Lazy AC-Pattern Matching for Rewriting

We define a lazy pattern-matching mechanism modulo associativity and commutativity. The solutions of a pattern-matching problem are stored in a lazy list composed of a first substitution at the head and a non-evaluated object that encodes the remaining computations. We integrate the lazy AC-matching in a strategy language: rewriting rule and strategy application produce a lazy list of terms.Comment: In Proceedings WRS 2011, arXiv:1204.531

A Symbolic Transformation Language and its Application to a Multiscale Method

The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale methods approximate it by another partial differential equation which can be numerically simulated in a reasonable time. The challenge consists in taking into account a wide range of geometries combining thin and periodic structures with the possibility of multiple nested scales. In this paper we present a transformation language that will make the development of MEMSALab more feasible. It is proposed as a Maple package for rule-based programming, rewriting strategies and their combination with standard Maple code. We illustrate the practical interest of this language by using it to encode two examples of multiscale derivations, namely the two-scale limit of the derivative operator and the two-scale model of the stationary heat equation.Comment: 36 page

Maude: specification and programming in rewriting logic

Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude

Propositional Encoding of Constraints over Tree-Shaped Data

We present a functional programming language for specifying constraints over tree-shaped data. The language allows for Haskell-like algebraic data types and pattern matching. Our constraint compiler CO4 translates these programs into satisfiability problems in propositional logic. We present an application from the area of automated analysis of (non-)termination of rewrite systems

Knowledge-infused and Consistent Complex Event Processing over Real-time and Persistent Streams

Emerging applications in Internet of Things (IoT) and Cyber-Physical Systems (CPS) present novel challenges to Big Data platforms for performing online analytics. Ubiquitous sensors from IoT deployments are able to generate data streams at high velocity, that include information from a variety of domains, and accumulate to large volumes on disk. Complex Event Processing (CEP) is recognized as an important real-time computing paradigm for analyzing continuous data streams. However, existing work on CEP is largely limited to relational query processing, exposing two distinctive gaps for query specification and execution: (1) infusing the relational query model with higher level knowledge semantics, and (2) seamless query evaluation across temporal spaces that span past, present and future events. These allow accessible analytics over data streams having properties from different disciplines, and help span the velocity (real-time) and volume (persistent) dimensions. In this article, we introduce a Knowledge-infused CEP (X-CEP) framework that provides domain-aware knowledge query constructs along with temporal operators that allow end-to-end queries to span across real-time and persistent streams. We translate this query model to efficient query execution over online and offline data streams, proposing several optimizations to mitigate the overheads introduced by evaluating semantic predicates and in accessing high-volume historic data streams. The proposed X-CEP query model and execution approaches are implemented in our prototype semantic CEP engine, SCEPter. We validate our query model using domain-aware CEP queries from a real-world Smart Power Grid application, and experimentally analyze the benefits of our optimizations for executing these queries, using event streams from a campus-microgrid IoT deployment.Comment: 34 pages, 16 figures, accepted in Future Generation Computer Systems, October 27, 201

A Semantics of ? into Dedukti

? is a semantical framework for formally describing the semantics of programming languages thanks to a BNF grammar and rewriting rules on configurations. It is also an environment that offers various tools to help programming with the languages specified in the formalism. For example, it is possible to execute programs thanks to the generated interpreter, or to check their properties thanks to the provided automatic theorem prover called the KProver. ? is based on la Matching Logic, a first-order logic with an application and fixed-point operators, extended with symbols to encode equality, typing and rewriting. This specific la Matching Logic theory is called Kore. Dedukti is a logical framework having for main goal the interoperability of proofs between different formal proof tools. Several translators to Dedukti exist or are under development, in order to automatically translate formalizations written, for instance, in Coq or PVS. Dedukti is based on the ??-calculus modulo theory, a ?-calculus with dependent types and extended with a primitive notion of computation defined by rewriting rules. The flexibility of this logical framework allows to encode many theories ranging from first-order logic to the Calculus of Constructions. In this article, we present a paper formalization of the translation from ? into Kore, and a paper formalization and an automatic translation tool, called KaMeLo, from Kore to Dedukti in order to execute programs in Dedukti