Non-Deterministic Functions as Non-Deterministic Processes

We study encodings of the ?-calculus into the ?-calculus in the unexplored case of calculi with non-determinism and failures. On the sequential side, we consider ?^?_?, a new non-deterministic calculus in which intersection types control resources (terms); on the concurrent side, we consider ??, a ?-calculus in which non-determinism and failure rest upon a Curry-Howard correspondence between linear logic and session types. We present a typed encoding of ?^?_? into ?? and establish its correctness. Our encoding precisely explains the interplay of non-deterministic and fail-prone evaluation in ?^?_? via typed processes in ??. In particular, it shows how failures in sequential evaluation (absence/excess of resources) can be neatly codified as interaction protocols

Asynchronous Multiparty Session Type Implementability is Decidable - Lessons Learned from Message Sequence Charts

Multiparty session types (MSTs) provide efficient means to specify and verify asynchronous message-passing systems. For a global type, which specifies all interactions between roles in a system, the implementability problem asks whether there are local specifications for all roles such that their composition is deadlock-free and generates precisely the specified executions. Decidability of the implementability problem is an open question. We answer it positively for global types with sender-driven choice, which allow a sender to send to different receivers upon branching and a receiver to receive from different senders. To achieve this, we generalise results from the domain of high-level message sequence charts (HMSCs). This connection also allows us to comprehensively investigate how HMSC techniques can be adapted to the MST setting. This comprises techniques to make the problem algorithmically more tractable as well as a variant of implementability that may open new design space for MSTs. Inspired by potential performance benefits, we introduce a generalisation of the implementability problem that we, unfortunately, prove to be undecidable

Generalising Projection in Asynchronous Multiparty Session Types

Multiparty session types (MSTs) provide an efficient methodology for specifying and verifying message passing software systems. In the theory of MSTs, a global type specifies the interaction among the roles at the global level. A local specification for each role is generated by projecting from the global type on to the message exchanges it participates in. Whenever a global type can be projected on to each role, the composition of the projections is deadlock free and has exactly the behaviours specified by the global type. The key to the usability of MSTs is the projection operation: a more expressive projection allows more systems to be type-checked but requires a more difficult soundness argument. In this paper, we generalise the standard projection operation in MSTs. This allows us to model and type-check many design patterns in distributed systems, such as load balancing, that are rejected by the standard projection. The key to the new projection is an analysis that tracks causality between messages. Our soundness proof uses novel graph-theoretic techniques from the theory of message-sequence charts. We demonstrate the efficacy of the new projection operation by showing many global types for common patterns that can be projected under our projection but not under the standard projection operation

Non-Deterministic Functions as Non-Deterministic Processes

We study encodings of the λ-calculus into the π-calculus in the unexplored case of calculi with non-determinism and failures. On the sequential side, we consider λ^↯_⊕, a new non-deterministic calculus in which intersection types control resources (terms); on the concurrent side, we consider sπ, a π-calculus in which non-determinism and failure rest upon a Curry-Howard correspondence between linear logic and session types. We present a typed encoding of λ^↯_⊕ into sπ and establish its correctness. Our encoding precisely explains the interplay of non-deterministic and fail-prone evaluation in λ^↯_⊕ via typed processes in sπ. In particular, it shows how failures in sequential evaluation (absence/excess of resources) can be neatly codified as interactio

Types and Semantics for Extensible Data Types (Extended Version)

Developing and maintaining software commonly requires (1) adding new data type constructors to existing applications, but also (2) adding new functions that work on existing data. Most programming languages have native support for defining data types and functions in a way that supports either (1) or (2), but not both. This lack of native support makes it difficult to use and extend libraries. A theoretically well-studied solution is to define data types and functions using initial algebra semantics. While it is possible to encode this solution in existing programming languages, such encodings add syntactic and interpretive overhead, and commonly fail to take advantage of the map and fold fusion laws of initial algebras which compilers could exploit to generate more efficient code. A solution to these is to provide native support for initial algebra semantics. In this paper, we develop such a solution and present a type discipline and core calculus for a language with native support for initial algebra semantics.Comment: Extended version (28 pages) of the eponymous paper to appear in the conference proceedings of APLAS 202

Learning Invariants using Decision Trees and Implication Counterexamples

Inductive invariants can be robustly synthesized using a learning model where the teacher is a program verifier who instructs the learner through concrete program configurations, classified as positive, negative, and implications. We propose the first learning algorithms in this model with implication counter-examples that are based on scalable machine learning techniques. In particular, we extend decision tree learning algorithms, building new scalable and heuristic ways to construct small decision trees using statistical measures that account for implication counterexamples. We implement the learners and an appropriate teacher, and show that they are scalable, efficient and convergent in synthesizing adequate inductive invariants in a suite of more than 50 programs.Ope

Pregrammars and Intersection Types

A representation of intersection types in terms of pregrammars is presented. Pregrammar based rewriting relations, corresponding respectively to type checking and inhabitation are defined and the latter is used to implement a Wajsberg/Ben-Yelles style alternating semi-decision algorithm for inhabitation. The usefulness of the framework is illustrated by revisiting and partially extending standard inhabitation related results for intersection types, as well as establishing new ones. It is shown how the notion of bounded multiset dimension emerges naturally and the relation between the two settings is clarified. A meaningful rank independent superset of the set of rank 2 types is identified for which EXPSPACE-completeness for inhabitation as well as for counting is proved. Finally, a standard result on negatively non-duplicated simple types is extended to intersection types