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Re: Re: Re: More /.{I->-1} craziness

  • To: mathgroup at
  • Subject: [mg106230] Re: [mg106172] Re: [mg106159] Re: More /.{I->-1} craziness
  • From: "E. Martin-Serrano" <eMartinSerrano at>
  • Date: Tue, 5 Jan 2010 01:49:16 -0500 (EST)
  • References: <>


It is well known that there are many books about syntax (and semantics) and
programming languages available in English. (of course, most of you know
that). But, for others interested in the subject, the following are good
sources to find any reference.

Lambda Calculus: (Close to the
Mathematica underlaying form.)

BNF grammars : (The
simplest form; only context-free syntax)

Affix-grammars: (Augmented BNF to
include context sensitive syntax and semantics)

Two-Level grammars:
(Meta-grammars and hyper-grammars togheter o more sophisticated form of
Affix Grammrs used to describe Algol 68)

Petri nets: (enriched finite state
machine grammars to include devices to trigger state transitions)

Phrase structured grammars:
(seminal work in the field)

And many others.

E. Martin-Serrano

-----Original Message-----
From: Andrzej Kozlowski [mailto:akoz at] 
Sent: Monday, January 04, 2010 11:58 AM
To: mathgroup at
Subject: [mg106230] [mg106172] Re: [mg106159] Re: More /.{I->-1} craziness

On 3 Jan 2010, at 17:41, Leonid Shifrin wrote:

> Hi Richard,
> Below I describe  rather extensively my view on the issues you raised.  J=
> to make myself clear, it is not my intention to get involved in an endles=
> debate on these topics. I try to adhere to DRY (don't repeat yourself)
> principle whenever I feel appropriate, so I detail my view on these subje=
> below with the intention to do it only once. But I will certainly appreci=
> your feedback.
> On Sat, Jan 2, 2010 at 9:06 AM, R Fateman <fateman at> wrote=
>> Leonid Shifrin wrote:
>>> Regarding this issue, I think I entirely agree with what David Bailey a=
>>> other people said: I don't consider replacement rules as a mathematical=
>>> for end users, but rather as an inner layer of Mathematica, which is al=
>>> exposed for flexibility / convenience and intended primarily to be used=
>>> the more advanced users.
>> Unfortunately many users or potential users are not as sophisticated in
>> their understanding of the distinction between the underlying mechanisms=
>> a syntax-driven
>> transformation system.  They simply take the marketing blurbs about "A
>> system for doing mathematics"  as a description suggesting that --hey, I=
>> mathematics too.  They don't really know what "syntax" means and they do=
>> think they need to know, because syntax is not part of their mathematics
>> education.
> Well, if these people don't understand the importance of syntax for doing
> any formal sicence, regardless of whether it is done by a human or a
> computer, and somehow believe that some software is able to completely
> automate this problem away without any further efforts on their side  -  =
> bad for them and their current and future employers. Every tool used blin=
> will eventually produce nonsense. Mathematica is a research tool. I view =
> as a tool for explorations, tests, verifications and sometimes discoverie=
> but not a substitute for domain knowledge, intuition, right questions to =
> and anticipation for possible correct answers.

I would add this: if someone does not know what syntax is he should take
some time off and read almost any introductory on mathematical logic. Need
not be written by anyone who has anything to do with computer science and
can be in fact pretty old.
The first example form my shelf: Yuri Manin "Lecture on Mathematical Logic"
vol 1., Chapter I, Section 2, Language of propositions: alphabet, syntax and
interpretation. (1974, in Russian but there is no shortage of equivalent
English texts).

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