The Rewriting Logic Semantics Project

Rewriting logic is a flexible and expressive logical framework that unifies denotational semantics and SOS in a novel way, avoiding their respective limitations and allowing very succinct semantic definitions. The fact that a rewrite theory's axioms include both equations and rewrite rules provides a very useful “abstraction knob” to find the right balance between abstraction and observability in semantic definitions. Such semantic definitions are directly executable as interpreters in a rewriting logic language such as Maude, whose generic formal tools can be used to endow those interpreters with powerful program analysis capabilities.     

Interpreters from functions and grammars

The addition of context free grammar rules to a functional language simplifies the construction of interpreters from denotational semantic language definitions. Functional abstraction over grammar rules enables the specification and processing of context sensitive language syntax aspects in a functional style.     

Oracle Semantics for Prolog

This paper proposes to specify semantic definitions for logic programming languages such as Prolog in terms of an oracle which specifies the control strategy and identifies which clauses are to be applied to resolve a given goal. The approach is quite general. It can be applied to Prolog to specify both operational and declarative semantics as well as other logic programming languages. Previous semantic definitions for Prolog typically encode the sequential depth-first search of the language into various mathematical frameworks. Such semantics mimic a Prolog interpreter in the sense that following the "leftmost" infinite path in the computation tree excludes computation to the right of this path from being considered by the semantics. The basic idea in this paper is to abstract away from the sequential control of Prolog and to provide a declarative characterization of the clauses to apply to a given goal. The decision whether or not to apply a clause is viewed as a query to an oracle which is specified from within the semantics and reasoned about from outside. This approach results in simple and concise semantic definitions which are more useful for arguing the correctness of program transformations and providing the basis for abstract interpretations than previous proposals.     

Building Interpreters with Rewriting Strategies

Programming language semantics based on pure rewrite rules suffers from the gap between the rewriting strategy implemented in rewriting engines and the intended evaluation strategy. This paper shows how programmable rewriting strategies can be used to implement interpreters for programming languages based on rewrite rules. The advantage of this approach is that reduction rules are first class entities that can be reused in different strategies, even in other kinds of program transformations such as optimizers. The approach is illustrated with several interpreters for the lambda calculus based on implicit and explicit (parallel) substitution, different strategies including normalization, eager evaluation, lazy evaluation, and lazy evaluation with updates. An extension with pattern matching and choice shows that such interpreters can easily be extended.     

Semantic foundations for generalized rewrite theories

Rewriting logic (RL) is a logic of actions whose models are concurrent systems. Rewrite theories involve the specification of equational theories of data and state structures together with a set of rewrite rules that model the dynamics of concurrent systems. Since its introduction, more than one decade ago, RL has attracted the interest of both theorists and practitioners, who have contributed in showing its generality as a semantic and logical framework and also as a programming paradigm. The experimentation conducted in these years has suggested that some significant extensions to the original definition of the logic would be very useful in practice. These extensions may develop along several dimensions, like the choice of the underlying equational logic, the kind of side conditions allowed in rewrite rules and operational concerns for the execution of certain rewrites. In particular, the Maude system now supports subsorting and conditional sentences in the equational logic for data, and also frozen arguments to block undesired nested rewrites; moreover, it allows equality and membership assertions in rule conditions. In this paper, we give a detailed presentation of the inference rules, model theory, and completeness of such generalized rewrite theories. Our results provide a mathematical semantics for Maude, and a foundation for formal reasoning about Maude specifications.     

Detecting redundancy among production rules using term rewrite semantics

We present a general method for detecting wide classes of redundant production rules (PRs) based on the term rewrite semantics. We present the semantic account, define rule execution over both ground memories and memory schemas, and define redundancy for the PRs. From those definitions, an algorithm is developed that detects wide classes of redundant rules, and which improves upon the previously published methods.     

Two Case Studies of Semantics Execution in Maude: CCS and LOTOS

We explore the features of rewriting logic and, in particular, of the rewriting logic language Maude as a logical and semantic framework for representing and executing inference systems. In order to illustrate the general ideas we consider two substantial case studies. In the first one, we represent both the semantics of Milner’s CCS and a modal logic for describing local capabilities of CCS processes. Although a rewriting logic representation of the CCS semantics is already known, it cannot be directly executed in the default interpreter of Maude. Moreover, it cannot be used to answer questions such as which are the successors of a process after performing an action, which is used to define the semantics of Hennessy-Milner modal logic. Basically, the problems are the existence of new variables in the righthand side of the rewrite rules and the nondeterministic application of the semantic rules, inherent to CCS. We show how these problems can be solved in a general, not CCS dependent way by controlling the rewriting process by means of reflection. This executable specification plus the reflective control of rewriting can be used to analyze CCS processes. The same techniques are also used to implement a symbolic semantics for LOTOS in our second case study. The good properties of Maude as a metalanguage allow us to implement a whole formal tool where LOTOS specifications without restrictions in their data types (given as ACT ONE specifications) can be executed. In summary, we present Maude as an executable semantic framework by providing easy-tool-building techniques for a language given its operational semantics.Research supported by CICYT projects Desarrollo Formal de Sistemas Distribuidos (TIC97-0669-C03-01) and Desarrollo Formal de Sistemas Basados en Agentes Móviles (TIC2000-0701-C02-01).     

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.     

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.     

An initial algebra approach to term rewriting systems with variable binders

We present an extension of first-order term rewriting systems. It involves variable binding in the term language. We develop systems called binding term rewriting systems (BTRSs) in a stepwise manner. First we present the term language, then formulate equational logic. Finally, we define rewriting systems. This development is novel because we follow the initial algebra approach in an extended notion of Σ-algebras in various functor categories. These are based on Fiore-Plotkin-Turi’s presheaf semantics of variable binding and Lüth-Ghani’s monadic semantics of term rewriting systems. We characterise the terms, equational logic and rewrite systems for BTRSs as initial algebras in suitable categories. Then, we show an important rewriting property of BTRSs: orthogonal BTRSs are confluent. Moreover, by using the initial algebra semantics, we give a complete characterisation of termination of BTRSs. Finally, we discuss our design choice of BTRSs from a semantic perspective. An erlier version appeared in Proc. Fifth ACM-SIGPLAN International Conference on Principles and Practice of Declarative Programming (PPDP2003).     

一种面向构件的行为语义模型及其应用研究

以SOFA/CDL作为刻画动态行为的形式化语义基础,从交互语义层面入手,提出面向SMC(softMancomponent)构件的行为描述语言(BDL);同时,针对CDL在行为刻画上的不足进行扩展,给出了针对SMC的行为描述框架。在此基础上,选取典型的构件动态替换作为应用背景,得到基于BDL表达的构件上下文无关替换定义及其判定定理,验证了上述模型在构件行为语义抽象中的有效性和正确性。     

Abduction in logic programming: A new definition and an abductive procedure based on rewriting

A long outstanding problem for abduction in logic programming has been on how minimality might be defined. Without minimality, an abductive procedure is often required to generate exponentially many subsumed explanations for a given observation. In this paper, we propose a new definition of abduction in logic programming where the set of minimal explanations can be viewed as a succinct representation of the set of all explanations. We then propose an abductive procedure where the problem of generating explanations is formalized as rewriting with confluent and terminating rewrite systems. We show that these rewrite systems are sound and complete under the partial stable model semantics, and sound and complete under the answer set semantics when the underlying program is so-called odd-loop free. We discuss an application of abduction in logic programming to a problem in reasoning about actions and provide some experimental results.     

A logical approach to multilevel security of probabilistic systems

Summary. We set out a modal logic for reasoning about multilevel security of probabilistic systems. This logic contains expressions for time, probability, and knowledge. Making use of the Halpern-Tuttle framework for reasoning about knowledge and probability, we give a semantics for our logic and prove it is sound. We give two syntactic definitions of perfect multilevel security and show that their semantic interpretations are equivalent to earlier, independently motivated characterizations. We also discuss the relation between these characterizations of security and between their usefulness in security analysis.     

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.     

Mobile Objects as Mobile Processes

Obliq is a lexically scoped, distributed, object-based programming language. In Obliq, the migration of an object is proposed as creating a clone of the object at the target site, whereafter the original object is turned into an alias for the clone. Obliq has only an informal semantics, so there is no proof that this style of migration is safe, i.e., transparent to object clients. In previous work, we introduced Ø, an abstraction of Obliq, where, by lexical scoping, sites have been abstracted away. We used Ø in order to exhibit how the semantics behind Obliq's implementation renders migration unsafe. We also suggested a modified semantics that we conjectured instead to be safe. In this paper, we rewrite our modified semantics of Ø in terms of the π-calculus, and we use it to formally prove the correctness of object surrogation, the abstraction of object migration in Ø.     

Ontology and rule-based natural language processing approach for interpreting textual regulations on underground utility infrastructure

The nation’s massive underground utility infrastructure must comply with a multitude of regulations. The regulatory compliance checking of underground utilities requires an objective and consistent interpretation of the regulations. However, utility regulations contain a variety of domain-specific terms and numerous spatial constraints regarding the location and clearance of underground utilities. It is challenging for the interpreters to understand both the domain and spatial semantics in utility regulations. To address the challenge, this paper adopts an ontology and rule-based Natural Language Processing (NLP) framework to automate the interpretation of utility regulations – the extraction of regulatory information and the subsequent transformation into logic clauses. Two new ontologies have been developed. The urban product ontology (UPO) is domain-specific to model domain concepts and capture domain semantics on top of heterogeneous terminologies in utility regulations. The spatial ontology (SO) consists of two layers of semantics – linguistic spatial expressions and formal spatial relations – for better understanding the spatial language in utility regulations. Pattern-matching rules defined on syntactic features (captured using common NLP techniques) and semantic features (captured using ontologies) were encoded for information extraction. The extracted information elements were then mapped to their semantic correspondences via ontologies and finally transformed into deontic logic (DL) clauses to achieve the semantic and logical formalization. The approach was tested on the spatial configuration-related requirements in utility accommodation policies. Results show it achieves a 98.2% precision and a 94.7% recall in information extraction, a 94.4% precision and a 90.1% recall in semantic formalization, and an 83% accuracy in logical formalization.     

Mechanizing CSP trace theory in higher order logic

How a mechanized tool for reasoning about CSP (communicating sequential processes) can be developed by customizing an existing general-purpose theorem prover based on higher-order logic is described. How the trace semantics of CSP operators can be mechanized in higher-order logic is investigated, and how the laws associated with these operators can be proved from their semantic definitions is shown. The resulting system is one in which natural-deduction style proofs can be conducted using the standard CSP laws     

Uniform semantic treatment of default and autoepistemic logics

We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs. For each logic, we introduce a monotone operator on the lattice of belief pairs. We then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator (or as fixpoints of certain closely related operators). Our approach elucidates fundamental constructive principles in which agents form their belief sets, and leads to approximation semantics for autoepistemic and default logics. It also allows us to establish a precise one-to-one correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic. The correspondence exploits the modal interpretation of a default proposed by Konolige. Our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic, a result that has been long anticipated. At the same time, they explain the source of the difficulty to formally relate the semantics of default extensions by Reiter and autoepistemic expansions by Moore. These two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics.     

基于重写技术的语义Web服务研究

随着对Web服务的不断深入研究和应用,出于各种服务自动化任务的需要,语义Web服务逐渐成为学术界的研究热点。可以看出这些研究大都基于服务单个操作级别的语义进行推理,而对于多个操作之间的语义联系却很少涉及。提出Web服务的重写模型,通过为Web服务添加操作之间的重写规则语义,将Web服务建模为服务重写系统,利用重写技术中的推理机制,实现对Web服务的分析和挖掘。这个方法可应用于服务的QoS优化,以及服务的组合与融合等方面。