From: Peter Murray-Rust <pm286@cam.ac.uk>

Date: Tue, 27 Mar 2012 09:25:21 +0100

Message-ID: <CAD2k14P4jO7-SgRZ6Y4fhUPQBT3iyNKGYnoyZNoaLJoSRzqbmg@mail.gmail.com>

To: www-math@w3.org

Cc: davidc@nag.co.uk, "Andreas.strotmann" <andreas.strotmann@gmail.com>

Date: Tue, 27 Mar 2012 09:25:21 +0100

Message-ID: <CAD2k14P4jO7-SgRZ6Y4fhUPQBT3iyNKGYnoyZNoaLJoSRzqbmg@mail.gmail.com>

To: www-math@w3.org

Cc: davidc@nag.co.uk, "Andreas.strotmann" <andreas.strotmann@gmail.com>

Very many thanks to all contributors. I have made extremely good progress with my project to implement a declarative approach to numerical physical science (this derives from a symposium I ran in January "Semantic Physical Science" http://www-pmr.ch.cam.ac.uk/wiki/Semantic_Physical_Science) and have implemented the core in Java, both for the chemistry/physics and for the maths. My current concern is about the implementation of the declarative-imperative MathML engine. Ideally it shouldn't be (just) me doing this (and if there are volunteers I'd be delighted). But actually it isn't a huge amount of effort to code it for physical science. I have added a differentiation engine which is good enough for what I need and added all the major operators and functions that I currently need (things like the 20 "unary elementary classical functions" get added while watching cricket). As an example of the problem I am tackling, see the first equation in http://en.wikipedia.org/wiki/AMBER ("Functional form"). This is an empirical description of the relationship between the geometry of molecules and their energies. It is the basis of a huge amount of current supercomputing for predicting the geometry and ihteraction of proteins, materials, minerals, etc. The current codes are archaic and arcane and many are 25 years old, and hundreds of KLOC. With declarative programming in MathML and CML It can be reduced to 2-3 pages of readable material (and some parameter files). My overriding problem is semantics. The chemistry is my problem, and I have done that - e.g. "bonds" in the first summation is now a declarative - imperative statement. I now need to couple that to the MathML. My current impression is that MathML takes the approaches: - everyone agrees on the semantics so we don't need to spell them out - OR noone agrees on the semantics so you can do what you like - OR the semantics are irrelevant As an example summations are often indicated with a bvar: <bvar><ci>x</ci></bvar> but what are the constraints on implementing this? Is "x" necessarily an integer? The spec doesn't say so. Is there therefore an agreed definition of "sum index" that constrains it to be an integer? What happens if the end index is less than the start? An error? a no-op? or a negatively decreasing step? Without strict explicit constraints people will build engines that behave in different ways. My own recommendation is that there should be a reference declarative-imperative MathML engine (with unit tests) that defines the semantics operationally. This is what I did for CML - the JUMBO engine has thousands of unit tests defining the explicit semantics of CML. Of course we also try to explain this in words, but words are often fragile. My current mathml engine is at https://bitbucket.org/petermr/mathml/overview- it's all Open Source and I can add developers. P. -- Peter Murray-Rust Reader in Molecular Informatics Unilever Centre, Dep. Of Chemistry University of Cambridge CB2 1EW, UK +44-1223-763069Received on Tuesday, 27 March 2012 08:25:55 UTC

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