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A type system for the relational calculus of object systems

Liang Zhao, Xiangpeng Zhao, Quan Long, Zong Yan
11th IEEE International Conference on Engineering of Complex Computer Systems (ICECCS'06)  
Within many formalisms, rCOS, a refinement calculus of object-oriented systems based on Unifying Theories of Programming (UTP), has been proven a promising one in the sense of its applications on incremental  ...  We believe introducing static checking will numerously extend the power of rCOS. In this paper, as a first step, we develop a type system for rCOS with type safety theorems.  ...  T ::= B | C The syntax of a command c is listed as follows. 3 The Type System of rCOS Sub-typing We use the symbol <: Cdecls to denote the subtype relation defined by Cdecls.  ... 
doi:10.1109/iceccs.2006.1690368 fatcat:7bjibqxtefawva4yx2oqjr37qy

Semantics of Objects As Processes (SOAP) [chapter]

Uwe Nestmann, António Ravara
1999 Lecture Notes in Computer Science  
Gérard Boudol proposes a dynamic type system for the blue calculus (a variant of the π-calculus directly incorporating the λ-calculus) [5] .  ...  Franz Puntigam [38, 39, 40, 41] defines a calculus of concurrent objects, a process-algebra of types (with the expressiveness of a non-regular language), and a type system which guarantees that all messages  ... 
doi:10.1007/3-540-46589-8_18 fatcat:njv6znlwo5f65fiw6ellpuovfm

An extended Theory of Primitive Objects: First order system [chapter]

Luigi Liquori
1997 Lecture Notes in Computer Science  
This extended calculus has a sound type system which allows static detection of run-time errors such as message-not-understood, \width" subtyping and a typed equational theory on objects.  ...  Categories: Type systems, design and semantics of object-oriented languages.  ...  Acknowledgments We wish to thank Martin Abadi and Luca Cardelli for their precious @-discussions, and the anonymous referees for their comments and suggestions.  ... 
doi:10.1007/bfb0053378 fatcat:jbcgpqgpyfc5jlogquej2fbxqi

Mobile Processes: A Commented Bibliography [chapter]

Silvano Dal Zilio
2001 Lecture Notes in Computer Science  
as modelled in the π-calculus of Milner, Parrow and Walker for example, and motile processes, which can exhibit motion, as modelled in the ambient calculus of Cardelli and Gordon.  ...  A common characteristic of the algebraic frameworks presented in this paper is the use of names as first class values and the support for the dynamic generation of new, fresh names.  ...  Acknowledgments I would like to thank Uwe Nestmann and Peter Sewell for helpful comments. Luca Cardelli and Andy Gordon commented on a previous version of this text.  ... 
doi:10.1007/3-540-45510-8_11 fatcat:ksp2ci37rbc5jbwokvcs2ugspq

A Well-typed Lightweight Situation Calculus [article]

Li Tan
2012 arXiv   pre-print
This modified version of a lightweight situation calculus is proved to be a robust and well-typed system.  ...  In this paper, we propose to add more typing mechanisms to the current version of situation calculus, especially for three basic elements in situation calculus: situations, actions and objects, and then  ...  Acknowledgements The author would like to thank all anonymous reviewers for their generous and constructive directives and comments on this paper.  ... 
arXiv:1201.2430v2 fatcat:3g2vjmffb5ai3jwfrt472tm55i

An interoperable calculus for external object access

Atsushi Ohori, Kiyoshi Yamatodani
2002 Proceedings of the seventh ACM SIGPLAN international conference on Functional programming - ICFP '02  
To establish type safety, we define a sample object-oriented language with multiple inheritance as the target for interoperability, define an operational semantics of the calculus, and show that the type  ...  This calculus enjoys the features of both higher-order programming with ML polymorphism and class-based object-oriented programming with dynamic method dispatch.  ...  Acknowledgments We would like to thank anonymous reviewers for their helpful comments, which have been very useful for improving the presentation of this paper.  ... 
doi:10.1145/581478.581485 dblp:conf/icfp/OhoriY02 fatcat:jsbsugltyzhyfjbofoz3eqql2m

An Interpretation of Typed Concurrent Objects in the Blue Calculus [chapter]

Silvano Dal Zilio
2000 Lecture Notes in Computer Science  
We propose an interpretation of a typed concurrent calculus of objects based on the imperative object calculus of Abadi and Cardelli.  ...  The target of our interpretation is a version of the blue calculus, a variant of the π-calculus that directly contains functions, with record and firstorder types.  ...  This work took place in the context of collaboration with Gérard Boudol at INRIA Sophia-Antipolis. He has greatly influenced the present development.  ... 
doi:10.1007/3-540-44929-9_29 fatcat:n7gnrdh4tzejnkufx7yguyx77i

A pattern-based object calculus

Nabil Kamel, Ping Wu, Stanley Y. W. Su
1994 The VLDB journal  
The pattern-based object calculus presented in this article provides such a theoretical foundation for describing and processing objectoriented databases.  ...  The object calculus is based on first-order logic. It provides the formalism for interpreting precisely and unifor/nly the semantics of queries and integrity constraints in object-oriented databases.  ...  From the above examples, one can see that the object calculus can express many types of constraints for OO databases.  ... 
doi:10.1007/bf01231358 fatcat:nt2i3gevj5dxpk5imb4cyh45hu

Convolution $\bar\lambda\mu$ -Calculus [chapter]

Lionel Vaux
2007 Lecture Notes in Computer Science  
We demonstrate this correspondence by providing this calculus with a denotational semantics inside a lambda-model in the category of sets and relations.  ...  We define an extension of Herbelin'sλµ-calculus, introducing a product operation on contexts (in the sense of lists of arguments, or stacks in environment machines), similar to the convolution product  ...  Now we introduce type system Rλ µ * for the objects of convolutionλµ-calculus.  ... 
doi:10.1007/978-3-540-73228-0_27 fatcat:owzjymhiybhjvc5lr6w5frrwqu

A Resource Aware Computational Interpretation for Herbelin's Syntax [chapter]

Delia Kesner, Daniel Ventura
2015 Lecture Notes in Computer Science  
For that, we associate to Herbelin's syntax a type system based on non-idempotent intersection types, together with a set of reduction rules -inspired from the substitution at a distance paradigm-that  ...  preserves (and decreases the size of) typing derivations.  ...  The reduction relation → E is confluent. A Non-Idempotent Typing System for I-Terms In this section we restrict to I-objects the system Q E introduced in Sec. 3.  ... 
doi:10.1007/978-3-319-25150-9_23 fatcat:a4pnehwarnechmoedtf3bqrhma

Spatial Dynamic Structures and Mobility in Computation [article]

Bogdan Aman
2011 arXiv   pre-print
On the other hand, we relate systems of mobile membranes to process algebra (mobile ambients, timed mobile ambients, pi-calculus, brane calculus) by providing some encodings and adding some concepts inspired  ...  Specifically, we address issues concerning the power of operations for modifying the membrane structure of a system of mobile membranes by mobility: endocytosis (moving a membrane inside a neighbouring  ...  I thanks the anonymous referees for their comments and suggestions which helped improve the quality of the papers in which parts of this thesis were published.  ... 
arXiv:1108.0496v1 fatcat:tm7gmvmhvfbd3m7ptyf6kscx5q

Characterizing Convergent Terms in Object Calculi via Intersection Types [chapter]

Ugo de'Liguoro
2001 Lecture Notes in Computer Science  
We give a simple characterization of convergent terms in Abadi and Cardelli untyped Object Calculus (&-calculus) via intersection types.  ...  We consider a -calculus with records and its intersection type assignment system. We p r o ve that convergent -terms are characterized by their types.  ...  Acknowledgment We wish to thank Mariangiola Dezani for reading a preliminary version of this paper, and Viviana Bono for representing the point of view of object oriented people.  ... 
doi:10.1007/3-540-45413-6_25 fatcat:gapr723wnrbfnornkiu5p3ovhu

On object extension [chapter]

Luigi Liquori
1998 Lecture Notes in Computer Science  
In this paper, we apply four type systems to the functional Lambda Calculus of Objects: (a) the Original type system [15]; (b) the Fisher's Ph.D type system [14]; (c) the Bruce's Matching-based type systems  ...  Type Systems of object-oriented languages (panorama). 1 Byà la Curry, we mean that the terms of the calculus are not annotated with types. This does not signify that a type system does not exist.  ...  I would like to thank the Logics of Programs group of the Department of Computer Science of Turin, for the time spent to teach me the fundamentals of Theoretical Computer Science, to Furio Honsell for  ... 
doi:10.1007/bfb0054105 fatcat:j2kaybejhraapkv6ntmngh6yn4

A First-Order Calculus for Allegories [chapter]

Bahar Aameri, Michael Winter
2011 Lecture Notes in Computer Science  
In this paper we a language and first-order calculus for formal reasoning about relations based on the theory of allegories. Since allegories are categories the language is typed in Church-style.  ...  We show soundness and completeness of the calculus and demonstrate its usability by presenting the RelAPS system; a proof assistant for relational categories based on the calculus presented here.  ...  If s is an object term, then I s is a relational term of type s → s. 4. If t is a relational term of type s 1 → s 2 , then t is a relational term of type s 2 → s 1 . 5.  ... 
doi:10.1007/978-3-642-21070-9_8 fatcat:awpqebnyabamllsnkhi4sqp3ju

Membrane Calculus: a formal method for Grid transactions

Zhengwei Qi, Minglu Li, Cheng Fu, Dongyu Shi, Jinyuan You
2006 Concurrency and Computation  
Finally, a typical long-running transaction example is presented to demonstrate the usage of Membrane Calculus.  ...  We introduce five kinds of transition rules in Membrane Calculus (including object rules and membrane rules) and the operational semantics of transition rules is defined.  ...  The elementary membrane consists of the multiset of objects (every object owns its color type) and transitions corresponding to the rules in P systems.  ... 
doi:10.1002/cpe.1030 fatcat:snoqtn3asje7dc7jgasmrnzlwm
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