Well-behaved translations between structural operational semantics

We examine two versions of maps between distributive laws as candidates for wellbehaved translations between structural operational semantics, and validate that by using simple coalgebraic arguments. We give some concrete examples of wellbehaved translations that are maps between distributive laws. The modelling of structural operational semantics uses Turi and Plotkin's categorical models of GSOS. These maps between distributive laws come from the previous work on 2-categories of distributive laws.

Presenting Morphisms of Distributive Laws

A format for well-behaved translations between structural operational specifications is derived from a notion of distributive law morphism, previously studied by Power and Watanabe

Presenting Distributive Laws

Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when T is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of context-free languages

On the Expressive Power of User-Defined Effects: Effect Handlers, Monadic Reflection, Delimited Control

We compare the expressive power of three programming abstractions for user-defined computational effects: Bauer and Pretnar's effect handlers, Filinski's monadic reflection, and delimited control without answer-type-modification. This comparison allows a precise discussion about the relative expressiveness of each programming abstraction. It also demonstrates the sensitivity of the relative expressiveness of user-defined effects to seemingly orthogonal language features. We present three calculi, one per abstraction, extending Levy's call-by-push-value. For each calculus, we present syntax, operational semantics, a natural type-and-effect system, and, for effect handlers and monadic reflection, a set-theoretic denotational semantics. We establish their basic meta-theoretic properties: safety, termination, and, where applicable, soundness and adequacy. Using Felleisen's notion of a macro translation, we show that these abstractions can macro-express each other, and show which translations preserve typeability. We use the adequate finitary set-theoretic denotational semantics for the monadic calculus to show that effect handlers cannot be macro-expressed while preserving typeability either by monadic reflection or by delimited control. We supplement our development with a mechanised Abella formalisation

Classical logic, continuation semantics and abstract machines

One of the goals of this paper is to demonstrate that denotational semantics is useful for operational issues like implementation of functional languages by abstract machines. This is exemplified in a tutorial way by studying the case of extensional untyped call-by-name λ-calculus with Felleisen's control operator 𝒞. We derive the transition rules for an abstract machine from a continuation semantics which appears as a generalization of the ¬¬-translation known from logic. The resulting abstract machine appears as an extension of Krivine's machine implementing head reduction. Though the result, namely Krivine's machine, is well known our method of deriving it from continuation semantics is new and applicable to other languages (as e.g. call-by-value variants). Further new results are that Scott's D∞-models are all instances of continuation models. Moreover, we extend our continuation semantics to Parigot's λμ-calculus from which we derive an extension of Krivine's machine for λμ-calculus. The relation between continuation semantics and the abstract machines is made precise by proving computational adequacy results employing an elegant method introduced by Pitts

Reactive Systems over Cospans

The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of well-behaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need to be constructed separately within each model. In this paper, we offer a general construction of such bicolimits in a class of bicategories of cospans. The construction sheds light on as well as extends Ehrig and Konig’s rewriting via borrowed contexts and opens the way to a unified treatment of several applications

Connector algebras for C/E and P/T nets interactions

A quite fourishing research thread in the recent literature on component based system is concerned with the algebraic properties of different classes of connectors. In a recent paper, an algebra of stateless connectors was presented that consists of five kinds of basic connectors, namely symmetry, synchronization, mutual exclusion, hiding and inaction, plus their duals and it was shown how they can be freely composed in series and in parallel to model sophisticated "glues". In this paper we explore the expressiveness of stateful connectors obtained by adding one-place buffers or unbounded buffers to the stateless connectors. The main results are: i) we show how different classes of connectors exactly correspond to suitable classes of Petri nets equipped with compositional interfaces, called nets with boundaries; ii) we show that the difference between strong and weak semantics in stateful connectors is reflected in the semantics of nets with boundaries by moving from the classic step semantics (strong case) to a novel banking semantics (weak case), where a step can be executed by taking some "debit" tokens to be given back during the same step; iii) we show that the corresponding bisimilarities are congruences (w.r.t. composition of connectors in series and in parallel); iv) we show that suitable monoidality laws, like those arising when representing stateful connectors in the tile model, can nicely capture concurrency aspects; and v) as a side result, we provide a basic algebra, with a finite set of symbols, out of which we can compose all P/T nets, fulfilling a long standing quest