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Reasonig about combinators (a lambdacalculus puzzle on composing compositions)In Haskell, \f > \g > (((f.).).) g is equivalent to \x y z > f (g x y z), and more generally, \f > \g > (((f.)... .) g with n compositions is equivalent to x1 ... xn > f (g x1 ... xn) with n arguments. But what is \f > \g > (.(.(.f))) g? Can you generalize? What about arbitrary left and right compositions, like (.(.((.f).)))? Can a general description be given? I am interested in your strategies in tackling such questions. I find reasoning about combinators quickly overwhelming. Sure, I can mechanically reduce a lambda term to normal form, but it's usually not that insightful. Is the key once more abstraction, through understanding of combinators at a high operational level? Any pointers to resources for reasoning about combinators would be appreciated. By namin at 20090106 04:43  LtU Forum  previous forum topic  next forum topic  other blogs  2909 reads

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