Thoughts on "extending" a species

[Martin Rubey]

I just wanted to archive some thoughts here...

we would like to be able to give the user the abilitity to "use" the structures
of a species he defined, possibly recursively, using other, "basic" species.

For example, having modified

Times so that it exports "left: % -> F L" and "right: % -> G L" and

Plus so that it exports "struct: % -> Union(left: F L, right: G L)"

the following "works":

A(L: LabelType): CombinatorialSpecies L with {
height: % -> Integer;
#if Axiom
pretty: % -> OutputForm;
#endif
} == Plus(SingletonSpecies, Times(A, A))(L) add {
Rep == Plus(SingletonSpecies, Times(A, A))(L); import from Rep;
import from Union(left: SingletonSpecies(L), right: Times(A, A)(L));
import from Times(A, A)(L);

height(x: %): Integer == {
import from Integer;
X := struct rep x;
-- if X is a Singleton, the height is zero
X case left => 0;
-- otherwise, we have to compare the height of the left and the right branch
1+max(height left X.right, height right X.right);
}
#if Axiom
pretty(x: %): OutputForm == {
X := struct rep x;
-- if X is a Singleton...
X case left => (X.left)::OutputForm;
-- otherwise...
import from Integer, String, OutputForm, List OutputForm;

vconcat [
hconcat [hspace 1, message "o"],
hconcat [message "/", hspace 1, message "\"],
hconcat [
pretty left X.right,
hspace 3,
pretty right X.right]];
}
#endif
};

(note that "pretty" does not *really* work, since vconcat produces a
rectangular box, thus, the output looks wrong. I did not bother to fix this,
but it should be doable. As an example:

(19) -> pretty retract partialNext! s

(19) o
/ \
1 o
/ \
3 o
/ \
o 5
/ \
2 4
Type: OutputForm

(To see the difficulty, consider the subtree with labels 2 and 4. it is
produced by a "pretty" invocation, which produces a box 3 rows high and 5
columns wide. Recursion then wants to print the subtree with labels 2,4 and 5,
and puts this box to the left, leaves a space of 3 columns, and prints 5 on the
right...)

But this is maybe not the most natural way one can think of. We would like to
state

* what is the height of X
* what is the height of Plus(A, B), given the height of A and B
* what is the height of Times(A, B), given the height of A and B

Two more things:

* we would like to be able to produce several different functions using the
recursive definition

* the coercion to output should be a possible application

Martin


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