Introducing a Calculus of Effects and Handlers for Natural Language Semantics

In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the same pattern: they are instances of a monad. In this paper, we present an extension of the simply-typed lambda calculus that exploits this uniformity using the recently discovered technique of effect handlers. We prove that our calculus exhibits some of the key formal properties of the lambda calculus and we use it to construct a modular semantics for a small fragment that involves multiple distinct semantic phenomena

On Asynchronous Session Semantics

This paper studies a behavioural theory of the π-calculus with session types under the fundamental principles of the practice of distributed computing — asynchronous communication which is order-preserving inside each connection (session), augmented with asynchronous inspection of events (message arrivals). A new theory of bisimulations is introduced, distinct from either standard asynchronous or synchronous bisimilarity, accurately capturing the semantic nature of session-based asynchronously communicating processes augmented with event primitives. The bisimilarity coincides with the reduction-closed barbed congruence. We examine its properties and compare them with existing semantics. Using the behavioural theory, we verify that the program transformation of multithreaded into event-driven session based processes, using Lauer-Needham duality, is type and semantic preserving

Enhancing Semantic Bidirectionalization via Shape Bidirectionalizer Plug-ins

Matsuda et al. (2007) and Voigtlander (2009) have introduced two techniques that given a source-to-view function provide an update propagation function mapping an original source and an updated view back to an updated source, subject to standard consistency conditions. Previously, we developed a synthesis of the two techniques, based on a separation of shape and content aspects (Voigtlander et al. 2010). Here, we carry that idea further, reworking the technique of Voigtlander such that any shape bidirectionalizer (based on the work of Matsuda et al. or not) can be used as a plug-in, to good effect. We also provide a data-type-generic account, enabling wider reuse, including the use of pluggable bidirectionalization itself as a plug-in

Complexity of Grammar Induction for Quantum Types

Most categorical models of meaning use a functor from the syntactic category to the semantic category. When semantic information is available, the problem of grammar induction can therefore be defined as finding preimages of the semantic types under this forgetful functor, lifting the information flow from the semantic level to a valid reduction at the syntactic level. We study the complexity of grammar induction, and show that for a variety of type systems, including pivotal and compact closed categories, the grammar induction problem is NP-complete. Our approach could be extended to linguistic type systems such as autonomous or bi-closed categories.Comment: In Proceedings QPL 2014, arXiv:1412.810

Towards a Step Semantics for Story-Driven Modelling

Graph Transformation (GraTra) provides a formal, declarative means of specifying model transformation. In practice, GraTra rule applications are often programmed via an additional language with which the order of rule applications can be suitably controlled. Story-Driven Modelling (SDM) is a dialect of programmed GraTra, originally developed as part of the Fujaba CASE tool suite. Using an intuitive, UML-inspired visual syntax, SDM provides usual imperative control flow constructs such as sequences, conditionals and loops that are fairly simple, but whose interaction with individual GraTra rules is nonetheless non-trivial. In this paper, we present the first results of our ongoing work towards providing a formal step semantics for SDM, which focuses on the execution of an SDM specification.Comment: In Proceedings GaM 2016, arXiv:1612.0105