[texhax] help with identifying some macros

[Uwe Lück]

ok, as Philip Taylor & Donald Arseneau observe, \[...\] is the LaTeX way of 
writing $$...$$. \also may be a Spivey-defined macro. I think rather than 
understanding the remaining plainTeX constructs, Paul Stanley wants to know 
what you see if you are able to:

At 22:49 15.10.09, P. R. Stanley wrote:
>Here's an example of two of them in use taken from The Z Notation: a 
>Reference Manual by Michael Spivey.
>
>$birthday$:
>\[
>         known = \{\,{\rm John, Mike, Susan}\,\} \\
>\also
>         birthday = \{\,\vtop{\halign{\strut#\hfil&${}\mapsto{}$#\hfil\cr
>                         John&  25--Mar,\cr
>                         Mike&  20--Dec,\cr
>                         Susan& 20--Dec\,\}.\cr}}
>\]

"Z Notation" seems to be a kind of program language referring to formal 
logic and set theory, therefore math mode is preferred. Spivey seems to use 
the primitive \halign because with little typing you get nice tricks.

"birthday" seems to refer to a map defined on the set containing John, 
Mike, and Susan.
The notation typesets "birthday:" (in an ugly way, as DA notes), preceding 
something horizontally centered. This thing first specifies "known" to 
declare the domain set of the map, using curly braces. Then there is a 
table describing the map. It has three rows and two columns. \halign is 
used to automatically insert the mapping left-to-right arrow \mapsto 
between the two cells of a row. This arrow has a little vertical bar at the 
left, saying which member of the domain gets which value under the map, not 
to be confused with the left-to-right arrow declaring domain and codomain 
of the map. This map "birthday" accordingly maps John to 25--Mar, Mike to 
20--Dec, and Susan to the same. A curly brace opens at the left of "John" 
in the first row, and another closes the third row.

\also may be a Z notation symbol that is in a line between the "known" 
declaration and the first row of the table.

like "birthday", "known", "John", "Mike", and "Susan" are typeset in a way 
they shouldn't be.

Hope anybody reads this -- Uwe.