\P Version of August 22, 2019
% This is a sample data file for sublatts.exe
%        Do not change its STRUCTURE!
% In particular, do not change the order of the commands, 
%        and do not leave a command. 
% For instruction, see the end of this file, and see the comment 
%        lines in the data part.
% See also the related paper, G. Czédli:
% Planar semilattices and nearlattices with eighty-three subnearlattices
% http://arxiv.org/pdf/1908.08155
%
%
\verbose=false  % or =true for more details like derived constrains.
%
\subtrahend-in-exponent=8  % Small natural number, for another form of |Sub(A)|
%
\operationsymbols=+*  % The order of the operation symbols is arbitrary.
% 
% Although the program is designed for lattices and qn-lattices,
% it is possible to use it for any sort of partial algebras.
% If the algebra in question is NOT a lattice, then either we
% can use different operation symbols, or we can use
% the equality relation as ordering in order to avoid that
% some lattice properties are taken into account.
% However, for algebras that are NOT (partial) lattices,
% our earlier program called    subsize   is recommended,
% because it is a bit faster. (It is faster because it spends
% no time on using the trivial ordering.)
%   Note that whenever the ordering is not the trivial one, the
% equality relation, then + is always stands for the join 
% operation while * stands for the meet. 
%   Empty lines are allowed but neglected. Everything is 
% case-sensitive. "%" introduces comments that are dropped, but
% <backslach>P introduces comments that are printed (copied) into the
% output file. Both forms of comments are optional, of course.
% There is a third form of comment but only in the list of
% edges and that of constraints; it is carried over the output file 
% and it starts with "\w"; see later for examples. ("w" comes from
% "write"). And, only in the "edges" and "constraints" parts, there is 
% fourth way: namely, we can use a "parenthesized command"; see later.
%
\beginjob
%
\P    First,  we are dealing with the pentagon lattice.
% Any line containing the <backslash>P command is printed into the 
% output file and to the screen. <backslash>P is suggested only 
% after places where the program automatically prints a line-break.

\name
N_5  % The name of the partial lattice; here it it is a lattice.
% Here a backslash>P  line is not suggested because of the 
% possibility of an ugly line-break, even if such a line would not 
% disturb the computation.
%
\size
 5  % The number of elements of the (partial) lattice
\elements
01abc   % the elements of the algebra; a single character each, 
        % case-sensitive, without spaces
\edges 
0a 0b ac b1, c1  \w comment to be printed,
(Casename: superfluous "edge" but not forbidden:) 01 
% Here 01 is superfluous but not forbidden; the program uses the
% ordering generated by the given pairs and does not check if these
% pairs are indeed coverings. However, as a defense against typos,
% repetition like 0b instead of 01 generates an error message.
% In this "edges" part, use \w, because \P is not allowed here!
% The edges are separated by spaces or commas, multiple 
% separators are allowed. The "\w "command is allowed only in the
% scope of the \edges or \constraints (see later) commands. The 
% parenthesized comment is optional; if it is present then it is printed.
% Note its syntax: either there are no parentheses, or there are exactly 
% one "(" and exactly one ")" in the same line later.
% Of course, if there is a "\w" in the line, then it can be followed
% by anything (even by many parentheses) in the same line!
% 
\constraints 
(Case-name1)  a*b=0,  a+b=1 \w Explanation: complemantary pair - to be output. 
% Except that here equations rather than edges are required,
% the sytanx for the \constraints part is exactly the same as
% those for the \edges part.  In particular, you can use \w 
% but \P is not allowed here, and you can also use a case name
% in parentheses.
 (Subcase-name) c*b=0  \w Explanation/2 to be printed % 
  (Superfluous: )   c+b=1 \w Follows from <= and the earlier equalities! 
% The spaces preceding the opening parenthesis are also printed.
% This feature and the parenthesized part are very appropriate to 
% organize our work. Also, the leading spaces are printed even if
% we use the \w after a command; this feature was used in the data files
% associated with the paper.
\endofjob


\P Comments on the result above (free text)
\P    (free text, continued)
 
\beginjob
\name
M_3 % Five-element modular but not distributive lattice
\size
 5  
\elements
01abc % as usual
\edges
(lower edges:) 0a 0b 0c
(upper edges:) a1 b1 c1
\constraints
(C1) a*b=0 \w %The empty print gives only a colon and a line break.
 (C1a)  a+b=1  \w  but this algebra needs no cases to distinguish! 
   (C1a.1)  b*c=0 \w "C" in parentheses stands for "Case" 
    (C1a.1b) b+c=1 c*a=0,  c+a=1 
\endofjob


\enddata

The rest of the file will not be read by the program!

                  INSTRUCTION     
%*******************************************************************

In such a file, arbitrarily many partial lattices or
even other partial algebras can be given. 
(Here, we give only two.) That is, we have to give the generating
set of the ordering relation; typically, we give the edges (that is,
the covering relation). Also, we give the joins (denoted by +)
and the meets (denoted by *) of certain pairs of elements; not 
necessarily all pairs. 
  The constraints are nontrivial equalities that hold in the 
partial lattice. However,  for  x <= y (in particular, for if x=y), both
x+y=x and x*y=x hold (provided they are defined) but they may not occur 
in the input file. (As a way of checking typos, we get an error message 
if they occur.)  After these initially given constraints,
their consequences are computed and added; see the paper.
Percentage sign (%) means that the rest  
of the line is only a comment, which does not influence the 
computation. Note that if we have a unary operation f and f(x)=y, 
then we have to type the corresponding constraint as  xfx=y .

Notes on the syntax: no line can exceed 250 characters but it is 
suggested that 80 characters  should not be exceeded. The 
constraints are separated by commas or spaces, in a single line 
or in more lines. The same holds for the edges. The elements 
of the algebra should be denoted by letters or decimals; some 
characters are forbidden, and the characters are case-sensitive.

For more information, study the comments on the syntax in the comment 
lines that occur among the data above.

Improper data will lead to irregular termination of the program!

                  ALGORITHM
%*******************************************************************

After computing the derived constraints, the program lists 
ALL subsets of the base set and counts those that
are closed with respect to all constraints. Except for + and *,
no property of the operations are taken into account. In fact, 
even multiple-valued partial operations are allowed; for example,  
xfy=u  and xfy=v can both occur among the constraints. Since 
the running time is exponential, the program is not effective for 
large partial algebras. For |A|<26, the program is likely to compute 
the result in a reasonable time in any reasonable computer. For 
|A|>30, this is not always so. In addition to |A|, the running 
time depends also on the constraints.

                  AS IT IS

The program is for Windows 10; it is likely to run under Windows 7 
or higher. The program is "as it is", nothing is guaranteed.