Toby Bartels <toby+categories@ugcs.caltech.edu> wrote in part:
The point is that one can recognise that two syntactic expressions, such as x and x, are the same, ...
Sorry, Toby, when I see "such as x and x" I have to struggle to treat the expression between "as" and "and" as anything other than different from the expression following the "and" -- for, if they were really the same, there would be but one expression, not two, it would be in one of those positions only, not both (I'm put in mind of the good old "Cheech and Chong"-ism, "How can you be in two places at once, if you're not anywhere at all?"), and you'd have used not the plural verb form "are" but the singular "is". An illustration from another realm: each time the clerk behind the deli counter finishes with one customer and shouts "Next!" so as to bring up another one, the expression the clerk shouts refers to an entirely different customer than it did the time just before.
... or even that one reduces to another, such as fst(x,y) and x (where fst: A x B -> A is the usual projection),
Again I'm puzzled: what can fst(x,y) (where fst: A x B -> A is as you say) possibly have to do with x (as in A x B, presumably -- or did you mean as in fst(x,y), which could be problematic for void B)? Sorry to be so obtuse, but ...; cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]