The term algebra is used ... to denote abstract
behaviour of a class of objects ...
While a calculus is a
general-purpose syntactic system of transformation rules, an algebra
is a special-purpose semantic system that captures specific
behaviour such as that of the integers or of stacks, persons or
vehicles. A given algebra can generally be captured by a variety of
syntactic calculi. For example, the behaviour of integers can be
realised by decimal or binary number systems or even by lambda
calculus representations. An algebra may be thought of as an
equivalence class of calculi with common behaviour or as an
abstraction from a specific syntactic realisation of a calculus to a
semantic specification of the underlying behaviour.
Classification Paradigm. 1987