Combining algebraic effects with continuations. Festschrift for John Reynolds' 70th birthday

We consider the natural combinations of algebraic computational effects such as side-effects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor extend, with effort, to include commonly used combinations of the various algebraic effects with continuations. Continuations also give rise to a third sort of combination, that given by applying the continuations monad transformer to an algebraic effect. We investigate the extent to which sum and tensor extend from algebraic effects to arbitrary monads, and the extent to which Felleisen et al.’s C operator extends from continuations to its combination with algebraic effects. To do all this, we use Dubuc’s characterisation of strong monads in terms of enriched large Lawvere theories

Resource-Tracking Concurrent Games

International audienceWe present a framework for game semantics based on concurrentgames, that keeps track of resources as data modified throughoutexecution but not affecting its control flow. Our leading exampleis time, yet the construction is in fact parametrized by aresource bimonoid R, an algebraic structure expressing resourcesand the effect of their consumption either sequentially or inparallel. Relying on our construction, we give a soundresource-sensitive denotation to R-IPA, an affine higher-orderconcurrent programming language with shared state and a primitivefor resource consumption in R. Compared with general operationalsemantics parametrized by R, our resource analysis turns out tobe finer, leading to non-adequacy. Yet, our model is notdegenerate as adequacy holds for an operational semanticsspecialized to time.In regard to earlier semantic frameworks for tracking resources,the main novelty of our work is that it is based on anon-interleaving semantics, and as such accounts for parallel useof resources accurately

A Dialectica-Like Interpretation of a Linear MSO on Infinite Words

We devise a variant of Dialectica interpretation of intuitionistic linear logic for Open image in new window, a linear logic-based version MSO over infinite words. Open image in new window was known to be correct and complete w.r.t. Church’s synthesis, thanks to an automata-based realizability model. Invoking Büchi-Landweber Theorem and building on a complete axiomatization of MSO on infinite words, our interpretation provides us with a syntactic approach, without any further construction of automata on infinite words. Via Dialectica, as linear negation directly corresponds to switching players in games, we furthermore obtain a complete logic: either a closed formula or its linear negation is provable. This completely axiomatizes the theory of the realizability model of Open image in new window. Besides, this shows that in principle, one can solve Church’s synthesis for a given ∀∃ -formula by only looking for proofs of either that formula or its linear negation

A Trace Semantics for System F Parametric Polymorphism

International audienc