I have now (hopefully) implemented functional composition using operator dot: //--------------------- fun f(x:int)=>x + x; fun g(x:int)=> x * x; // simple case, rhs is a name val k = f . g; //println$ 1 . k; println$ 1 . f . g; var z = (f . g) 1; println$ 1 . (f . g); println$ 1 . (g . f);
// here the rhs is itself a composition and this not a simple name println$ 1 . (f . (f . f)); fun h (x:int) (y:int) => x + 10 * y; println$ 1 . (f . (h 1)); // #1 println$ 1 . ((f . h) 1); // #2 println$ 1 . (f . h 1); // dot has higher precedence, so this is same as #2 //---------------- You should note the algorithm says: given f.g, first try to apply g to f, if that fails and g is function and dom(g)=cod(f), then create a composite function such that (f . g) x = g( f (x) ) Note the order reversal. This is reverse composition. It is because we want x . f . g = (x . f) . g = x . (f . g) and of course (x . f) . g = g (f (x))\ At present, closures of composites don't work, just as closures of anonymous sums are not working. I'll make this work soon I hope (both cases). The problem is that at present, when the need for a closure is discovered in the C++ code generator, it is too late to synthesise one easily: it could be done, creating an entry in the bound symbol table, but it is risky because we're in the process of iterating through it, and it's a hash table, so mutation is dangerous during an iteration. A set wouldn't have this problem .. Anyhow, the solution is to make the closures in the closure making pass (in mkcls I think), and replace the compositions which will need to become closures with the closure term, refering to the synthesised function. It sounds hard but the closure is just the wrapper: fun clos (x:t) => g ( f ( x ) ); and the same for the failing sum component closure. Generally this is all a pain. Felix can't tolerate lambdas in the term structure at code generation time, nor indeed at any other time after binding. All lambdas have to be lifted out and put in the symbol table with some "name", since closures are only supported for such functions (if a closure has to be generated it is nothing more than a new'd class value). I plan to also implement the parallel composition (product) of functions: (f * g) (1,2) = (f 1, g 2) and of course the sum (f + g) case 0 of (int+float) 1 = f 1 (f + g) case 1 of (int+float) 2.0 = g 2.0 These are standard "categorical operators". There are a couple more: "delta" in CT is called "dup" in programming: delta x = x,x and there's an operator which does x -> (f x, g x) i.e. x . dup . (f * g) and a few others. Note that whilst "compose" and "parallel_compose" can be easily defined in the library **for two arguments** generically it is NOT possible at this time to write a definition for an arbitrary number of arguments: Felix is polymorphic but not polyadic. In fact, polyadic fold operators COULD be implemented for syntactic terms in the parser action code using Scheme. however this is not real polyadic programming because it only works on literal terms, not on structured values. For example you might implement a fold that coped with (f * g * h) (1,2,3) but would fail on (f * g * h) x where x = 1,2,3 since the parser doesn't know the structure (type) of x. So we have to do this kind of thing in the compiler at present, in Ocaml. (The above case is easy, it is just f x.mem0, g x.mem1, h x.mem2, which works for all x, literally tuples, a variable, or indeed any expression yielding a triple). I can't figure out how to set it up so the user can write this kind of rule (in user code as opposed to hard coding into the compiler). -- john skaller skal...@users.sourceforge.net ------------------------------------------------------------------------------ Nokia and AT&T present the 2010 Calling All Innovators-North America contest Create new apps & games for the Nokia N8 for consumers in U.S. and Canada $10 million total in prizes - $4M cash, 500 devices, nearly $6M in marketing Develop with Nokia Qt SDK, Web Runtime, or Java and Publish to Ovi Store http://p.sf.net/sfu/nokia-dev2dev _______________________________________________ Felix-language mailing list Felix-language@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/felix-language
