Elementary Universal Algebra and Computer Science
Eric G. Wagner,
Universal algebra is a branch of mathematics which was originally
concerned with abstract generalizations of algebraic concepts.
It is perhaps surprising then that the ideas of universal algebra
have played a significant role in such areas of computer science
as the specification of data types, the semantics of programming
languages, and the theory of compilers. Equally surprising
is that the seemingly abstract fundamental
constructs of universal algebra can be easily implemented on a
computer using a symbolic computation system such as
Mathematica in a manner that makes it possible to construct and
explore interesting computer science examples.
In this talk we will give an introduction to universal algebra
for non-mathematicians, illustrate its application to the syntax
and semantics of programming languages, and describe how the
basic constructs of universal algebra can be implemented within
Demonstrations of the Mathematica programs (notebooks)
implementing the material in the talk will
be given on a later date and, if there is sufficient interest,
more detailed talks may also be given.
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