I recognize that I'm far out of my depth here--both in Haskell and in mathematics--but I'll ask anyway. In what ways are dependent types (http://haskell.org/hawiki/FunDeps, http://www.cse.ogi.edu/~mpj/pubs/fundeps.html) insufficient to address these issues? On Friday, August 27, 2004, at 10:04AM, Jacques Carette <[EMAIL PROTECTED]> wrote:
>> I think Jacques possibly means the ability to do static checking of matrix >> and vector extents, to make sure that you don't try to perform operations >> like matrix-vector multiply on operands whose extents do not match. If you >> want to have this ability on your language, then you will have to restrict >> the way you are allowed to construct array bounds so the equations that >> arise can be solved. Possibly a dependent type system can be helpful for >> this. > >This is indeed what I meant. > >If one is going to move from a dynamically typed language (like Matlab, >Maple, Mathematica, etc) to something statically typed, then the expectation >is that this is going to truly help. And, for many applications, it does >[this is partly why I have an MSc student coding a reverse engineering >application in Haskell]. > >Since the claim of static typing is that things cannot go wrong at run-time, >one start to think (incorrectly, but optimistically) that this means that >'nonsense' cannot happen at run-time. And multiplying matricies with >non-matching sizes is nonsense, so it is rather disappointing that, without >tricks, this is not caught at compilation time. > >Matrix length are one of many commonly occuring dependent types in >mathematics. Variable names for polynomials, expansion point and 'scale' >for generalized series expansions, coefficient ring for normalization and >factorization of polynomials, and so on up the food chain. The dependencies >get quite interesting when one is dealing with modelling mixed PDEs and >recurrence equations as ideals in rings of Ore polynomials! > >Jacques > >_______________________________________________ >Haskell mailing list >[EMAIL PROTECTED] >http://www.haskell.org/mailman/listinfo/haskell > > Michael Manti [EMAIL PROTECTED] _______________________________________________ Haskell mailing list [EMAIL PROTECTED] http://www.haskell.org/mailman/listinfo/haskell
