On the Relation of Interaction Semantics to Continuations and Defunctionalization

In game semantics and related approaches to programming language semantics, programs are modelled by interaction dialogues. Such models have recently been used in the design of new compilation methods, e.g. for hardware synthesis or for programming with sublinear space. This paper relates such semantically motivated non-standard compilation methods to more standard techniques in the compilation of functional programming languages, namely continuation passing and defunctionalization. We first show for the linear {\lambda}-calculus that interpretation in a model of computation by interaction can be described as a call-by-name CPS-translation followed by a defunctionalization procedure that takes into account control-flow information. We then establish a relation between these two compilation methods for the simply-typed {\lambda}-calculus and end by considering recursion

Type-Based Termination, Inflationary Fixed-Points, and Mixed Inductive-Coinductive Types

Type systems certify program properties in a compositional way. From a bigger program one can abstract out a part and certify the properties of the resulting abstract program by just using the type of the part that was abstracted away. Termination and productivity are non-trivial yet desired program properties, and several type systems have been put forward that guarantee termination, compositionally. These type systems are intimately connected to the definition of least and greatest fixed-points by ordinal iteration. While most type systems use conventional iteration, we consider inflationary iteration in this article. We demonstrate how this leads to a more principled type system, with recursion based on well-founded induction. The type system has a prototypical implementation, MiniAgda, and we show in particular how it certifies productivity of corecursive and mixed recursive-corecursive functions.Comment: In Proceedings FICS 2012, arXiv:1202.317

Compositional Reasoning for Explicit Resource Management in Channel-Based Concurrency

We define a pi-calculus variant with a costed semantics where channels are treated as resources that must explicitly be allocated before they are used and can be deallocated when no longer required. We use a substructural type system tracking permission transfer to construct coinductive proof techniques for comparing behaviour and resource usage efficiency of concurrent processes. We establish full abstraction results between our coinductive definitions and a contextual behavioural preorder describing a notion of process efficiency w.r.t. its management of resources. We also justify these definitions and respective proof techniques through numerous examples and a case study comparing two concurrent implementations of an extensible buffer.Comment: 51 pages, 7 figure

FunTAL: Reasonably Mixing a Functional Language with Assembly

We present FunTAL, the first multi-language system to formalize safe interoperability between a high-level functional language and low-level assembly code while supporting compositional reasoning about the mix. A central challenge in developing such a multi-language is bridging the gap between assembly, which is staged into jumps to continuations, and high-level code, where subterms return a result. We present a compositional stack-based typed assembly language that supports components, comprised of one or more basic blocks, that may be embedded in high-level contexts. We also present a logical relation for FunTAL that supports reasoning about equivalence of high-level components and their assembly replacements, mixed-language programs with callbacks between languages, and assembly components comprised of different numbers of basic blocks.Comment: 15 pages; implementation at https://dbp.io/artifacts/funtal/; published in PLDI '17, Proceedings of the 38th ACM SIGPLAN Conference on Programming Language Design and Implementation, June 18 - 23, 2017, Barcelona, Spai

Work Analysis with Resource-Aware Session Types

While there exist several successful techniques for supporting programmers in deriving static resource bounds for sequential code, analyzing the resource usage of message-passing concurrent processes poses additional challenges. To meet these challenges, this article presents an analysis for statically deriving worst-case bounds on the total work performed by message-passing processes. To decompose interacting processes into components that can be analyzed in isolation, the analysis is based on novel resource-aware session types, which describe protocols and resource contracts for inter-process communication. A key innovation is that both messages and processes carry potential to share and amortize cost while communicating. To symbolically express resource usage in a setting without static data structures and intrinsic sizes, resource contracts describe bounds that are functions of interactions between processes. Resource-aware session types combine standard binary session types and type-based amortized resource analysis in a linear type system. This type system is formulated for a core session-type calculus of the language SILL and proved sound with respect to a multiset-based operational cost semantics that tracks the total number of messages that are exchanged in a system. The effectiveness of the analysis is demonstrated by analyzing standard examples from amortized analysis and the literature on session types and by a comparative performance analysis of different concurrent programs implementing the same interface.Comment: 25 pages, 2 pages of references, 11 pages of appendix, Accepted at LICS 201

On Role Logic

We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of first-order logic in lambda calculus, and a simple rule for implicit arguments of unary and binary predicates. The unrestricted version of role logic has the expressive power of first-order logic with transitive closure. Using a syntactic restriction on role logic formulas, we identify a natural fragment RL^2 of role logic. We show that the RL^2 fragment has the same expressive power as two-variable logic with counting C^2 and is therefore decidable. We present a translation of an imperative language into the decidable fragment RL^2, which allows compositional verification of programs that manipulate relational structures. In addition, we show how RL^2 encodes boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor

Ontology and Formal Semantics - Integration Overdue

In this note we suggest that difficulties encountered in natural language semantics are, for the most part, due to the use of mere symbol manipulation systems that are devoid of any content. In such systems, where there is hardly any link with our common-sense view of the world, and it is quite difficult to envision how one can formally account for the considerable amount of content that is often implicit, but almost never explicitly stated in our everyday discourse. \ud The solution, in our opinion, is a compositional semantics grounded in an ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. In the compositional logic we envision there are ontological (or first-intension) concepts, and logical (or second-intension) concepts, and where the ontological concepts include not only Davidsonian events, but other abstract objects as well (e.g., states, processes, properties, activities, attributes, etc.) \ud It will be demonstrated here that in such a framework, a number of challenges in the semantics of natural language (e.g., metonymy, intensionality, metaphor, etc.) can be properly and uniformly addressed.\u