Sound refactorings

Refactoring consists in restructuring an object-oriented program without changing its behaviour. In this paper, we present refactorings as transformation rules for programs written in a refinement language inspired on Java that allows reasoning about object-oriented programs and specifications. A set of programming laws is available for the imperative constructs of this language as well as for its object-oriented features; soundness of the laws is proved against a weakest precondition semantics. The proof that the refactoring rules preserve behaviour (semantics) is accomplished by the application of these programming laws and data simulation. As illustration of our approach to refactoring, we use our rules to restructure a program to be in accordance with a design pattern.     

An operational semantics for object-oriented concepts based on the class hierarchy

The formalisation of object-oriented languages is essential for describing the implementation details of specific programming languages or for developing program verification techniques. However there has been relatively little formalisation work aimed at abstractly describing the fundamental concepts of object-oriented programming, separate from specific language considerations or suitability for a particular verification style. In this paper we address this issue by formalising a language that includes the core object-oriented programming language concepts of field tests and updates, methods, constructors, subclassing, multithreading, and synchronisation, built on top of standard sequential programming constructs. The abstract syntax is relatively close to the core of typical object-oriented programming languages such as Java. A novel aspect of the syntax is that objects and classes are encapsulated within a single syntactic term, including their fields and methods. Furthermore, class terms are structured according to the class hierarchy, and objects appear as subterms of their class (and method instances as subterms of the relevant object). This helps to narrow the gap between how a programmer thinks about their code and the underlying mathematical objects in the semantics. The semantics is defined operationally, so that all actions a program may take, such as testing or setting local variables and fields, or invoking methods on other objects, appear on the labels of the transitions. A process-algebraic style of interprocess communication is used for object and class interactions. A benefit of this label-based approach to the semantics is that a separation of concerns can be made when defining the rules of the different constructs, and the rules tend to be more concise. The basic rules for individual commands may be composed into more powerful rules that operate at the level of classes and objects. The traces generated by the operational semantics are used as the basis for establishing equivalence between classes.     

RELOOP, an algebra based query language for an object-oriented database system

In most object-oriented databases, as opposed to value-oriented databases, data are accessed by a programming language instead of a declarative query language. End users do not have a simple tool to perform their queries. This paper is concerned with the definition of an SQL-like query language on top of the O₂ object-oriented database system. We study the influence of the object-oriented paradigm on a query language, describe our language through examples, define its semantics by means of an algebra and sketch the compilation of RELOOP in one of the languages supported by the O₂ system.     

A timed semantics of Orc

Orc is a kernel language for structured concurrent programming. Orc provides three powerful combinators that define the structure of a concurrent computation. These combinators support sequential and concurrent execution, and concurrent execution with blocking and termination.Orc is particularly well-suited for task orchestration, a form of concurrent programming with applications in workflow, business process management, and web service orchestration. Orc provides constructs to orchestrate the concurrent invocation of services while managing time-outs, priorities, and failures of services or communication.Our previous work on the semantics of Orc focused on its asynchronous behavior. The inclusion of time or the effect of delay on a computation had not been modeled. In this paper, we define an operational semantics of Orc that allows reasoning about delays, which are introduced explicitly by time-based constructs or implicitly by network delays. We develop a number of identities among Orc expressions and define an equality relation that is a congruence. We also present a denotational semantics in which the meaning of an Orc program is a set of traces, and show that the two semantics are equivalent.     

Toward a programming theory for rational agents

An important problem in agent verification is a lack of proper understanding of the relation between agent programs on the one hand and agent logics on the other. Understanding this relation would help to establish that an agent programming language is both conceptually well-founded and well-behaved, as well as yield a way to reason about agent programs by means of agent logics. As a step toward bridging this gap, we study several issues that need to be resolved in order to establish a precise mathematical relation between a modal agent logic and an agent programming language specified by means of an operational semantics. In this paper, we present an agent programming theory that provides both an agent programming language as well as a corresponding agent verification logic to verify agent programs. The theory is developed in stages to show, first, how a modal semantics can be grounded in a state-based semantics, and, second, how denotational semantics can be used to define the mathematical relation connecting the logic and agent programming language. Additionally, it is shown how to integrate declarative goals and add precompiled plans to the programming theory. In particular, we discuss the use of the concept of higher-order goals in our theory. Other issues such as a complete axiomatization and the complexity of decision procedures for the verification logic are not the focus of this paper and remain for future investigation. Part of this research was carried out while the first author was affiliated with the Nijmegen Institute for Cognition and Information, Radboud University Nijmegen.     

Abstract interpretation and types for systems biology

Abstract interpretation is a theory of abstraction that has been introduced for the analysis of programs. In particular, it has proved useful for organizing the multiple semantics of a given programming language in a hierarchy corresponding to different detail levels, and for defining type systems for programming languages and program analyzers in software engineering. In this paper, we investigate the application of these concepts to systems biology formalisms. More specifically, we consider the Systems Biology Markup Language SBML, and the Biochemical Abstract Machine BIOCHAM with its differential, stochastic, discrete and boolean semantics. We first show how all of these different semantics, except the differential one, can be formally related by simple Galois connections. Then we define three type systems: one for checking or inferring the functions of proteins in a reaction model, one for checking or inferring the activation and inhibition effects of proteins in a reaction model, and another one for checking or inferring the topology of compartments or locations. We show that the framework of abstract interpretation elegantly applies to the formalization of these further abstractions, and to the implementation of linear or quadratic time type checking as well as type inference algorithms. Furthermore, we show a theorem of independence of the graph of activation and inhibition effects from the kinetic expressions in the reaction model, under general conditions. Through some examples, we show that the analysis of biochemical models by type inference provides accurate and useful information. Interestingly, such a mathematical formalization of the abstractions commonly used in systems biology already provides some guidelines for the extensions of biochemical reaction rule languages.     

An Operational Approach to the Semantics of Classes: Application to Type Checking

This paper presents a simple and natural semantics for object-oriented languages with classes and multiple inheritance. The model, called the Formal Class model, is an intermediate level between the algebraic specification of data type, and the implementation within an object-oriented language. Our model is equipped with an operational semantics based on conditional term rewriting. One important characteristic is the use of conditional selectors. It allows one to define a type with a flat or an ordered design. In this context, we define a safe and simple type system with single dispatch and simply covariant methods. This type system is extended to some practical aspects, such as abstract classes, abstract methods, protected methods, and super methods. We describe and compare flat and ordered designs and prove that the latter is finer than the former one. We also look at multicovariant methods and show ways to fix type-checking problems using single dispatch. We describe the least pessimistic solution. Lastly, we discuss the extension of our type checking to multiple dispatch and side effects. This paper synthesizes several practical results, their proofs, and algorithms.     

Full Abstraction for a Shared-Variable Parallel Language

We give a new denotational semantics for a shared-variable parallel programming language and prove full abstraction: the semantics gives identical meanings to commands if and only if they induce the same behavior in all program contexts. The meaning of a command is a set of “transition traces,” which record the ways in which a command may interact with and be affected by its environment. We show how to modify the semantics to incorporate new program constructs, to allow for different levels of granularity or atomicity, and to model fair infinite computation, in each case achieving full abstraction with respect to an appropriate notion of program behavior.     

The semantics of the combination of atomized statements and parallel choice

In this paper we define a uniform language that is an extension of the language underlying the process algebraPA. One of the main extensions of this language overPA is given by so-called atomizing brackets. If we place these brackets around a statement then we treat this statement as an atomic action. Put differently, these brackets remove all interleaving points. We present a transition system for the language and derive its operational semantics. We show that there are several options for defining a transition system such that the resulting operational semantics is a conservative extension of the semantics forPA. We define a semantic domain and a denotational model for the language. Next we define a closure operator on the semantic domain and show how to use this closure operator to derive a fully abstract denotational semantics. Then the algebraic theory of the language is considered. We define a collection of axioms and a term rewrite system based on these axioms. Using this term rewrite system we are able to identify normal forms for the language. It is shown that these axioms capture the denotational equality. It follows that if two terms are provably equal then they have the same operational semantics. Finally, we show how to extend the axiomatization in order to axiomatize its operational equivalence.     

面向对象程序设计体裁嵌入FFP-AST系统

FFP语言是这样的一种纯粹的泛函程序设计语言,它奠基于严格的数学理论基础之上,是归约语言L₄的一个子类^[2,3]。本文将面向对象编程(OOP)体裁相当简洁地嵌入到FFP-AST系统中。这样,一方面,揭示了面向对象编程体裁(OOPP)与泛函编程体裁(FPP)之间的近亲关系;另一方面,为OOPP奠定了 FFP-AST语义描述。本文实质上也提供了一种“加于FFP语言之上的兼备FPP和OOPP的编程语言”。贯穿文中的方法论归结为:紧密联系和使用自动机这一概念。     

Computability concepts for programming language semantics

This paper is about mathematical problems in programming language semantics and their influence on recursive function theory. We define a notion of computability on continuous higher types (for all types) and show its equivalence to effective operators. This resuit shows that our computable operators can model mathematically (i.e. extensionally) everything that can be done in an operational semantics. These new recursion theoretic concepts which are appropriate to semantics also allow us to construct Scott models for the λ-calculus which contain all and only computably elements. Depending on the choice of the initial cpo, our general theory yields a theory for either strictly determinate or else arbitrary non-deterministic objects (parallelism). The formal theory is developed in Part II of this paper. Part I gives motivation and comparison with related work.     

Goals in conflict: semantic foundations of goals in agent programming

This paper addresses the notion of (declarative) goals as used in agent programming. Goals describe desirable states, and semantics of these goals in an agent programming context can be defined in various ways. We focus in this paper on the representation of conflicting goals. In particular, we define two semantics for goals, one for unconditional goals and one for conditional goals. The first is based on propositional logic, and the latter is based on default logic. We establish relations between and properties of these semantics. This title was inspired by the title of the PhD thesis of Harrenstein: Logic in conflict: logical explorations in strategic equilibrium [25].     

A Formal Semantics for DAI Language NUML

Traditional AI systems are brittle in the sense that they fail miserably when presented with problems even sliphtly outside of their limited range of expertise.A powerful,extensible strategy of Distributed Artificial Intelligence (DAI) for overcoming such bounds is to put the system in a society of systems.So the ability to coordinate group activities of individuals and to communicate between each other is necessary for a language describing DAI systems.Agent-oriented language NUML is such a language.It is a specific kind of object-oriented language.To give formal semantics to NUML,there is the problem to formalise object-oriented programming paradigm which is still open.The theory of higher-order π-calculus is a concurrent computation model with sufficient capability,which provides us a mathematical tool to do the formalization.This paper tries to use higher-order π-calculus to formalise NUML.     

An executable object-oriented semantics and its application to firewall verification

This paper presents a formal executable semantics of object-oriented models. We made it possible to conduct both simulation and theorem proving on the semantics by implementing it within the expressive intersection of the functional programming language ML and the theorem prover HOL. In this paper, we present the definition and implementation of the semantics. We also present a prototype verification tool ObjectLogic which supports simulation and theorem proving on the semantics. As a case study, we show the verification of a practical firewall system.     

The object-oriented functional data language

The object-oriented functional data language (O²FDL) is an interactive strongly typed database programming language that integrates the object-oriented and functional programming paradigms. It was designed for advanced applications that require a powerful and uniform database programming language supporting the software engineering principles of these tow paradigms. To this end, the O² FDL supports inheritance and encapsulation of object-oriented languages, and an equational notation and strong typing of functional programming. Strong typing is extended with type restrictions to constrain the instantiations of type variables in function interfaces, while inheritance is augmented with a monotonic subtype rule for function redefinition. The O²FDL also supports novel features. For the core of the O²FDL, a denotational semantics based on an extended λ-calculus is provided. For selected system-defined functions, operational semantics are provided and it is demonstrated that a subset of the O²FDL is at least as expressive as the relational algebra     

Integrating discrete controller synthesis into a reactive programming language compiler

We define a mixed imperative/declarative programming language: declarative contracts are enforced upon imperatively described behaviors. This paper describes the semantics of the language, making use of the notion of Discrete Controller Synthesis (DCS). We target the application domain of adaptive and reconfigurable systems: our language can serve programming closed-loop adaptation controllers, enabling flexible execution of functionalities w.r.t. changing resource and environment conditions. DCS is integrated into a1 programming language compiler, which facilitates its use by users and programmers, performing executable code generation. The tool is concretely built upon the basis of a reactive programming language compiler, where the nodes describe behaviors that can be modeled in terms of transition systems. Our compiler integrates this with a DCS tool, making it a new environment for formal methods. We define the trace semantics of our contracts language, describe its compilation and establish its correctness, and discuss implementation and examples.     

SCHOOL: a Small Chorded Object-Oriented Language

Chords are a declarative synchronisation construct based on the Join-calculus, available in the programming language C-omega. To our knowledge, chords have no formal model in an object-oriented setting. In this paper we suggest SCHOOL, a formal model for an imperative, object-oriented language with chords. We give an operational semantics and type system, and can prove soundness of the type system.     

Two-level grammar as an implementable metalanguage for axiomatic semantics

Two-level grammars can define the syntax and the operational semantics of programming languages and these definitions are directly executable by interpretation. In this paper it is shown that axiomatic semantics can also be defined using a two-level grammar with the result being a partially automatic program verification system accomplished within the framework of a language definition. These results imply that a programming language can be defined operationally and axiomatically together in complementary definitions as advocated by Hoare and Lauer. Because two-level grammars are executable, these complementary definitions accomplish a system for interpreting and verifying programs.     

Distributed quantum programming

In this paper we explore the structure and applicability of the Distributed Measurement Calculus (DMC), an assembly language for distributed measurement-based quantum computations. We describe the formal language’s syntax and semantics, both operational and denotational, and state several properties that are crucial to the practical usability of our language, such as equivalence of our semantics, as well as compositionality and context-freeness of DMC programs. We show how to put these properties to use by constructing a composite program that implements distributed controlled operations, in the knowledge that the semantics of this program does not change under the various composition operations. Our formal model is the basis of a quantum virtual machine construction for distributed quantum computations, which we elaborate upon in the latter part of this work. This virtual machine embodies the formal semantics of DMC such that programming execution no longer needs to be analysed by hand. Far from a literal translation, it requires a substantial concretisation of the formal model at the level of data structures, naming conventions and abstraction mechanisms. At the same time we provide automatisation techniques for program specification where possible to obtain an expressive and user-friendly programming environment.