On 10/24/07, Gabriel Dos Reis wrote: > > On Tue, 23 Oct 2007, Bill Page wrote: > > | But as I said earlier in this thread, this sort of construction is not > | as general as I would hope for. How would I write for example? > | > | [i for i in Product(OVAR [a,b,c], 1..3)] > | > | [ (a,1), (a,2), (a,3), (b,1), ... ] > > My fundemantal issue to understand is making 1..9 a domain. I'm fine > with no having the most general construct, but I'm concerned with > semantics and typeing rules. In general, I'm suspicious of any > extension that is driven by just syntax. >
I understand your suspicion however I do believe (as you may also believe) that syntax is quite critical - particularly in *mathematics* where I think it has often been demonstrated that proper notation is 90% (99% ?) of the problem. A good notation should help "suggest" a solution and the language itself should be economical and dense in the sense that almost everything that you *can* write that is syntactically correct should have some presumably sensible and useful meaning. Attempting to find the most general construct (: As abstract as possible but not abstract nonsense :) is one way to approach this. Earlier in this thread I suggested introducing a new domain I called 'IntegerSegment(S)' abbreviated INTS that would be the domain equivalent to a given 'S:Segment(Integer)'. Then we could write: [i for i in Product(OVAR [a,b,c], INTS 1..3)] This does not require that '1..3' denote a domain although it does seem less "economical". Regards, Bill Page. _______________________________________________ Axiom-math mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-math
