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*To*: Qobi@research.nj.nec.com, rrrs-authors@martigny.ai.mit.edu, hbaker@netcom.com, jgm@cs.cornell.edu, shriram@cs.rice.edu, ramsdell@linus.mitre.org, feeley@iro.umontreal.ca, kelsey@research.nj.nec.com, will@ccs.neu.edu*Subject*: mathematical models*From*: Matthias Felleisen <matthias@cs.rice.edu>*Date*: Tue, 3 Jun 1997 20:50:54 -0500 (CDT)*Reply-To*: matthias@rice.edu

On the role of mathematical models: 1. Mathematical models have helped physicists a lot for their study of properties of the real world and for describing to laymen what they find. I am (still) hoping that mathematical models will help programming language researchers to study properties of PLs and to explain programming languages in standards. We started out that way. In the early days, Schemers (speak Guy and Gerry) used interpreters as mostly mathematical models for this purpose. Interpreters are okay to study some things but are probably ill-suited for many explanatory purposes. R3RS contains a denotational semantics. If take as such, it is too extensional for many purposes. If misinterpreted as an interpreter, it is equally ill-suited as an interpreter. Some of us have used rewriting models to validate properties of program transformations, type systems, garbage collectors, and other properties. They too suffer from problems. Different models are good for different purposes. 2. Should mathematical models be included in or should they be language definitions? ML is the only language (I know of) that has a fully mathematical specification. Is/was this experiment successful? I believe it failed for technical reasons. They too understood that a mathematical model couldn't be the only specification. They wrote a commentary. Did they _benefit_ from constructing and working with a fully mathematical model? Most definitely. Their explanations of things (how ML works, how type checking works, what it accomplishes, what it doesn't accomplish, how GC can be extended beyond rachability) are often crisp, unambiguous, and accessible. Their new effort (sml1996, ml2000) benefits a lot from playing with mathematical models. I believe that a full-fledged model of Scheme (or several related models) would help us formulate what the language provides, what properties it should satisfy, etc. The model should be used to construct English descriptions and to validate descriptions of ideas. It may accompany the report or it may be available in the Scheme repository at Indiana. That part is probably irrelevant. Having precise models of what we want to say is important. -- Matthias

**Follow-Ups**:**Re: mathematical models***From:*Jeffrey Mark Siskind <qobi@qobi.nj.nec.com>

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