From: Matthias Blume (find@my.address.elsewhere) Subject: Re: [OT] Finns and education Newsgroups: comp.lang.scheme Date: 2004-09-04 20:58:16 PST richter@math.northwestern.edu (Bill Richter) writes: > Matthias Blume responds to me in message > news:... > > [... Moreover, what you say about your function definition is > arguably wrong -- but I am too tired of this to go into any detail > as to why.] > > That's the story of this thread, Matthias: folks say I'm wrong, but > won't explain why (or if they do "explain", it's so obviously nonsense > that there's no reason to think they understood what I did). Ok, hint: You claim your semantics captures how Scheme treats application. But in reality it -- at best -- only captures how Scheme treats applications that are not under a lambda. Proof: Your semantics for everything under a lambda is the indentity function. As a result, your semantics is actually just one beta step away from the "add a new start symbol semantics". Here is why: In Scheme, a closed expression E and the expression ((lambda (x) E) 1) are equivalent. But your semantics treats the second term by first applying the identity function to E and subsequently running the OpS on the result. That is precisely what the "add a new start symbol" semantics does. > > There is absolutely no reason to think that Will thought his "add > > a new start symbol" semantics is compositional. > > There is every reason. Why else would he even have brought it up? > > I sure thought Will's purpose was to show that my semantics was not > compositional. Will actually had 2 different semantics's in his "why > BS isn't DS" thread, and the 2nd was closer to mine. But for both: > > 1) he used OpS to define total semantic functions, as I do > > 2) he claimed (& proved I think) that his semantic functions satisfied > Bill-compositionality, and he did not claim that his semantic > functions had a compositional definition. Suppose I want to define some mathematical object A without invoking some method (for defining A-like objects) M, but I can't think of any way of achieving this. So I first define B (invoking M) the way I would have defined A if I were allowed to use M. Then I define: A ::= B See, no M there! Have I now succeeded defining A without using M? Once you solve this puzzle, you will see why Will does not think your (or his) semantics is compositional. > > And if we take the liberty of changing the grammar of the > > language, the first definition is also meaningless as it makes > > all functions on syntax trees compositional. > > > > OK, but that goes for the 2nd def as well. > > Nonsense. If you change the grammar, you subsequently have to > change the definition of the function. Once you chance the > definition, anything you say about the new definition has no > bearing on the original one. > > Sure, but what's that have to do with what I said? Maybe you didn't > understand me: By `2nd def' I meant the established cls def of > compositionality. Not the 2nd def of a set of sem functions. I perfectly understood you. You didn't understand my reply, evidently. > You & others should understand my semantics if you're going to flame > it, I have. Now give it a rest, will you! > You seem to say (top of my message) that I don't have a compositional > definition. You have a compositional definition of the identity function. Your "compositional definition" of your semantics still refers to a non-compositional definition of the exact same semantics. > So (in my understanding of how careful scientists behave) > you have an obligation to understand my semantics! And you have the obligation of acknowledging when I did, or else shut up! > But why should I understand yours? What will I learn? Why don't you > explain it mathematically as Will & I did instead of in ML? I used ML because it is close enough to mathematical notation, but standardized and far more readable in an all-ASCII forum, IMO. One problem I have with what you write is that dreaded pseudo-latex which just gets on my nerve. > Why don't you just tell me the moral, and maybe I'll believe it? Why don't you sit down and learn something first. In time it took to post several hundreds of messages you could have learned ML, or even just have gotten a clue on DS. > I certainly haven't flamed your semantics, so there's no obvious > obligation. Given that you don't understand it, flaming my semantics would have been just par for the course in your world, I guess. > In your framework, a function on programs is compositional if one > can find a grammar for the function such that there exists a > corresponding compositional definition of the function in question. > > But I've never said that. I don't talk about a single function being > compositional. I speak, as C-F do, of a collection of sem functions > E_i being compositional, w.r.t. to a given BNF as Schmidt describes. But you don't use the given BNF! (BTW, I was also talking about the collection of functions. I merely abbreviated. I though this would have been obvious, but apparently it was not.) > [ ... ] I find my grammar to be meaningful, as it reflects my OpS > understanding of Scheme. In this case I have to conclude that you don't even have an OpS understanding of Scheme. > If you find my grammar to be > meaningless, we're not having a mathematical argument. I am not saying that your grammar is meaningless. However, one property of DS is that it assigns the same meaning to an expression E no matter where it occurs. Yours does not. > > No, I'm really confident in my pure Math skills, and this is just > > a pure Math problem. > > The whole problem with the world is that fools and fanatics are > always so certain of themselves, but wiser people so full of > doubts. -Russell > > Then I'm the wise person, because you cls folks haven't entertained > any doubts at all so far, but I've realized during this thread that I > misunderstood many things, chiefly, how ZFC formalized pure Math. I > remember my first misunderstanding pungently: Lauri (and Joe too, who > got the ball rolling, asking tough questions about judgments & > antecedents) explained how my claim about PLAI was false: Shriram's > big-step OpS ( called natural semantics by Nielson^2) does not > instantly translate into a total semantic function. That's the > purpose of my talking about small step OpS, which I did 2 years ago as > well, but I'm not sure I understood the point 2 years ago, and if I > did, I certainly forgot it. Corollary: Fools and fanatics, when confronted with Russell's aphorism, will always claim to be those doubtful and wise people. Matthias