A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems -- and of programming languages from a type-theoretic perspective -- has important applications in software engineering, language design, high-performance compilers, and security.This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material.The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.

https://www.seas.upenn.edu/~bcpierce/tapl/contents.pdf

Types and Programming Languages

We introduce the spi calculus, an extension of the pi calculus designed for describing and analyzing cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the spi calculus enables us to consider cryptographic issues in more detail. We represent protocols as processes in the spi calculus and state their security properties in terms of coarse-grained notions of protocol equivalence. ] 1999 Academic Press

/pdf/a-calculus-for-cryptographic-protocols-the-spi-calculus-3i1wvj2u10.pdf

A calculus for cryptographic protocols: the spi calculus

[서평]「Component Software」 - Beyond Object-Oriented Programming -

In this paper we introduce a variant of temporal logic tailored for specifying desired properties of continuous signals. The logic is based on a bounded subset of the real-time logic mitl, augmented with a static mapping from continuous domains into propositions. From formulae in this logic we create automatically property monitors that can check whether a given signal of bounded length and finite variability satisfies the property. A prototype implementation of this procedure was used to check properties of simulation traces generated by Matlab/Simulink.

/pdf/monitoring-temporal-properties-of-continuous-signals-4691an6o8x.pdf

Monitoring Temporal Properties of Continuous Signals

We study the interaction of the "new" construct with a rich but common form of (first-order) communication. This interaction is crucial in security protocols, which are the main motivating examples for our work; it also appears in other programming-language contexts. Specifically, we introduce a simple, general extension of the pi calculus with value passing, primitive functions, and equations among terms. We develop semantics and proof techniques for this extended language and apply them in reasoning about some security protocols.

/pdf/mobile-values-new-names-and-secure-communication-r85hn7w4ep.pdf

Mobile values, new names, and secure communication

From the Publisher:
Mobile systems, whose components communicate and change their structure, now pervade the informational world and the wider world of which it is a part. The science of mobile systems is as yet immature, however. This book presents the pi-calculus, a theory of mobile systems. The pi-calculus provides a conceptual framework for understanding mobility, and mathematical tools for expressing systems and reasoning about their behaviors. 
The book serves both as a reference for the theory and as an extended demonstration of how to use pi-calculus to describe systems and analyze their properties. It covers the basic theory of pi-calculus, typed pi-calculi, higher-order processes, the relationship between pi-calculus and lambda-calculus, and applications of pi-calculus to object-oriented design and programming. 
The book is written at the graduate level, assuming no prior acquaintance with the subject, and is intended for computer scientists interested in mobile systems.

/pdf/the-pi-calculus-a-theory-of-mobile-processes-v2p06ak9w5.pdf

The Pi-Calculus: A Theory of Mobile Processes

Communicating and Mobile Systems: the π-calculus,

We study mobile systems, i.e. systems with a dynamically changing communication topology, from a process algebras point of view. Mobility can be introduced in process algebras by allowing names or terms to be transmitted. We distinguish these two approaches as first-order and higher-order. The major target of the thesis is the comparison between them. The prototypical calculus in the first-order paradigm is the 7r-calculus. By generalising its sort discipline we derive an w-order extension called Higher-Order ur-calculus (HOir). We show that such an extension does not add expressiveness to the ur-calculus: Higher-order processes can be faithfully compiled down to first-order, and respecting the behavioural equivalence we adopted in the calculi. Such an equivalence is based on the notion of bisimulation, a fundamental concept of process algebras. Unfortunately, the standard definition of bisimulation is unsatisfactory in a higher-order calculus because it is over-discriminating. To overcome the problem, we propose barbed bisimulation. Its advantage is that it can be defined uniformly in different calculi because it only requires that the calculus possesses an interaction or reduction relation. As a test for barbed bisimulation, we show that in CCS and ur-calculus, it allows us to recover the familiar bisimulation-based equivalences. We also give simpler characterisations of the equivalences utilised in HOir. For this we exploit a special kind of agents called triggers, with which it is possible to reason fairly efficiently in a higher-order calculus notwithstanding the complexity of its transitions. Finally, we use the compilation from HO7r to ur-calculus to investigate Milner's

Expressing mobility in process algebras: first-order and higher-order paradigms

Barbed Bisimulation

The pi -calculus is a process algebra that supports process mobility by focusing on the communication of channels R Milner's (1991) presentation of the pi -calculus includes a type system assigning arities to channels and enforcing a corresponding discipline in their use The authors extend Milner's language of types by distinguishing between the ability to read from a channel, the ability to write to a channel, and the ability both to read and to write This refinement gives rise to a natural subtype relation similar to those studied in typed lambda -calculi The greater precision of their type discipline yields stronger versions of some standard theorems about the pi -calculus These can be used, for example, to obtain the validity of beta -reduction for the more efficient of Milner's encodings of the call-by-value lambda -calculus, for which beta -reduction does not hold in the ordinary pi -calculus The authors define the syntax, typing, subtyping, and operational semantics of their calculus, prove that the typing rules are sound, apply the system to Milner's lambda -calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing >

Davide Sangiorgi

Papers

The Pi-Calculus: A Theory of Mobile Processes

Communicating and Mobile Systems: the π-calculus,

Expressing mobility in process algebras: first-order and higher-order paradigms

Barbed Bisimulation

Typing and subtyping for mobile processes