Edit detail for SandBoxCombinat revision 2 of 8

aldor
#include "axiom.as"
macro CCC == CombinatorialClassCategory;
import from Integer;
import from List Integer;
import from OutputForm;
CombinatorialClassCategory: Category == with {        
        list: Integer -> List %;
        count: Integer -> Integer;
        import from NonNegativeInteger;
        default count(i: Integer): Integer == (#list(i))::Integer;
        coerce: % -> OutputForm;
} 
Primitive(n: Integer): CombinatorialClassCategory == add {
        Rep == Integer;
        count(i: Integer): Integer == if i=n then 1 else 0;
        list(i: Integer): List % == if i=n then [per 1] else [];
        coerce(x: %): OutputForm == message(" ")
}
Epsilon: CombinatorialClassCategory == Primitive(0) add;
Atom: CombinatorialClassCategory == Primitive(1) add;
UnionClass(S1: CCC, S2: CCC): CCC == add {
        Rep == Union(s1: S1, s2: S2);
        count(i: Integer): Integer == count(i)$S1 + count(i)$S2;
        import from Rep;
        import from List S1;
        import from List S2;
        list(i: Integer): List % == {
                result: List % := [];
                for a in list(i)$S1 repeat result := cons(per union a, result);
                for b in list(i)$S2 repeat result := cons(per union b, result);
                result;
        }
        coerce(x: %): OutputForm == {
                (rep x) case s1 => ((rep x).s1)::OutputForm;
                ((rep x).s2)::OutputForm;
        }
}
CrossClass(S1: CCC, S2: CCC): with {
        CombinatorialClassCategory
} == add {
        Rep == Record(t1: S1, t2: S2);
        count(i: Integer): Integer == {
                result := 0;
                for k in 1 .. i-1 repeat {
                        result := result + count(k)$S1 * count(i-k)$S2;
                }
                result;
        }
        import from Rep;
        import from List S1;
        import from List S2;
        list(i: Integer): List % == {
                result: List % := [];
                for k in 1..i-1 repeat {
                  for a in list(k)$S1 repeat {
                    for b in list(i-k)$S2 repeat {
                      result := cons(per record(a, b), result);
                    }
                  }
                }
                result;
        }
        coerce(x: %): OutputForm == {
                a := ((rep x).t1)::OutputForm;
                b := ((rep x).t2)::OutputForm;
                c: List OutputForm := [a, b];
                vconcat [hconcat [hspace 1, message("o")], hconcat [hspace 1, message("/"), hspace 1, message("\")], hconcat [a,hspace 3,b]]
        }
}
TreeClass: CombinatorialClassCategory == UnionClass(Atom, CrossClass(TreeClass, TreeClass)
) add;

axiom
[count(i)$TreeClass for i in 1..7]

axiom
)set output tex off
)set output algebra on
(list(5)$TreeClass)::List OutputForm
   (2)
   [        o        ,         o        ,         o        ,         o        ,
           / \                / \                / \
/ \
              o                  o                  o                  o
             / \                / \                / \
/ \
                o                  o            o       o            o
               / \                / \          / \     / \
/ \
                  o              o                                     o
                 / \            / \                                   /
\
            o        ,         o        ,         o        ,         o        ,
           / \                / \                / \
/ \
              o          o         o        o         o          o         o
             / \        / \       / \      / \       / \
/ \       / \
            o                        o              o              o
           / \                      / \            / \            /
\
          o
         / \
            o        ,         o        ,         o        ,         o        ,
           / \                / \                / \
/ \
        o         o          o                  o                  o
       / \       / \        / \                / \
/ \
      o                        o                  o            o       o
     / \                      / \                / \          /
\     / \
                                 o              o
                                / \            / \
            o        ,         o        ]
           / \                / \
          o                  o
         / \                / \
        o                  o
       / \                / \
          o              o
         / \            / \

axiom
)cd /home/page/iso-experiment/combinat/src
   The current FriCAS default directory is
      /home/page/iso-experiment/combinat/src
)re ../lib/combinat.input
)lib cscombinatversion.ao
   Reading /home/page/iso-experiment/combinat/src/cscombinatversion.asy
   LibraryInformationCombinat is now explicitly exposed in frame
      initial
   LibraryInformationCombinat will be automatically loaded when needed
      from /home/page/iso-experiment/combinat/src/cscombinatversion
   >> System error:
   Cannot create the file temp.text.

axiom
lab: SetSpecies ACINT := set [i::ACINT for i in 1..4]
   Category, domain or package constructor SetSpecies is not available.
structures(lab)$Partition ACINT
   The constructor Partition takes 0 arguments and you have given  1  .