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"constraints placed on the nodes to enforce rules about which nodes can
connect to which nodes" I couldn't agree more but I guess I don't see how
to express certain constraints in this particular framework.

say you have a function F : (forall a. a -> a) -> Int (where ':' means "of
type") and a function G : (Int -> Int) -> Int. As well say there are two
expressions, X : forall a. a -> a and Y : Int -> Int

Assume two trees (call them A and B) have forms (F X) and (G
Y) respectively and A and B are selected for crossover. The nodes for X and
Y are chosen to be swapped. sense X's type unifies with Int -> Int and Y's
type unifies with forall a. a -> a the crossover is allowed. That said it
should not be allowed that Y be passed to F. The expression (F Y) is
ill-typed. On the other hand the expression (G X) is fine
and perfectly valid.

How then can I express the constraint that Y can not be passed to F but
that X can be passed to G? Sense compatibleWith is commutative and the
constraint I specify is not it would appear that this cannot be expressed
using compatibleWith; something else must be needed.

I like functional programming and type systems, hence the choice of types.
I can reformulate this in terms of Java or some other language however. For
instance say there is an interface class "Shape" and another class
"Square". say F : Square -> Int, G : Shape -> Int, X has type Square, and Y
has type Shape. The same issue arises F Y is ill-typed but G X is not.

The issue seems to arise anytime a return type is allowed to be more than
atomic, that is there is a notion of more than 1 type "belonging" to the
return type weather it be parametric polymorphism, set types, or subclass
polymorphism.

Am I missing something and/or is there a way to express the desired
constraint?

On Jan 11, 2014 10:21 AM, "Sean Luke" <[log in to unmask]> wrote:

> Types are not data passed between nodes.  They are merely constraints
> placed on the nodes to enforce rules about which nodes can connect to which
> nodes.
>
> Now, it's true that types often are correlated with the kinds of data that
> nodes send to each other, but that's hardly a requirement.  For example,
> we're using types right now simply to force certain kinds of nodes to
> appear in the top area of a tree but not down near the leaf nodes.
>
> The most common situation you'll find is argument types which are set
> types, and return types which are atomic types.  For example, you might
> have a node which returns int plugged into an argument which can accept int
> or double.  You've seen that before in real programming languages I'm sure:
> the + operator in most programming languages can take floats, ints,
> doubles, longs, bytes, indeed in some cases strings.
>
> All you have to do is handle multiple kinds of data in your GPData object.
>  The typing mechanism merely guarantees that when a node receives a GPData
> object, what you receive has been constrained in a way that you had
> specified.
>
> Sean
>
> On Jan 11, 2014, at 10:52 AM, Jake Ehrlich wrote:
>
> > OK that explains more. Thanks for the clarification
> >
> > As to the example, yes you understood. I am still confused however on
> how something of type {s, i} can be passed in to something expecting an
> integer. What if that something returned a string?
> >
> > On Jan 11, 2014 8:59 AM, "Sean Luke" <[log in to unmask]> wrote:
> > On Jan 11, 2014, at 2:00 AM, Jake Ehrlich wrote:
> >
> > > In the documentation for ec.gp.koza.CrossoverPipeline it says "Then a
> random
> > > node is chosen in each tree such that the two nodes have the same
> return
> > > type". Does "same return type" in that quote mean that the types "fit"
> by
> > > GType's compatibleWith method?
> >
> > The documentation is misleading.  The correct form is:
> >
> > Two nodes M and N are chosen.  Let R(N) and R(M) be the return types of
> > M and N respective.  Let A(N) and A(M) be the types of the argument slots
> > which N and M respectively fill in their parents.  Then M and N are only
> > valid if R(N) is type compatible with A(M) and R(M) is type compatible
> > with A(N).
> >
> > > First off as I understand it GType.compatibleWith is assumed to be
> > > commutative (that is t1.compatibleWith(init, t2) is true if and only if
> > > t2.compatibleWith(init, t1) is true). Is this correct or is it just
> one way?
> >
> > compatibleWith is commutative.
> >
> >
> > > Say you have a node X of type {string, int} (a set type) and another
> node Y of
> > > type int (an atomic type). X and Y are being passed in as parameters
> of type
> > > {string, int} and int respeticvlly. These return types are
> "compatible" ("fit") by
> > > the definition of compatibleWith for GPAtomicType and GPSetType yet you
> > > shouldn't be allowed to swap them sense the parameter type of X's
> parent
> > > can't handle a string, only an int.
> >
> > Let me make sure I understand what you're saying.  Node X is of return
> type {s,i} and it's attached to an argument slot of type {s,i}.  And node Y
> is of return type i and is attached to an argument slot of type i. If you
> swapped them, then node X would now be in the argument slot i (which it is
> type-compatible with) and node Y would now be in argument slot {s,i} (which
> it is also type-compatible with) so everything would be fine.
> >
> > Sean
>