We seek a unified account of modularity for computational effects. We begin by reformulating Moggi’s monadic paradigm for modelling computational effects using the notion of enriched Lawvere theory, together with its relationship with strong monads; this emphasises the importance of the operations that produce the effects. Effects qua theories are then combined by appropriate bifunctors on the ...

Object-oriented frameworks are often based on `skeleton' methods that determine the overall control ow and that carry around `contextual information'. Changing the signature of a skeleton method often induces a combinatorial explosion of changes to other methods spread over the di erent classes of the framework. Our work materialises these skeleton methods as that carry around monadic informati...

Courcelle, B., The monadic second-order logic of graphs V: on closing the gap between definability and recognizability, Theoretical Computer Science 80 (1991) 153-202. Context-free graph-grammars are considered such that, in every generated graph (3, a derivation tree of G can be constructed by means of monadic second-order formulas that specify its nodes, its labels, the successors of a node e...

We expose a strict hierarchy within monotone monadic strict NP without inequalities (MMSNP), based on the number of second-order monadic quantifiers. We do this by studying a finer strict hierarchy within a class of forbidden patterns problems (FPP), based on the number of permitted colours. Through an adaptation of a preservation theorem of Feder and Vardi, we are able to prove that this stric...

The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the logical viewpoint, we provide Equational Metalogic as a general formal deductive system for the derivability of equational consequences. Relating the two, a canonical model theory for Monadic Equational S...