[TYPES] The type/object distinction and possible synthesis of OOP and imperative programming languages

Uday S Reddy u.s.reddy at cs.bham.ac.uk
Fri Apr 19 03:21:09 EDT 2013

Mark Janssen writes:

> The main thing that I notice is that there is a heavy "bias" in
> academia towards mathematical models.  I understand that Turing
> Machines, for example, were originally abstract computational concepts
> before there was an implementation in hardware, so I have some
> sympathies with that view, yet, should not the "Science" of "Computer
> Science" concern itself with how to map these abstract computational
> concepts into actual computational hardware?

I think there is some misunderstanding here.  Being "mathematical" in
academic work is a way of making our ideas rigorous and precise, instead of
trying to peddle wooly nonsense.  Providing a mathematical description does
not imply in any way that these ideas are not implementable on machines.  In
fact, very often these mathematical descriptions state precisely how to
implement the concepts (called operational semantics), but using
mathematical notation instead of program code.  The mathematical notation
used here is usually no more than high school set theory, used in a
stylized way.

In contrast, there are deeper "mathematical models" (called denotational
semantics and axiomatic semantics) which are invented to describe how
programming language features work in a deep, intrinsic way.  This is
similar to, for instance, how Physics invents mathematical models to capture
how the nature around us works.  Physicists don't need to "implement"
nature.  It has already been "implemented" for us before we are born.
However, to understand how it works, and how to design systems using
physical materials in a predictable way, we need the mathematical models
that Physics has develeped.

Similarly, the mathematical models of programming languages help us to
obtain a deep understanding of how languages work and how to build systems
in a predictable, reliable way.  It seems too much to expect, at the present
stage of our field, that all programmers should understand the mathematical
models.  But I would definitely expect that programming language designers
who are trying to build new languages should understand the mathematical
models.  Otherwise, they would be like automotive engineers trying to build
cars without knowing any Mechanics.

Uday Reddy

Prof. Uday Reddy                Tel: +44 121 414 2740             
Professor of Computer Science   Fax: +44 121 414 4281
School of Computer Science      
University of Birmingham        Email: U.S.Reddy at cs.bham.ac.uk      
Birmingham B15 2TT              Web: http://www.cs.bham.ac.uk/~udr

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