This paper, a revised version of Rutten and Turi (1993), is
part of a programme aiming at
formulating a mathematical theory of structural operational semantics to
complement the
established theory of domains and denotational semantics to form a coherent
whole
(Turi 1996; Turi and Plotkin 1997). The programme is based on a suitable
interplay between
the induction principle, which pervades modern mathematics, and
a dual, non-standard
‘coinduction principle’, which underlies many of the
recursive
phenomena occurring in computer science.
The aim of the present survey is to show that the elementary
categorical notion of a final
coalgebra is a suitable foundation for such a coinduction principle.
The properties of
coalgebraic coinduction are studied both at an abstract categorical level
and in some specific
categories used in semantics, namely categories of non-well-founded sets,
partial orders and
metric spaces.