Matching Logic

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values that match it), in contrast to FOL where functions and predicates map into a regular domain. Matching logic uniformly generalizes several logical frameworks important for program analysis, such as: propositional logic, algebraic specification, FOL with equality, modal logic, and separation logic. Patterns can specify separation requirements at any level in any program configuration, not only in the heaps or stores, without any special logical constructs for that: the very nature of pattern matching is that if two structures are matched as part of a pattern, then they can only be spatially separated. Like FOL, matching logic can also be translated into pure predicate logic with equality, at the same time admitting its own sound and complete proof system. A practical aspect of matching logic is that FOL reasoning with equality remains sound, so off-the-shelf provers and SMT solvers can be used for matching logic reasoning. Matching logic is particularly well-suited for reasoning about programs in programming languages that have an operational semantics, but it is not limited to this

Functional declarative language design and predicate calculus: A practical approach

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An Open Challenge Problem Repository for Systems Supporting Binders

A variety of logical frameworks support the use of higher-order abstract syntax in representing formal systems; however, each system has its own set of benchmarks. Even worse, general proof assistants that provide special libraries for dealing with binders offer a very limited evaluation of such libraries, and the examples given often do not exercise and stress-test key aspects that arise in the presence of binders. In this paper we design an open repository ORBI (Open challenge problem Repository for systems supporting reasoning with BInders). We believe the field of reasoning about languages with binders has matured, and a common set of benchmarks provides an important basis for evaluation and qualitative comparison of different systems and libraries that support binders, and it will help to advance the field.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759

Modular Composition of Language Features through Extensions of Semantic Language Models

Today, programming or specification languages are often extended in order to customize them for a particular application domain or to refine the language definition. The extension of a semantic model is often at the centre of such an extension. We will present a framework for linking basic and extended models. The example which we are going to use is the RSL concurrency model. The RAISE specification language RSL is a formal wide-spectrum specification language which integrates different features, such as state-basedness, concurrency and modules. The concurrency features of RSL are based on a refinement of a classical denotational model for process algebras. A modification was necessary to integrate state-based features into the basic model in order to meet requirements in the design of RSL. We will investigate this integration, formalising the relationship between the basic model and the adapted version in a rigorous way. The result will be a modular composition of the basic process model and new language features, such as state-based features or input/output. We will show general mechanisms for integration of new features into a language by extending language models in a structured, modular way. In particular, we will concentrate on the preservation of properties of the basic model in these extensions

A Survey of Languages for Specifying Dynamics: A Knowledge Engineering Perspective

A number of formal specification languages for knowledge-based systems has been developed. Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Specification languages for knowledge-based systems have to cover both aspects. They have to provide the means to specify a complex and large amount of knowledge and they have to provide the means to specify the dynamic reasoning behavior of a knowledge-based system. We focus on the second aspect. For this purpose, we survey existing approaches for specifying dynamic behavior in related areas of research. In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (Transaction Logic and Dynamic Database Logic) and the generic specification framework of abstract state machine

Meta SOS - A Maude Based SOS Meta-Theory Framework

Meta SOS is a software framework designed to integrate the results from the meta-theory of structural operational semantics (SOS). These results include deriving semantic properties of language constructs just by syntactically analyzing their rule-based definition, as well as automatically deriving sound and ground-complete axiomatizations for languages, when considering a notion of behavioural equivalence. This paper describes the Meta SOS framework by blending aspects from the meta-theory of SOS, details on their implementation in Maude, and running examples.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

A general conservative extension theorem in process algebras with inequalities

We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc

JWalk: a tool for lazy, systematic testing of java classes by design introspection and user interaction

Popular software testing tools, such as JUnit, allow frequent retesting of modified code; yet the manually created test scripts are often seriously incomplete. A unit-testing tool called JWalk has therefore been developed to address the need for systematic unit testing within the context of agile methods. The tool operates directly on the compiled code for Java classes and uses a new lazy method for inducing the changing design of a class on the fly. This is achieved partly through introspection, using Java’s reflection capability, and partly through interaction with the user, constructing and saving test oracles on the fly. Predictive rules reduce the number of oracle values that must be confirmed by the tester. Without human intervention, JWalk performs bounded exhaustive exploration of the class’s method protocols and may be directed to explore the space of algebraic constructions, or the intended design state-space of the tested class. With some human interaction, JWalk performs up to the equivalent of fully automated state-based testing, from a specification that was acquired incrementally