From: Andreas Strotmann <strotman@cs.fsu.edu>

Date: Wed, 12 Jul 2000 19:47:20 -0400 (EDT)

To: Stan Devitt <jsdevitt@radicalflow.com>

cc: Gérald QUINTANA <quintana@lyon.objectif.fr>, www-math@w3.org

Message-ID: <Pine.GSO.4.10.10007121913430.1848-100000@xi.cs.fsu.edu>

Date: Wed, 12 Jul 2000 19:47:20 -0400 (EDT)

To: Stan Devitt <jsdevitt@radicalflow.com>

cc: Gérald QUINTANA <quintana@lyon.objectif.fr>, www-math@w3.org

Message-ID: <Pine.GSO.4.10.10007121913430.1848-100000@xi.cs.fsu.edu>

> The advantage of a tagged data-structure over a lambda construct > is: that can be recognized as being a piecewise definition. > > In particular, this means that it can be quickly recognized as such > and for display purposes, it means that you can invoke a special > transformation immmediately instead of having to do sophisticated > pattern matching on the arguments to lambda to see if you want > a special notation for display. Yes, I agree with you here, Stan. With respect to the actual representation of the "cases" or "pieces", my quick-and-dirty solution would require some multi-level pattern matching for discovering the proper rendering, and I would certainly welcome the introduction of special-purpose MathML content markup for something close to the "cond" or "if-then-else" or something a little closer to the mathematical notation / -1 for x<0 | sign(x)=< 0 for x=0 | \ +1 for x>0 Special notation for "otherwise" (and, come to think of it, the concept of "undefined" that is necessary once you're talking piece-wise defs) could be added as well. My main point was that I do not think that a conditional expression like that should involve a <bvar>, as the notions of "piece-wise" and "function" are clearly separable and orthogonal, and I'm not aware of a mathematical notation that mixes them together in a way that is comparable to the way that, say, notations for integration and differentiation mix them. I also wanted to point out that there is available in MathML a way of expressing quite cleanly the concepts behind piece-wise functions, as a vindication of MathML as it stands. Taken together, these two points simply argue that it is a matter of choice (taste) whether to add the "pieces"/"cases"/"cond" concept to MathML directly or via an extension mechanism like OpenMath. Personally, and based on the historical precedence from its ubiquity as primitive construct in the programming world, I would prefer adding something like Lisp's "cond" or like "if-then-else" as a MathML primitive. In this, I very much agree with you, Stan. -- Andreas PS: a piece-wise function in this sense would therefore be represented as lambda(x, choice( case(x<0,-1), case(x=0,0), case(x>0,+1) )) where the lambda construct says "function" and the choice one says "pieces". In addition, a declare construct (like lambda already available for this purpose in MathML) would say "definition". I do not think that anything would be gained by adding to MathML a construct that mixes together all three. A lot would be gained by adding one that deals exclusively with the missing concept. (Note that it is indeed missing, despite providing a way to emulate it.)Received on Wednesday, 12 July 2000 19:47:22 GMT

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