Work Analysis with Resource-Aware Session Types

Abstract

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. arXiv:1712.08310v2 [cs.PL] 27 Apr 2018components that can be analyzed in isolation. After all, the resource usage of each component crucially depends on its interactions with the world.In this paper, we study the foundations of worst-case resource analysis for message-passing processes. A key idea of our approach is to rely on resourceaware session types to describe structure, protocols, and resource bounds for inter-process communication that we can use to perform a compositional and precise amortized analysis. Session types [32,33,12,13,45] prescribe bidirectional communication protocols for message-passing processes. Binary session types govern the interaction of two processes along a single channel, prescribing complementary send and receive actions for the processes at the two endpoints of a channel. We use such protocols as the basis of resource usage contracts that not only specify the type but also the potential of a message that is sent along a channel. The potential (in the sense of classic amortized analysis [43]) may be spent sending other messages as part of the network of interacting processes, or maintained locally for future interactions. Resource analysis is static, using the type system, and the runtime behavior of programs is not affected.

A Calculus for Modeling Floating Authorizations

“…is also not typable since a contextual authorization is expected for name exam. Notice this configuration leads to an error like the one shown in (5). However process !(license)license?x.…”

Types for Complexity of Parallel Computation in Pi-Calculus

“…It is not clear to us if everything can be adapted to reason only about our parallel complexity, but we plan to study it in future work. More recently Das et al in [9,10] proposed a type system with temporal session types to capture several parallel cost models with the use of a tick constructor. Our usage of time was inspired by their types with the usual next modality of temporal logic, but in this paper they also use the always and eventually modalities to gain expressivity.…”

“…We use for that π-calculus, a process calculus which provides process creation, channel name creation and name-passing in communication. An alternative approach could be to use a language described with session types, as in [9,10]. We will discuss the expressivity for both languages in Section 4.2.…”

Verified Linear Session-Typed Concurrent Programming

“…This comes down to deciding certain chains of linear inequalities. For readers familiar with ergometric types [10], we show how we can bound the number of reductions using an amortized analysis of work. For this, we assign 1 erg (unit of potential) to each λexpression.…”

“…All examples in this paper have been type-checked and executed in Rast and are publicly available [27]. Due to space constraints, there is an important aspect of Rast that we do not cover in this paper: it provides ergometric [10] and temporal [9] types to measure and verify (amortized) work and span of concurrently executing session-typed programs. The abovecited prior works manually compute and check complexity bounds at an informal metalevel.…”