Am Donnerstag 07 Mai 2009 10:23:41 schrieb j.waldmann:
* in the Appendix on notation, he defines composition of functions the "wrong way around" (i.e., the Haskell way, (f.g)(x) = f(g(x)). This is of course very awkward, especially considering that functions are relations, and an element of a relation is a directed edge, and there's a very obvious meaning of how edges are composed to give a path. Well, the book's "solution" is to avoid to define composition of relations! (p. 1155, they only define the n-fold composition of a relation with itself, and there the problem does not show.)
PS: I was shocked to find recently that Bourbaki (!) also defines functional composition "wrongly" (at least in the English edition of Elements of Math./Theory of Sets, II.3.7) but at least they are consistent and define composition of relations ("graphs") accordingly. They are very honest about this, e.g. "Let G1, G2, G3 be graphs. Then (G3 * G2) * G1 = G3 * (G2 * G1)." (note the order of the variables)
That's the way composition of functions (and more generally relations) has been done for ages in mathematics. And since one writes f(x) and not x.f, it's the consistent way to define the composition. Of course, if centuries ago people had decided to write the argument before the function, composition would've been defined the other way round. They haven't.