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A type system for the relational calculus of object systems

*
11th IEEE International Conference on Engineering of Complex Computer Systems (ICECCS'06)
*

Within many formalisms, rCOS,

doi:10.1109/iceccs.2006.1690368
fatcat:7bjibqxtefawva4yx2oqjr37qy
*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. ...##
###
Semantics of Objects As Processes (SOAP)
[chapter]

1999
*
Lecture Notes in Computer Science
*

Gérard Boudol proposes

doi:10.1007/3-540-46589-8_18
fatcat:njv6znlwo5f65fiw6ellpuovfm
*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 ...##
###
An extended Theory of Primitive Objects: First order system
[chapter]

1997
*
Lecture Notes in Computer Science
*

This extended

doi:10.1007/bfb0053378
fatcat:jbcgpqgpyfc5jlogquej2fbxqi
*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. ...##
###
Mobile Processes: A Commented Bibliography
[chapter]

2001
*
Lecture Notes in Computer Science
*

as modelled in

doi:10.1007/3-540-45510-8_11
fatcat:ksp2ci37rbc5jbwokvcs2ugspq
*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. ...##
###
A Well-typed Lightweight Situation Calculus
[article]

2012
*
arXiv
*
pre-print

This modified version

arXiv:1201.2430v2
fatcat:3g2vjmffb5ai3jwfrt472tm55i
*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. ...##
###
An interoperable calculus for external object access

2002
*
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming - ICFP '02
*

To establish

doi:10.1145/581478.581485
dblp:conf/icfp/OhoriY02
fatcat:jsbsugltyzhyfjbofoz3eqql2m
*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. ...##
###
An Interpretation of Typed Concurrent Objects in the Blue Calculus
[chapter]

2000
*
Lecture Notes in Computer Science
*

We propose an interpretation

doi:10.1007/3-540-44929-9_29
fatcat:n7gnrdh4tzejnkufx7yguyx77i
*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. ...##
###
A pattern-based object calculus

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. ...

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

2007
*
Lecture Notes in Computer Science
*

We demonstrate this correspondence by providing this

doi:10.1007/978-3-540-73228-0_27
fatcat:owzjymhiybhjvc5lr6w5frrwqu
*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*. ...##
###
A Resource Aware Computational Interpretation for Herbelin's Syntax
[chapter]

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. ...

##
###
Spatial Dynamic Structures and Mobility in Computation
[article]

2011
*
arXiv
*
pre-print

On

arXiv:1108.0496v1
fatcat:tm7gmvmhvfbd3m7ptyf6kscx5q
*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. ...##
###
Characterizing Convergent Terms in Object Calculi via Intersection Types
[chapter]

2001
*
Lecture Notes in Computer Science
*

We give

doi:10.1007/3-540-45413-6_25
fatcat:gapr723wnrbfnornkiu5p3ovhu
*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. ...##
###
On object extension
[chapter]

1998
*
Lecture Notes in Computer Science
*

In this paper, we apply four

doi:10.1007/bfb0054105
fatcat:j2kaybejhraapkv6ntmngh6yn4
*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*...##
###
A First-Order Calculus for Allegories
[chapter]

2011
*
Lecture Notes in Computer Science
*

In this paper we

doi:10.1007/978-3-642-21070-9_8
fatcat:awpqebnyabamllsnkhi4sqp3ju
*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. ...##
###
Membrane Calculus: a formal method for Grid transactions

2006
*
Concurrency and Computation
*

Finally,

doi:10.1002/cpe.1030
fatcat:snoqtn3asje7dc7jgasmrnzlwm
*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*. ...
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