On 10/31/07, Ralf Hemmecke <[EMAIL PROTECTED]> wrote: > > The main issue has to do with programming style. The for-loop is a > > construction from imperative-style programming. Operations like > > 'product' above operate directly on functions and return functions. > > This is most common in a functional-programming style and might be > > used for example in conjuction with another operation such as 'map' to > > produce the same results a a for-loop constrcut: > > > map(product(Float,wholePart,sin),[1.1,2.2,3.3]) > > > > versus > > > > [makeprod(wholePart x, sin x)$Product(Integer,Float) for x in [1.1,2.2,3.3]] > > Bill, > > you probably mean something like > > map(product(wholePart, sin), [1.1,2.2,3.3]) > > right? >
No. The signature must include a dependent type, like this: product: (A:Type, A->X,A->Y) -> (A->%) > Let's look at the signatures: > > wholePart: Float -> Integer > sin: Float -> Float; -- I don't like Float, by the way... ;-) > [1.1,2.2,3.3]: List Float > > So we must have > > product: (Float -> Integer, Float -> Float) -> > (Float -> Product(Integer, Float)) > > and a corresponding signature for map. You surely believe that I can > program exactly that in Aldor. > To define 'product' in general (i.e. as a categorical limit) for any domain Product(A,B) and domain C we must have product(C,f,g):C->Product(A,B) defined for any functions f:C->A g:C->B I don't think you can do that without passing the independent domain C. > But I guesss that is not your point. Your point is (please correct) that > you want a categorical definition of "Product". > > Product(A, B) should automatically export > > product: (A, B) -> % No, this is not well defined. > > as well as > > product: (X -> A, X -> B) -> X -> %. What is X above? > > You don't want to write down that function definition yourself, right? > Well, I would actually expect it to be exported by a basic built-in domain like 'Record' since that is what most directly corresponds to categorical Product. If this was made sufficiently general, there would be no need for a separately programmed domain in the library. > In terms of Aldor, we have Product = Cross and that is a built-in type. > So it should be possible (and perhaps be reasonable to extend Cross > through the compiler, ie, give it a few more exports than it has now. > Yes exactly, although I am not sure why we need both Cross and Record. > But maybe your proposal goes further and you want to be able to define > domains/functors through categorical limit constructions. So, in fact, > you want to enrich Aldor/SPAD by new keywords "Limit" and "CoLimit" and > make "Cross" a library defined type. > Yes, maybe. What might be even nicer is if it were possible to implement adjoint functors as described by Saul Youssef as an even more basic concept in Aldor/SPAD. He shows how to define Limits and CoLimits in this more fundamental way. > If that is what you think/want, then I can somehow understand you and > would even support it. But to my taste that was not clear enough yet in > all the previous discussions. > > (I have no problem if you forward this and/or my previous mail to the > lists.) > Ok, thanks. Regards, Bill Page. ------------------------------------------------------------------------- This SF.net email is sponsored by: Splunk Inc. Still grepping through log files to find problems? Stop. Now Search log events and configuration files using AJAX and a browser. Download your FREE copy of Splunk now >> http://get.splunk.com/ _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
