Agreed. The original note confuses programs (syntax) with functions (semantics). -- Conal
On Thu, Apr 5, 2012 at 8:52 AM, Dan Doel <dan.d...@gmail.com> wrote: > On Thu, Apr 5, 2012 at 10:14 AM, Grigory Sarnitskiy <sargrig...@ya.ru> > wrote: > > First, what are 'functions' we are interested at? It can't be the usual > set-theoretic definition, since it is not constructive. The constructive > definition should imply functions that can be constructed, computed. Thus > these are computable functions that should be of our concern. But > computable functions in essence are just a synonym for programs. > > This is a flawed premise. The point of working with functions is > abstraction, and that abstraction is given by extensional equality of > functions: > > f = g iff forall x. f x = g x > > So functions are not synonymous with programs or algorithms, they > correspond to an equivalence class of algorithms that produce the same > results from the same starting points. If you can access the source of > functions within the language, this abstraction has been broken. > > And this abstraction is useful, because it allows you to switch freely > between programs that do the same thing without having to worry that > someone somewhere is relying on the particular algorithm or source. > This is the heart of optimization and refactoring and the like. > > There are places for metaprogramming, or perhaps even a type of > algorithms that can be distinguished by means other than the functions > they compute. But to say that functions are that type is false, and > that functions should mean that is, I think, wrong headed. > > -- Dan > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe >
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