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

Polarized Substructural Session Types

Abstract. The deep connection between session-typed concurrency and linear logic is embodied in the language SILL that integrates functional and message-passing concurrent programming. The exacting nature of linear typing provides strong guarantees, such as global progress, absence of deadlock, and race freedom, but it also requires explicit resource man-agement by the programmer. This burden is alleviated in an affine type system where resources need not be used, relying on a simple form of garbage collection. In this paper we show how to effectively support both linear and affine typing in a single language, in addition to the already present unre-stricted (intuitionistic) types. The approach, based on Benton’s adjoint construction, suggests that the usual distinction between synchronous and asynchronous communication can be viewed through the lens of modal logic. We show how polarizing the propositions into positive and negative connectives allows us to elegantly express synchronization in the type instead of encoding it by extra-logical means.

Benefits of Session Types for software Development

Session types are a formalism used to specify and check the correctness of communication based systems. Within their scope, they can guarantee the absence of communication errors such as deadlock, sending an unexpected message or failing to handle an incoming message. Introduced over two decades ago, they have developed into a significant theme in programming languages. In this paper we examine the beliefs that drive research into this area and make it popular. We look at the claims and motivation behind session types throughout the literature. We identify the hypotheses upon which session types have been designed and implemented, and attempt to clarify and formulate them in a more suitable manner for testing

Linear/non-Linear Types For Embedded Domain-Specific Languages

Domain-specific languages are often embedded inside of general-purpose host languages so that the embedded language can take advantage of host-language data structures, libraries, and tools. However, when the domain-specific language uses linear types, existing techniques for embedded languages fall short. Linear type systems, which have applications in a wide variety of programming domains including mutable state, I/O, concurrency, and quantum computing, can manipulate embedded non-linear data via the linear type !σ. However, prior work has not been able to produce linear embedded languages that have full and easy access to host-language data, libraries, and tools. This dissertation proposes a new perspective on linear, embedded, domain-specific languages derived from the linear/non-linear (LNL) interpretation of linear logic. The LNL model consists of two distinct fragments---one with linear types and another with non-linear types---and provides a simple categorical interface between the two. This dissertation identifies the linear fragment with the linear embedded language and the non-linear fragment with the general-purpose host language. The effectiveness of this framework is illustrated via a number of examples, implemented in a variety of host languages. In Haskell, linear domain-specific languages using mutable state and concurrency can take advantage of the monad that arises from the LNL model. In Coq, the QWIRE quantum circuit language uses linearity to enforce the no-cloning axiom of quantum mechanics. In homotopy type theory, quantum transformations can be encoded as higher inductive types to simplify the presentation of a quantum equational theory. These examples serve as case studies that prove linear/non-linear type theory is a natural and expressive interface in which to embed linear domain-specific languages

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