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

Behavioral equivalence of hidden k-logics: an abstract algebraic approach

This work advances a research agenda which has as its main aim the application of Abstract Algebraic Logic (AAL) methods and tools to the specification and verification of software systems. It uses a generalization of the notion of an abstract deductive system to handle multi-sorted deductive systems which differentiate visible and hidden sorts. Two main results of the paper are obtained by generalizing properties of the Leibniz congruence — the central notion in AAL. In this paper we discuss a question we posed in [1] about the relationship between the behavioral equivalences of equivalent hidden logics. We also present a necessary and sufficient intrinsic condition for two hidden logics to be equivalent

"Bagatelle in C arranged for VDM SoLo"

This paper sketches a reverse engineering discipline which combines formal and semi-formal methods. Central to the former is denotational semantics, expressed in the ISO/IEC 13817-1 standard specification language (VDM-SL). This is strengthened with algebra of pro- gramming, which is applied in “reverse order” so as to reconstruct formal specifications from legacy code. The latter include code slicing, a “shortcut” which trims down the complexity of handling the formal semantics of all program variables at the same time. A key point of the approach is its constructive style. Reverse calculations go as far as absorbing auxiliary variables, introducing mutual recursion (if applicable) and reversing semantic denota- tions into standard generic programming schemata such as cata/paramorphisms. The approach is illustrated for a small piece of code already studied in the code-slicing literature: Kernighan and Richtie’s word count C programming “bagatelle”.FC

A Simple and Practical Approach to Unit Testing: The JML and JUnit Way

Writing unit test code is labor-intensive, hence it is often not done as an integral part of programming. However, unit testing is a practical approach to increasing the correctness and quality of software; for example, the Extreme Programming approach relies on frequent unit testing. In this paper we present a new approach that makes writing unit tests easier. It uses a formal specification language\u27s runtime assertion checker to decide whether methods are working correctly, thus automating the writing of unit test oracles. These oracles can be easily combined with hand-written test data. Instead of writing testing code, the programmer writes formal specifications (e.g., pre- and postconditions). This makes the programmer\u27s task easier, because specifications are more concise and abstract than the equivalent test code, and hence more readable and maintainable. Furthermore, by using specifications in testing, specification errors are quickly discovered, so the specifications are more likely to provide useful documentation and inputs to other tools. We have implemented this idea using the Java Modeling Language (JML) and the JUnit testing framework, but the approach could be easily implemented with other combinations of formal specification languages and unit test tools

Logic of fusion

The starting point of this work is the observation that the Curry-Howard isomorphism, relating types and propositions, programs and proofs, composition and cut, extends to the correspondence of program fusion and cut elimination. This simple idea suggests logical interpretations of some of the basic methods of generic and transformational programming. In the present paper, we provide a logical analysis of the general form of build fusion, also known as deforestation, over the inductive and the coinductive datatypes, regular or nested. The analysis is based on a novel logical interpretation of parametricity in terms of the paranatural transformations, introduced in the paper.Comment: 17 pages, 6 diagrams; Andre Scedrov FestSchrif

Maude: specification and programming in rewriting logic

AbstractMaude 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