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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*: Re: mathematical models*From*: Mitchell Wand <wand@ccs.neu.edu>*Date*: Wed, 4 Jun 1997 09:30:53 -0400 (EDT)*In-Reply-To*: Jeffrey Mark Siskind's message of Wed, 4 Jun 1997 08:31:31 -0400*References*: <199706041231.IAA15772@qobi.nj.nec.com>

>>>>> On Wed, 4 Jun 1997 08:31:31 -0400, Jeffrey Mark Siskind <qobi@qobi.nj.nec.com> said: MF> ML is the only language (I know of) that has a fully mathematical MF> specification. JMS> I remember reading a paper around 1977 that contained a W-grammar JMS> specification of the syntax and semantics of an Algol-68-like JMS> language. (No it was not the Algol-68 report. That contained a JMS> specification only of the (context sensitive) syntax of Algol-68.) The JMS> basic idea was that the W-grammar generated strings of the form JMS> input$program$output. JMS> I have long forgotten the title and author of the paper. Can someone JMS> refresh my memory? I remember being rather impressed with it at the time. I don't know what Matthias means by a "fully mathematical specification". There have been "mathematical" specifications written for lots of languages. I've seen them for everything from Algol 60 to SNOBOL. They have been written in a variety of styles (denotational/operational/axiomatic), but the important differences (for the purpose of this discussion, so far as I can make it out) is what portions of the language behavior are specified. The R3RS denotational semantics and the ML definition both contain incomplete or informal specifications of the constants of the language. For example, the initial dynamic basis in SML (Appendix D of the definition) describes the arithmetic operations only in an informal way. It does not specify sizes of integers, what a "real" is, etc. The Scheme number specification is far more sophisticated. The most comprehensive language specification that I am aware of is that for Java, for whose creators "works the same on every screen" was a mantra from the start. --Mitch

**Follow-Ups**:**Re: mathematical models***From:*Matthias Blume <blume@CS.Princeton.EDU>

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

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