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Re: [Axiomdeveloper] B#
From: 
Gabriel Dos Reis 
Subject: 
Re: [Axiomdeveloper] B# 
Date: 
25 Mar 2006 01:54:45 +0100 
"Page, Bill" <address@hidden> writes:
[...]
 In this context I would not call it vague or hand waving.
 They are simply referring to the behavior of the Axiom
 interpreter as it is now defined. Unfortunately I am not
 able to point you to any clear and complete systemlevel
 documentation of the actual algorithms used :(.
yes, that is what I have been saying :). I read the codes in
src/interp/i*.spad.pamphlet; although I don't understand all of it,
it still is not a specification of the AXIOM type system rules.
 But in the
 final analysis we do have the full source code for the
 interpreter plus we can do some experiments to test our
 understanding.
yes; however that assumes the existing code base is correct AND we do
understand it sufficiently well. I'm far from meeting those criteria
now. I'm trying to being overly critical of the paper. I find it
quite very useful and delightful by moment. However, the formal type
system rules are not there, not in any other paper I can have access
to through ACM. I hope Tim would be able to make some of the
technical reports available to us.
[...]
 > Type User has exported operations that allow the user to
 > do general formula manipulation, to transform parse forms
 > and results as symbolic formulae under rather complete user
 > control. Transformations can be done by patternmatching
 > or direct manipulation. Expression trees provide a simple
 > and intuitive model of a formula.

 To me this sounds very much like the 'InputForm' domain that
 is already part of the Axiom Interpreter.
and not SExpression?
 I have a feeling
 that the Axiom developers were already incrementally moving
 toward a B# implementation by a series of smaller steps
 involving extensions to the Axiom library and to the Axiom
 interpreter.
My general feeling after reading the paper several times is that they
beleive in twolevel systems: one for library writer where the full
rigor or strongly typed language is there to assist the library
writer; and one level (top level?) to introduce novices to the
system. This is to be contrasted (as they said in the paper) with the
approach taken by Maple (it is interesting to note their comparison
with the GAUSS system). I believe they wanted to make the system more
accesible, but I don't think they wanted to move away from A#.
[...]
 as a representation for the type User. In principle it
 would not be a difficult job to implement parser for B#
 in SPAD or Aldor that would generate InputForm expressions
 directly from B# input and perform the type of coercions
 that are now down by the Axiom interpreter.
Implementing the parser is indeed not difficult at all. The
interesting bit is connecting to the rest of the system.
 Gaby
 Re: [Axiomdeveloper] B#, (continued)
 RE: [Axiomdeveloper] B#, Page, Bill, 2006/03/23
 RE: [Axiomdeveloper] B#, Page, Bill, 2006/03/23
 RE: [Axiomdeveloper] B#, Page, Bill, 2006/03/24
 RE: [Axiomdeveloper] B#, Page, Bill, 2006/03/24
 Re: [Axiomdeveloper] B#,
Gabriel Dos Reis <=