Unguarded Recursion on Coinductive Resumptions

We study a model of side-effecting processes obtained by starting from a monad modelling base effects and adjoining free operations using a cofree coalgebra construction; one thus arrives at what one may think of as types of non-wellfounded side-effecting trees, generalizing the infinite resumption monad. Correspondingly, the arising monad transformer has been termed the coinductive generalized resumption transformer. Monads of this kind have received some attention in the recent literature; in particular, it has been shown that they admit guarded iteration. Here, we show that they also admit unguarded iteration, i.e. form complete Elgot monads, provided that the underlying base effect supports unguarded iteration. Moreover, we provide a universal characterization of the coinductive resumption monad transformer in terms of coproducts of complete Elgot monads.Comment: 47 pages, extended version of http://www.sciencedirect.com/science/article/pii/S157106611500079

Interaction and observation, categorically

This paper proposes to use dialgebras to specify the semantics of interactive systems in a natural way. Dialgebras are a conservative extension of coalgebras. In this categorical model, from the point of view that we provide, the notions of observation and interaction are separate features. This is useful, for example, in the specification of process equivalences, which are obtained as kernels of the homomorphisms of dialgebras. As an example we present the asynchronous semantics of the CCS.Comment: In Proceedings ICE 2011, arXiv:1108.014

Coinductive Big-Step Semantics for Concurrency

In a paper presented at SOS 2010, we developed a framework for big-step semantics for interactive input-output in combination with divergence, based on coinductive and mixed inductive-coinductive notions of resumptions, evaluation and termination-sensitive weak bisimilarity. In contrast to standard inductively defined big-step semantics, this framework handles divergence properly; in particular, runs that produce some observable effects and then diverge, are not "lost". Here we scale this approach for shared-variable concurrency on a simple example language. We develop the metatheory of our semantics in a constructive logic.Comment: In Proceedings PLACES 2013, arXiv:1312.221

Programming Languages and Systems

This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019

Polarized substructural session types

Concurrent processes can be extremely difficult to reason about, both for programmers and formally. One approach to coping with this difficulty is to study new programming languages and type features such as Session Types. Session types take as their conceptual notion of concurrency as a collection of processes linked together via channels and provide type-level coordination between processes using these channels. Logically motivated programming languages exploit the idea that providing a proof of a theorem in a logic is similar to proving that a given term has a particular type in a programming language and vice versa. These connections can be interesting for a few different reasons. First, when language and logic are independently discovered and independently useful, the existence of a connection suggests that both are onto some fundamentally important idea. Additionally, a connection provides a basis both for sanity checking our ideas and also can be fruitful grounds for inspiration by seeing how variants of either the logic or the language are reflected through the connection. This thesis primarily describes an exploration of logically motivated session types, SILL. Polarization, classifying propositions as either positive or negative, provides a natural way to describe a logically based session typing language with asynchronous communication while retaining a semantics that is reasonably implementable. Additionally, polarization gives us a way to smoothly integrate synchronous channels into SILL without needing a semantic extension. When combined with Adjoint Logic, this gives us an ability to incorporate a variety of modalities with relatively little work. From a practical perspective, this gives SILL access to persistent processes and garbage collection. We additionally explore a trio of loosely related extensions to SILL, and their logical connections, inspired by the above results: bundled message passing to reduce the number of communications performed by processes; racy programs, enabled by a select/epoll-like mechanism; and asynchronous receiving, an almost generalization of the basic asynchronous semantics. We have three different implementations of SILL: a simple but relatively full featured interpreter written in OCaml; a fragment of SILL as an embedded domain specific language in Haskell; and a cleaner version of the same in Idris. Lastly, we show that Liquid Types and Session Types are compatible. This gives us one notion of a dependently session typed language

Monads with merging

Monoids are one of the simplest theories in which we can compose elements of a set. Similarly, monads have been used extensively to treat composition of effectful code and its denotational semantics. During the last forty years the theory of monoids has been extended with diverse merge-like operators. In this article, we replicate several of these extensions at the level of monads. Building on a well-known relation between monads and monoids, we introduce monads with additional structure that account for merging. We show how monads with merging generalise and relate to models for well-known algebraic theories for concurrency such as classic process algebras and the more recent concurrent monoids. With these results, we aim to facilitate the generalisation and comparison of different approaches to concurrency

Executable Denotational Semantics With Interaction Trees

Interaction trees are a representation of effectful and reactive systemsdesigned to be implemented in a proof assistant such as Coq. They are equipped with a rich algebra of combinators to construct recursive and effectful computations and to reason about them equationally. Interaction trees are also an executable structure, notably via extraction, which enables testing and directly developing executable programs in Coq. To demonstrate the usefulness of interaction trees, two applications are presented. First, I develop a novel approach to verify a compiler from a simple imperative language to assembly, by proving a semantic preservation theorem which is termination-sensitive, using an equational proof. Second, I present a framework of concurrent objects, inheriting the modularity, compositionality, and executability of interaction trees. Leveraging that framework, I formally prove the correctness of a transactionally predicated map, using a novel approach to reason about objects combining the notions of linearizability and strict serializability, two well-known correctness conditions for concurrent objects

A functional specification of effects

This dissertation is about effects and type theory. Functional programming languages such as Haskell illustrate how to encapsulate side effects using monads. Haskell compilers provide a handful of primitive effectful functions. Programmers can construct larger computations using the monadic return and bind operations. These primitive effectful functions, however, have no associated definition. At best, their semantics are specified separately on paper. This can make it difficult to test, debug, verify, or even predict the behaviour of effectful computations. This dissertation provides pure, functional specifications in Haskell of several different effects. Using these specifications, programmers can test and debug effectful programs. This is particularly useful in tandem with automatic testing tools such as QuickCheck. The specifications in Haskell are not total. This makes them unsuitable for the formal verification of effectful functions. This dissertation overcomes this limitation, by presenting total functional specifications in Agda, a programming language with dependent types. There have been alternative approaches to incorporating effects in a dependently typed programming language. Most notably, recent work on Hoare Type Theory proposes to extend type theory with axioms that postulate the existence of primitive effectful functions. This dissertation shows how the functional specifications implement these axioms, unifying the two approaches. The results presented in this dissertation may be used to write and verify effectful programs in the framework of type theory