Dear Sean,

I just got it. Thank you very much.

Best,
Márcio

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Prof. Dr. Márcio Porto Basgalupp
Instituto de Ciência e Tecnologia (ICT)
Universidade Federal de São Paulo (UNIFESP)
Tel: +55 12 3309-9500 (r: 9762)

On Thu, Nov 26, 2015 at 9:46 AM, Márcio Basgalupp wrote:
Dear Sean,

Thank you very much for your help.

Actually, I'm not using matrix operators. I tried to omit some details in order to simplify the question but it think I made a bad choice :-). I'm actually combining some bi-dimensional arrays and a multiplication for me would be like that: C = A * B, where C[i] = A[i] * B[i] for all i (it is sure that all arrays have the same dimension).

The problem is that I have to ensure that the final result (my individual) must be a bi-dimensional array. My application is to combine different bi-dimensional arrays. Instead of using A or B, I could use something like: 2*A + 3*B + A*B. But an individual like 2*3 is not feasible, since the final result is a number (6) and not an array. Then I think that that constraint in ECJ is perfect. I just need to ensure the return type of the individual is a double[][] instead of a 'nil' or 'boolean', like in the examples I found at Section 5.2.11 in ECJ's manual.

Best,
Márcio

--------
Prof. Dr. Márcio Porto Basgalupp
Instituto de Ciência e Tecnologia (ICT)
Universidade Federal de São Paulo (UNIFESP)
Tel: +55 12 3309-9500 (r: 9762)

On Thu, Nov 26, 2015 at 1:38 AM, Sean Luke wrote:
The basic issue is that matrix multiplication involves several varying constraints.  Basically you're saying that if the left child produces an AxB matrix and the right child produces a CxD matrix, and the parent produces an ExF matrix, then it must be the case that B=C, E=A, and F=D.  Notice it doesn't say that A, B, C, D, E, or F must be any *specific* values, just that there are functional constraints on them.  Essentially you have a countably infinite number of types.  Furthermore, you don't specify how these constraints will be enforced -- by forcing children to match a given parent or the other way around?  By forcing the right child to match the left child, or the other way around?

ECJ's typing is meant for situations where parents and children may have a small and finite set of types, children are forced to be constrained by their parents, and there are no constraints between children.  You have a much uglier situation which requires a form of polymorphic typing.

Polymorphic typing systems are nontrivial to implement, and nearly impossible to implement without putting strong restrictions on the tree builders and breeding operators available.  I decided it was not worth the downsides to implement as standard in ECJ's GP facility.   I believe that Maarten Keijzer did polymorphic typing for EO, you might look into that.  Tina Yu did her thesis on polymorphic typing but I don't know what system she used.  Otherwise you're probably stuck with GE [which ECJ can do, along with certain other systems].

Sean