scholarly journals Linear type theory for asynchronous session types

2009 ◽  
Vol 20 (1) ◽  
pp. 19-50 ◽  
Author(s):  
SIMON J. GAY ◽  
VASCO T. VASCONCELOS
Keyword(s):  
Type Theory ◽  
Business Processes ◽  
Operational Semantics ◽  
Synchronous Communication ◽  
Linear Type ◽  
Session Types ◽  
Secure Foundation ◽  
Linear Types ◽  
Session Type ◽  
Functional Setting

AbstractSession types support a type-theoretic formulation of structured patterns of communication, so that the communication behaviour of agents in a distributed system can be verified by static typechecking. Applications include network protocols, business processes and operating system services. In this paper we define a multithreaded functional language with session types, which unifies, simplifies and extends previous work. There are four main contributions. First is an operational semantics with buffered channels, instead of the synchronous communication of previous work. Second, we prove that the session type of a channel gives an upper bound on the necessary size of the buffer. Third, session types are manipulated by means of the standard structures of a linear type theory, rather than by means of new forms of typing judgement. Fourth, a notion of subtyping, including the standard subtyping relation for session types (imported into the functional setting), and a novel form of subtyping between standard and linear function types, which allows the typechecker to handle linear types conveniently. Our new approach significantly simplifies session types in the functional setting, clarifies their essential features and provides a secure foundation for language developments such as polymorphism and object-orientation.

scholarly journals Gradual session types

2019 ◽  
Vol 29 ◽  
Author(s):  
ATSUSHI IGARASHI ◽  
PETER THIEMANN ◽  
YUYA TSUDA ◽  
VASCO T. VASCONCELOS ◽  
PHILIP WADLER
Keyword(s):  
Operational Semantics ◽  
Type System ◽  
Type Systems ◽  
Session Types ◽  
Novel Approach ◽  
Seamless Transition ◽  
Linear Types ◽  
Gradual Typing ◽  
Session Type ◽  
Dynamic Typing

Abstract Session types are a rich type discipline, based on linear types, that lifts the sort of safety claims that come with type systems to communications. However, web-based applications and microservices are often written in a mix of languages, with type disciplines in a spectrum between static and dynamic typing. Gradual session types address this mixed setting by providing a framework which grants seamless transition between statically typed handling of sessions and any required degree of dynamic typing. We propose Gradual GV as a gradually typed extension of the functional session type system GV. Following a standard framework of gradual typing, Gradual GV consists of an external language, which relaxes the type system of GV using dynamic types; an internal language with casts, for which operational semantics is given; and a cast-insertion translation from the former to the latter. We demonstrate type and communication safety as well as blame safety, thus extending previous results to functional languages with session-based communication. The interplay of linearity and dynamic types requires a novel approach to specifying the dynamics of the language.

Service Discovery and Composition Based on Contracts and Choreographic Descriptions

2012 ◽  
pp. 60-88
Author(s):  
Mario Bravetti ◽  
Gianluigi Zavattaro
Keyword(s):  
Service Discovery ◽  
Operational Semantics ◽  
Asynchronous Communication ◽  
Synchronous Communication ◽  
Transition Systems ◽  
Service Contracts ◽  
Contract Compliance ◽  
Service Oriented ◽  
Labeled Transition System ◽  
Contract Language

The authors discuss the interplay between the notions of contract compliance, contract refinement, and choreography conformance in the context of service oriented computing, by considering both synchronous and asynchronous communication. Service contracts are specified in a language independent way by means of finite labeled transition systems. In this way, the theory is general and foundational as the authors abstract away from the syntax of contracts and simply assume that a contract language has an operational semantics defined in terms of a labeled transition system. The chapter makes a comparative analysis of synchronous and asynchronous communication. Concerning the latter, a realistic scenario is considered in which services are endowed with queues used to store the received messages. In the simpler context of synchronous communication, the authors are able to resort to the theory of fair testing to provide decidability results.

A simple library implementation of binary sessions

2016 ◽  
Vol 27 ◽  
Author(s):  
LUCA PADOVANI
Keyword(s):  
Programming Language ◽  
Protocol Analysis ◽  
Simple Approach ◽  
Type Inference ◽  
Hybrid Form ◽  
Type Checking ◽  
Session Types ◽  
Parametric Polymorphism ◽  
Session Type

AbstractInspired by the continuation-passing encoding of binary sessions, we describe a simple approach to embed a hybrid form of session type checking into any programming language that supports parametric polymorphism. The approach combines static protocol analysis with dynamic linearity checks. To demonstrate the effectiveness of the technique, we implement a well-integrated OCaml module for session communications. For free, OCaml provides us with equirecursive session types, parametric behavioural polymorphism, complete session type inference, and session subtyping.

scholarly journals Some Lambda Calculus and Type Theory Formalized

1997 ◽  
Vol 4 (51) ◽  
Author(s):  
James McKinna ◽  
Robert Pollack
Keyword(s):  
Type Theory ◽  
Operational Semantics ◽  
Lambda Calculus ◽  
Type Systems ◽  
Formal Proof ◽  
Type Checking ◽  
Formal Development ◽  
Formal Definitions ◽  
Pure Type Systems ◽  
System F

"This paper is about our hobby." That is the first sentence of [MP93], the first report on our formal development of lambda calculus and type theory, written in autumn 1992. We have continued to pursue this hobby on and off ever since, and have developed a substantial body of formal knowledge, including Church-Rosser and standardization<br />theorems for beta reduction, and the basic theory of<br />Pure Type Systems (PTS) leading to the strengthening theorem and type checking algorithms for PTS. Some of this work is reported in [MP93, vBJMP94, Pol94b, Pol95]. In the present paper we survey this work, including some new proofs, and point out what we feel has been learned about the general issues of formalizing mathematics. On the technical side, we describe an abstract, and simplified, proof of standardization for beta reduction, not previously published, that does<br />not mention redex positions or residuals. On the general issues, we emphasize the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts. The LEGO Proof Development System [LP92] was used to check the work in an implementation of the Extended Calculus of Constructions<br />(ECC) with inductive types [Luo94]. LEGO is a refinement style<br />proof checker, publicly available by ftp and WWW, with a User's Manual [LP92] and a large collection of examples. Section 1.3 contains information on accessing the formal development described in this paper. Other interesting examples formalized in LEGO include program specification and data refinement [Luo91], strong normalization of System F [Alt93], synthetic domain theory [Reu95, Reu96], and operational semantics for imperative programs [Sch97].

scholarly journals Contextual modal types for algebraic effects and handlers

2021 ◽  
Vol 5 (ICFP) ◽  
pp. 1-29
Author(s):  
Nikita Zyuzin ◽  
Aleksandar Nanevski
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Operational Semantics ◽  
Algebraic Theory ◽  
Type System ◽  
Effect Theory ◽  
Explicit Substitutions ◽  
Type And Effect Systems ◽  
Modal Type ◽  
Modal Types

Programming languages with algebraic effects often track the computations’ effects using type-and-effect systems. In this paper, we propose to view an algebraic effect theory of a computation as a variable context; consequently, we propose to track algebraic effects of a computation with contextual modal types . We develop ECMTT, a novel calculus which tracks algebraic effects by a contextualized variant of the modal □ (necessity) operator, that it inherits from Contextual Modal Type Theory (CMTT). Whereas type-and-effect systems add effect annotations on top of a prior programming language, the effect annotations in ECMTT are inherent to the language, as they are managed by programming constructs corresponding to the logical introduction and elimination forms for the □ modality. Thus, the type-and-effect system of ECMTT is actually just a type system. Our design obtains the properties of local soundness and completeness, and determines the operational semantics solely by β-reduction, as customary in other logic-based calculi. In this view, effect handlers arise naturally as a witness that one context (i.e., algebraic theory) can be reached from another, generalizing explicit substitutions from CMTT. To the best of our knowledge, ECMTT is the first system to relate algebraic effects to modal types. We also see it as a step towards providing a correspondence in the style of Curry and Howard that may transfer a number of results from the fields of modal logic and modal type theory to that of algebraic effects.

scholarly journals Modular Inference of Linear Types for Multiplicity-Annotated Arrows

2020 ◽  
pp. 456-483
Author(s):  
Kazutaka Matsuda
Keyword(s):  
Linear Code ◽  
Type System ◽  
Quantifier Elimination ◽  
Type Inference ◽  
Linear Type ◽  
Inference System ◽  
Technical Challenge ◽  
Non Linear ◽  
Linear Types ◽  
Higher Order Functions

AbstractBernardy et al. [2018] proposed a linear type system $$\lambda ^q_\rightarrow $$ λ → q as a core type system of Linear Haskell. In the system, linearity is represented by annotated arrow types $$A \rightarrow _m B$$ A → m B , where m denotes the multiplicity of the argument. Thanks to this representation, existing non-linear code typechecks as it is, and newly written linear code can be used with existing non-linear code in many cases. However, little is known about the type inference of $$\lambda ^q_\rightarrow $$ λ → q . Although the Linear Haskell implementation is equipped with type inference, its algorithm has not been formalized, and the implementation often fails to infer principal types, especially for higher-order functions. In this paper, based on OutsideIn(X) [Vytiniotis et al., 2011], we propose an inference system for a rank 1 qualified-typed variant of $$\lambda ^q_\rightarrow $$ λ → q , which infers principal types. A technical challenge in this new setting is to deal with ambiguous types inferred by naive qualified typing. We address this ambiguity issue through quantifier elimination and demonstrate the effectiveness of the approach with examples.

scholarly journals Lexical Semantics with Linear Types

10.29007/16s8 ◽  
2018 ◽  
Author(s):  
Bruno Mery
Keyword(s):  
Symbolic Computation ◽  
Type Theory ◽  
Semantic Analysis ◽  
Lexical Semantics ◽  
Higher Order ◽  
Order Linear ◽  
Integrated Framework ◽  
Linguistic Data ◽  
Linear Types ◽  
Lexical Data

We have proposed a framework based upon the λ -calculus with higher-order intuitionistic types for the symbolic computation of the semantic analysis, integrating lexical data. This proposal is sufficient for many phenomena and accurately incorporates lexical semantics by the means of type theory, but some issues linger in the linguistic data. In the present paper, we revisit this proposal with a version of the λ -calculus based upon higher-order linear types, that aims to resolve those issues and present an integrated framework for meaning assembly.

scholarly journals Session Coalgebras: A Coalgebraic View on Session Types and Communication Protocols

2021 ◽  
pp. 375-403
Author(s):  
Alex C. Keizer ◽  
Henning Basold ◽  
Jorge A. Pérez
Keyword(s):  
Communication Protocols ◽  
Type System ◽  
Type Systems ◽  
Software Systems ◽  
Compositional Techniques ◽  
Behavioural Type ◽  
Session Types ◽  
Session Type ◽  
Coalgebra Structure ◽  
Large Systems

AbstractCompositional methods are central to the development and verification of software systems. They allow breaking down large systems into smaller components, while enabling reasoning about the behaviour of the composed system. For concurrent and communicating systems, compositional techniques based on behavioural type systems have received much attention. By abstracting communication protocols as types, these type systems can statically check that programs interact with channels according to a certain protocol, whether the intended messages are exchanged in a certain order. In this paper, we put on our coalgebraic spectacles to investigate session types, a widely studied class of behavioural type systems. We provide a syntax-free description of session-based concurrency as states of coalgebras. As a result, we rediscover type equivalence, duality, and subtyping relations in terms of canonical coinductive presentations. In turn, this coinductive presentation makes it possible to elegantly derive a decidable type system with subtyping for $$\pi $$ π -calculus processes, in which the states of a coalgebra will serve as channel protocols. Going full circle, we exhibit a coalgebra structure on an existing session type system, and show that the relations and type system resulting from our coalgebraic perspective agree with the existing ones.

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