Linking operational semantics and algebraic semantics for a probabilistic timed shared-variable language

Complex software systems typically involve features like time, concurrency and probability, with probabilistic computations playing an increasing role. However, it is currently challenging to formalize languages incorporating all those features. Recently, the language PTSC has been proposed to integrate probability and time with shared-variable concurrency (Zhu et al. (2006, 2009) [51] and [53]), where the operational semantics has been explored and a set of algebraic laws has been investigated via bisimulation. This paper investigates the link between the operational and algebraic semantics of PTSC, highlighting both its theoretical and practical aspects.The link is obtained by deriving the operational semantics from the algebraic semantics, an approach that may be understood as establishing soundness of the operational semantics with respect to the algebraic semantics. Algebraic laws are provided that suffice to convert any PTSC program into a form consisting of a guarded choice or an internal choice between programs, which are initially deterministic. That form corresponds to a simple execution of the program, so it is used as a basis for an operational semantics. In that way, the operational semantics is derived from the algebraic semantics, with transition rules resulting from the derivation strategy. In fact the derived transition rules and the derivation strategy are shown to be equivalent, which may be understood as establishing completeness of the operational semantics with respect to the algebraic semantics.That theoretical approach to the link is complemented by a practical one, which animates the link using Prolog. The link between the two semantics proceeds via head normal form. Firstly, the generation of head normal form is explored, in particular animating the expansion laws for probabilistic interleaving. Then the derivation of the operational semantics is animated using a strategy that exploits head normal form. The operational semantics is also animated. These animations, which again supports to claim soundness and completeness of the operational semantics with respect to the algebraic, are interesting because they provide a practical demonstration of the theoretical results.     

Algebraic approach to linking the semantics of web services

Web services have become more and more important in these years, and BPEL4WS (BPEL) is a de facto standard for the web service composition and orchestration. It contains several distinct features, including the scope-based compensation and fault handling mechanism. We have considered the operational semantics and denotational semantics for BPEL, where a set of algebraic laws can be achieved via these two models, respectively. In this paper, we consider the inverse work, deriving the operational semantics and denotational semantics from algebraic semantics for BPEL. In our model, we introduce four types of typical programs, by which every program can be expressed as the summation of these four types. Based on the algebraic semantics, the strategy for deriving the operational semantics is provided and a transition system is derived by strict proof. This can be considered as the soundness exploration for the operational semantics based on the algebraic semantics. Further, the equivalence between the derivation strategy and the derived transition system is explored, which can be considered as the completeness of the operational semantics. Finally, the derivation of the denotational semantics from algebraic semantics is explored, which can support to reason about more program properties easily.     

Semantics of plan revision in intelligent agents

In this paper, we give an operational and denotational semantics for a meta-language of the 3APL agent programming language. With this meta-language, various 3APL interpreters can be programmed. We prove equivalence of the operational and denotational semantics. Furthermore, we give an operational semantics for object-level 3APL. Using this semantics, we relate the 3APL meta-language to object-level 3APL by providing a specific interpreter, the semantics of which will prove to be equivalent to object-level 3APL.     

χ-演算与π-演算的语义比较研究

Through the comparison of syntactic structure,operational semantics and algebraic semantics between χ-calculus and π-calculus, this paper concludes that χ-calculus has more succinct syntactic structure,more explicit operational semantics,more intuitionistic algebraic semantics and more favorable algebraic property. And a translation from π-calculus to χ-calculus is presented.     

Towards a theory of mathematical operational semantics

Turi and Plotkin gave a precise mathematical formulation of a notion of structural operational semantics in their paper “Towards a mathematical operational semantics.” Starting from that definition and at the level of generality of that definition, we give a mathematical formulation of some of the basic constructions one makes with structural operational semantics. In particular, given a single-step operational semantics, as is the spirit of their work, one composes transitions and considers streams of transitions in order to study the dynamics induced by the operational semantics. In all their leading examples, it is obvious that one can do that and it is obvious how to do it. But if their definition is to be taken seriously, one needs to be able to make such constructions at the level of generality of their definition rather than case-by-case. So this paper does so for several of the basic constructions associated with structural operational semantics, in particular those required in order to speak of a stream of transitions and hence of dynamics.     

A structural operational semantics for an Edison-like language (1)

A structural operational semantics for Edison. 1—an Edison-like language—is given. The static and dynamic (operational) semantics for various declarations and statements contained in this type of languages have been carefully studied by using a structural operational approach. The method used here can be generalised to cover more complicated concurrent programming languages. The paper is divided into two parts. In the first part, an abstract syntax of Edison. 1 is introduced and the static semantics of it is studied. In the second part, an operational (dynamic) semantics of Edison. 1 is given.     

Semantic theories of programs with nested interrupts

In the design of dependable software for embedded and real-time operating systems, time analysis is a crucial but extremely difficult issue, the challenge of which is exacerbated due to the randomness and nondeterminism of interrupt handling behaviors. Thus research into a theory that integrates interrupt behaviors and time analysis seems to be important and challenging. In this paper, we present a programming language to describe programs with interrupts that is comprised of two essential parts: main program and interrupt handling programs. We also explore a timed operational semantics and a denotational semantics to specify the meanings of our language. Furthermore, a strategy of deriving denotational semantics from the timed operational semantics is provided to demonstrate the soundness of our operational semantics by showing the consistency between the derived denotational semantics and the original denotational semantics.     

A rewriting logic framework for operational semantics of membrane systems

Existing results in membrane computing refer mainly to P systems’ characterization of Turing computability, also to some polynomial solutions to NP-complete problems by using an exponential workspace created in a “biological way”. In this paper we define an operational semantics of a basic class of P systems, and give two implementations of the operational semantics using rewriting logic. We present some results regarding these implementations, including two operational correspondence results, and discuss why these implementations are relevant in order to take advantage of good features of both structural operational semantics and rewriting logic.     

Contributions to the semantics of logic perpetual processes

Summary Logic perpetual processes (logic programs with infinite data structures) have been given several formal (operational and fixpoint) semantics. In this paper, we compare the various semantics and define a formal characterization of a least fixpoint semantics, which is based on a modified version of the logic programs and which is satisfactory for a large class of logical perpetual processes. Our results show that all the proposed fixpoint semantics are not equivalent to the operational semantics and suggest an improvement of the least fixpoint approach.     

Linear-Time Self-Interpretation of the Pure Lambda Calculus

We show that linear-time self-interpretation of the pure untyped lambda calculus is possible, in the sense that interpretation has a constant overhead compared to direct execution under various execution models. The present paper shows this result for reduction to weak head normal form under call-by-name, call-by-value and call-by-need.We use a self-interpreter based on previous work on self-interpretation and partial evaluation of the pure untyped lambda calculus.We use operational semantics to define each reduction strategy. For each of these we show a simulation lemma that states that each inference step in the evaluation of a term by the operational semantics is simulated by a sequence of steps in evaluation of the self-interpreter applied to the term (using the same operational semantics).By assigning costs to the inference rules in the operational semantics, we can compare the cost of normal evaluation and self-interpretation. Three different cost-measures are used: number of beta-reductions, cost of a substitution-based implementation (similar to graph reduction) and cost of an environment-based implementation.For call-by-need we use a non-deterministic semantics, which simplifies the proof considerably.     

prialt in Handel-C: an operational semantics

We describe an operational semantics for the hardware compilation language Handel-C [7], which is a C-like language with channel communication and parallel constructs which compiles down to mainly synchronously clocked hardware. The work in this paper builds on previous work describing the semantics of the “prialt” construct within Handel-C [5] and a denotational semantics for part of the language [6]. We describe a key subset of the language and show how a design decision for the real language, namely that default guards in a prialt statement executed in “zero-time”, has consequences for the complexity of the operational semantics. We present the operational semantics, along with a revised and completed prialt semantics, indicating clearly the interface between them. We then describe a notion of observational equivalence and present an example illustrating how we handle the complexity of nested prialts in default guards.     

A Rewriting Logic Approach to Operational Semantics (Extended Abstract)

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, and continuation-based semantics. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

函数／逻辑语言归约实现技术

ＲＦＵＮＬＯＧ是我们在ＬＮＦ演算基础上自行设计实现的一种函数／逻辑语言，它具有统一的操作语义。本文介绍ＲＦＵＮＬＯＧ语言的总体结构、归约操作语义及其解释实现技术。     

Gamma的语义研究

在推导程序属性方面,公理语义比操作语义具有更多的优点。本文定义Gamma 的时态语义,它是已有工作的进一步精确化;本文证明这种时态语义与结构化操作语义是一致的。     

A mathematical semantics for a nondeterministic typed λ-calculus

This paper is concerned with the problems encountered in defining the semantics of nondeterministic algorithms. A nondeterministic control structure is added to a typed λ-calculus and the usual operational semantics for the deterministic language is generalized to take into account the more complex behaviour of nondeterministic algorithms. A mathematical model is then given for the language and the relationship between the denotational and operational semantics is explored.     

A rewriting logic approach to operational semantics

This paper shows how rewriting logic semantics (RLS) can be used as a computational logic framework for operational semantic definitions of programming languages. Several operational semantics styles are addressed: big-step and small-step structural operational semantics (SOS), modular SOS, reduction semantics with evaluation contexts, continuation-based semantics, and the chemical abstract machine. Each of these language definitional styles can be faithfully captured as an RLS theory, in the sense that there is a one-to-one correspondence between computational steps in the original language definition and computational steps in the corresponding RLS theory. A major goal of this paper is to show that RLS does not force or pre-impose any given language definitional style, and that its flexibility and ease of use makes RLS an appealing framework for exploring new definitional styles.     

Inductive assertions and operational semantics

This paper shows how classic inductive assertions can be used in conjunction with a formal operational semantics to prove partial correctness properties of programs. The method imposes only the proof obligations that would be produced by a verification condition generator – but does not require the definition of a verification condition generator. All that is required is a theorem prover, a formal operational semantics, and the object program with appropriate assertions at user-selected cut points. The verification conditions are generated in the course of the theorem-proving process by straightforward symbolic evaluation of the formal operational semantics. The technique is demonstrated by proving the partial correctness of simple bytecode programs with respect to a preexisting operational model of the Java Virtual Machine.     

Semantics of EqL

The formal semantics of a novel language, called EqL, are presented for first-order functional and Horn logic programming. An EqL program is a set of conditional pattern-directed rules, where the conditions are expressed as a conjunction of equations. The programming paradigm provided by this language may be called equational programming. The declarative semantics of equations is given in terms of their complete set of solutions, and the operational semantics for solving equations is an extension of reduction, called object refinement. The correctness of the operational semantics is established through the soundness and completeness theorems. Examples are given to illustrate the language and its semantics.<>