A 2-category approach to critical pair completion

Abstract

The categorical presentation of the CPC algorithm scheme exposes the essential ingredients of the CPC algorithm scheme which are independent from the syntacic surface. This insight is a sufficient basis to transfer the CPC algorithm scheme to other formalisms. In mathematics on the metalevel only product types have been used so far. But, in recently used higher order formalisms the function type came additionally into use.

There are serious reasons to use also other types on the metalevels of formal systems. Those types could be lists or trees for instance. Since the above described decomposition properties are probably satisfied for all those type constructions which can be formalized as parameterized abstract data types without equations effecting the constructors, in the generalisation of the CPC algorithm scheme one has to focus the attention only on the pullback construction in the resulting category of types and terms.