# [racket] Re: [plt-scheme] Re: Typed scheme: Cannot apply expression of type Procedure, since it is not a function type

On Sat, Jun 5, 2010 at 7:44 AM, keydana at gmx.de <keydana at gmx.de> wrote:
>* I don't have a good explanation for this, but I think [of] sums and
*>* products as axes in 2D, and having the two allows you to escape the
*>* constraints of one axis.
*>*
*>*
*>* This sounds interesting. What kinds of constraints are these - or perhaps a
*>* quicker-to-answer question: where's this subject treated in mathematics
*>* (haven't read anything about it in my precious "Abstract Algebra" :-;)?
*
I don't have a ref for this, as this is just an intuitive model I use.
The constraints for sums and products are pretty straightforward: they
are or and and respectively and everything follows from that.
An example from machine learning, in case you have any experience
there: any linear program (in the optimisation sense) has a dual. The
dual is often easier to solve and this is one of the tricks used in
support vector machines IIRC. Wikipedia has the details; I don't
recall them all now.
HTH,
N