1
\def\ifOr#1#2{%
 \csname%
  \ifnum#1%
    iftrue%
  \else%
    \ifnum#2%
      iftrue%
    \else%
      iffalse%
    \fi%
  \fi%
 \endcsname%
}
\def\test#1{%
  \ifOr{0#1>\variable}{#1=0}%
    True%
  \else%
    False%
  \fi%
}

% Solution 2
\def\ifOR#1#2{%
 \csname%
  #1%
    iftrue%
  \else%
    #2%
      iftrue%
    \else%
      iffalse%
    \fi%
  \fi%
 \endcsname%
}
\def\Test#1{%
  \ifOR{\ifnum0#1>\variable}{\ifnum#1=0}%
    True%
  \else%
    False%
  \fi%
}

\test{8} \Test{8} \par
\test{4} \Test{4} \par
\test{3} \Test{3} \par
\test{2} \Test{2} \par
\test{1} \Test{1} \par
\test{0} \Test{0}