 
Summary: Lectures on Semantics:
The initial algebra and final coalgebra
perspectives
Peter Aczel
Departments of Mathematics and Computer Science
Manchester University,
Manchester, M13 9PL, UK
Abstract. These lectures give a nonstandard introduction, for computer
science students, to the mathematical semantics of formal languages. We do
not attempt to give a balanced treatment, but instead focus on some key
general ideas, illustrated with simple examples. The ideas are formulated
using some elementary category theoretic notions. All the required category
theory is introduced in the lectures. In addition to the familiar initial algebra
approach to syntax and semantics we examine the less familiar final coalgebra
approach to operational semantics. Our treatment of formal semantics is
intended to complement a more standard introduction.
Keywords. semantics, formal language, category theory, category, functor,
initial algebra, final coalgebra, operational semantics, CCS
Introduction
These lectures are primarily intended as an introduction, for computer science
