The standard operation refinement ordering is a kind of “meet of opposites”: non-determinism reduction suggests “smaller” behaviour while increase of definition suggests “larger” behaviour. Groves’ factorization of this ordering into two simpler relations, one per refinement concern, makes it more mathematically tractable but is far from fully exploited in the literature. We present a pointfree...

In this paper we present a unified study of functorial frame quasiuniformities by means of Weil entourages and frame congruences. In particular, we use the pointfree version of the Fletcher construction, introduced by the authors in a previous paper, to describe all functorial transitive quasi-uniformities.

We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism condition cannot be replaced by a single fixed-pointfree automorphism.

We describe an implementation of a pointfree proof of the Alaoglu and the Hahn-Banach theorems in Type Theory. The proofs described here are formalisations of the proofs presented in \The Hahn-Banach Theorem in Type Theory" 4]. The implementation was partially developed simultaneously with 4] and it was a help in the development of the informal proofs.

We explore a pointfree theory of bitopological spaces (that is, sets equipped with two topologies). In particular, here we regard finitary biframes as duals spaces. particular for biframe $$\mathcal {L}$$ the ordered collection all its bisubspaces (i.e. biquotients) is studied. It shown that this in three meaningful ways. it that, apart from assembly , there are other structures $$\mathsf {A}_{...

Genericity is a topic which is not sufficiently developed in state-based systems modelling, mainly due to a myriad of approaches and behaviour models which lack unification. This paper adopts coalgebra theory to propose a generic notion of a state-based software component, and an associated calculus, by quantifying over behavioural models specified as strong monads. This leads to the pointfree,...