Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold operator on the product comonad. Both versions capture functions that require extra arguments for their computation and are related with the notion of strong datatype. 1 Introduction One of the main features of recursive operators derivable from datatype definitions is that they impose a structure upon programs which can be exploited for program transformation. Recursive operators structure functional programs according to the data structures they traverse or generate and come equipped with a battery of algebraic laws, also derivable from type definitions, which are used in program calculations [24, 11, 5, 15]. Some of these laws, the so-called fusion laws, are particularly interesting in p...

Abstract. A wide variety of models for concurrent programs has been proposed during the past decades, each one focusing on various aspects of computations: trace equivalence, causality between events, conflicts and schedules due to resource accesses, etc. More recently, models with a geometrical flavor have been introduced, based on the notion of cubical set. These models are very rich and expressive since they can represent commutation between any number of events, thus generalizing the principle of true concurrency. While they seem to be very promising – because they make possible the use of techniques from algebraic topology in order to study concurrent computations – they have not yet been precisely related to the previous models, and the purpose of this paper is to fill this gap. In particular, we describe an adjunction between Petri nets and cubical sets which extends the previously known adjunction between Petri nets and asynchronous transition systems by Nielsen and Winskel. 1 1