From: Matthias Blume (find@my.address.elsewhere) Subject: Re: [OT] Finns and education Newsgroups: comp.lang.scheme Date: 2004-09-01 21:17:23 PST richter@math.northwestern.edu (Bill Richter) writes: > Matthias Blume responded to me in message news:... > > > The sort of simple facts I have in mind are: in DS, a function is > > a map, not a procedure, and a function=map is a set, a certain > > kind of subset even, same for partial functions, so functions do > > not come supplied with preferred definitions (as procedures would > > of course), > > I actually agree so far -- and have publicly said so before. > > Great, Matthias! Sure doesn't look like we have anything to argue > about now, looking at your post below: Well, I really meant to no longer feed the troll, but this one I can't let go. No, Bill, we don't have anything to argue about. But that is not because we agree on so much... > > and that we can define compositionality as property of either sem > > functions or their definitions, but we gotta make a choice, we > > can't artfully jump from one to the other. > > Here we begin to disagree. Compositionality is a property of the > /definition/ of a function > > Isn't that what I said? We can define compositionality as property of ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ > the definition of sem functions. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ > [...] > Yeah, if we go that route, but we could've gone a different route. We ^^ > could instead defined compositionality as property of sem functions. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ You contradict yourself (once again) within the space of a two paragraphs... > Now, your definition of the semantic function is, indeed, > compositional. > > My sem functions E_i which I posted about so often here? Including > > E_1: Exp ---> Value_bottom > > and all other E_i identity maps? Thanks, Matthias! That is, assuming you got all the details right. I did not have the patience of Will Clinger to check whether that is so. > You may be the first person to have agreed with me on this point. No, I am not. > However, I'm not convinced that you actually understand what my E_i > are. It is now obvious: You have converged. You are complete! You have reached point B! (**) To witness: Not only have I understood your E_i, I have also given a "better" version of them which can do without mucking with the grammar of the language. (Again, all this is assuming you got the details right.) Do you really think it is possible that I have not understood your E_i? > It just happens to have this major flaw of relying of an earlier > non-compositional definition of the same function! > > Right. But so what? That means I suppose my semantics doesn't > interest you. Nor does it interest anyone else. > That's the mathematical joke that Will Clinger has pointed out > early on, and which I have tried to explain to you in detail -- > with code and all that -- at least twice. > > Go ahead and laugh then! The question we've been arguing about for > months here is whether my semantics is compositional. Well, strictly speaking, only the part of your semantics that weaves an identity function into the earlier-defined operational semantics is. That operational semantics itself is not defined in a compositional manner. > As a matter of fact, for *every* function whose domain is the set > of abstract syntax trees of a language there is a compositional > definition if you take the liberty of changing the grammar -- as > you did. > > That's actually not what I did, that's what Will did, but we can > ignore this. I changed the grammar in a different way. Read what I wrote! You changed the grammar. Period. If one is allowed to change the grammar, one can also do so in the far simpler way that Will suggested. Your change is equally pointless as the simpler one, but you apparently think you can hide the joke that it is behind the needless complexity of your solution. > All one needs is a new start symbol and a single new production > from the new to the old start symbol. Thus, your entire exercise is > trivial (although still unnecessarily convoluted despite its > triviality) and uninteresting. > > That's fine if you find it uninteresting & trivial. But if you agree > that this joke semantics has a compositional definition, then you seem > to be agreeing with me on the point we've been arguing about, and > disagreeing with Will. No. Will does not disagree with that. After all, he is the one who suggested the "add a new start symbol" solution first. > And now I have to put you back up on the gold medal podium with Lauri, > who we congratulate for finishing his CS Masters degree! I don't consider this an honor. In fact, I decided to answer one last time (this is it) to make sure nobody else thinks I agree with you. Matthias (**) Greetings from Zeno and Will Clinger.