The Universe of Discourse
           
Mon, 22 Jan 2007

Linogram circular problems
The problems are not related to geometric circles; the are logically circular.

In the course of preparing my sample curve diagrams, one of which is shown at right, I ran into several related bugs in the way that arrays were being handled. What I really wanted to do was to define a labeled_curve object, something like this:

        define labeled_curve extends curve {
          spot s[N];
          constraints { s[i] = control[i]; }     
        }
That is, it is just like an ordinary curve, except that it also has a "spot" at each control point. A "spot" is a graphic element that marks the control point, probably with a small circle or something of the sort:

        define spot extends point {
           circle circ(r=0.05);
           constraints {
             circ.c.x = x;  circ.c.y = y;
           }
        }
A spot is like a point, and so it has an x and a y coordinate. But it also has a circle, circ, which is centered at this location. (circ.c is the center of the circle.)

When I first tried this, it didn't work because linogram didn't understand that a labeled_curve with N = 4 control points would also have four instances of circ, four of circ.c, four of circ.c.x, and so on. It did understand that the labeled curve would have four instances of s, but the multiplicity wasn't being propagated to the subobjects of s.

I fixed this up in pretty short order.

But the same bug persisted for circ.r, and this is not so easy to fix. The difference is that while circ.c is a full subobject, subject to equation solving, and expected to be unknown, circ.r is a parameter, which much be specified in advance.

N, the number of spots and control points, is another such parameter. So there's a first pass through the object hierarchy to collect the parameters, and then a later pass figures out the subobjects. You can't figure out the subobjects without the parameters, because until you know the value of parameters like N, you don't know how many subobjects there are in arrays like s[N].

For subobjects like S[N].circ.c.x, there is no issue. The program gathers up the parameters, including N, and then figures out the subobjects, including S[0].circ.c.x and so on. But S[0].circ.r, is a parameter, and I can't say that its value will be postponed until after the values of the parameters are collected. I need to know the values of the parameters before I can figure out what the parameters are.

This is not a show-stopper. I can think of at least three ways forward. For example, the program could do a separate pass for param index parameters, resolving those first. Or I could do a more sophisticated dependency analysis on the parameter values; a lot of the code for this is already around, to handle things like param number a = b*2, b=4, c=a+b+3, d=c*5+b. But I need to mull over the right way to proceed.

Consider this oddity in the meantime:

  define snark {
    param number p = 3;
  }
  define boojum {
    param number N = s[2].p;
    snark s[N];
  }
Here the program needs to know the value of N in order to decide how many snarks are in a boojum. But the number N itself is determined by examining the p parameter in snark 2, which itself will not exist if N is less than 3. Should this sort of nonsense be allowed? I'm not sure yet.

When you invent a new kind of program, there is an interesting tradeoff between what you want to allow, what you actually do allow, and what you know how to implement. I definitely want to allow the labeled_curve thing. But I'm quite willing to let the snark-boojum example turn into some sort of run-time failure.


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