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Membership Algebra as a Logical Framework for Equational Specification
, 1998
"... This paper proposes membership equational logica Horn logic in which the basic predicates are equations t = t 0 and membership assertions t : s stating that a term t belongs to a sort sas a logical framework in which a very wide range of total and partial equational specification formalisms ..."
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Cited by 177 (57 self)
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This paper proposes membership equational logica Horn logic in which the basic predicates are equations t = t 0 and membership assertions t : s stating that a term t belongs to a sort sas a logical framework in which a very wide range of total and partial equational specification formalisms can be naturally represented. Key features of this logic include: simplicity, liberality and equational character; generality and expressiveness in supporting subsorts, overloading, errors and partiality; and efficient implementability in systems such as Maude. The paper presents the basic properties of the logic and its models, and discusses in detail how many total and partial equational specification formalisms, including ordersorted algebra and partial membership equational logic, can be represented in it, as well as the practical benefits in terms of tool reusability that this opens up for other languages, including CASL.
Categorical Logic
 A CHAPTER IN THE FORTHCOMING VOLUME VI OF HANDBOOK OF LOGIC IN COMPUTER SCIENCE
, 1995
"... ..."
Equivalences among Various Logical Frameworks of Partial Algebras
 Computer Science Logic. 9th Workshop, CSL'95. Paderborn
, 1996
"... We examine a variety of liberal logical frameworks of partial algebras. Therefore we use simple, conjunctive and weak embeddings of institutions which preserve model categories and may map sentences to sentences, finite sets of sentences, or theory extensions using unique existential quantifiers, re ..."
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We examine a variety of liberal logical frameworks of partial algebras. Therefore we use simple, conjunctive and weak embeddings of institutions which preserve model categories and may map sentences to sentences, finite sets of sentences, or theory extensions using unique existential quantifiers, respectively. They faithfully represent theories, model categories, theory morphisms, colimit of theories, reducts etc. Moreover, along simple and conjunctive embeddings, theorem provers can be reused in a way that soundness and completeness is preserved. Our main result states the equivalence of all the logical frameworks with respect to weak embeddability. This gives us compilers between all frameworks. Thus it is a chance to unify the different branches of specification using liberal partial logics. This is important for reaching the goal of formal interoperability of different specification languages for software development. With formal interoperability, a specification can contain part...
Different Types of Arrow Between Logical Frameworks
 Proc. ICALP 96, LNCS 1099, 158169
, 1996
"... this paper we argue that these different types of arrow can be generated by one basic type of arrow and monadic constructions on categories of logical frameworks, with the effect of automatically having functors relating the new categories of logical frameworks with the old ones. The paper is organi ..."
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Cited by 7 (2 self)
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this paper we argue that these different types of arrow can be generated by one basic type of arrow and monadic constructions on categories of logical frameworks, with the effect of automatically having functors relating the new categories of logical frameworks with the old ones. The paper is organized as follows: in Sect. 2, some types of logical framework and some categorical notions are recalled. Section 3 then introduces, using monads and adjunctions, one wellknown and three new notions of maps between institutions, which vary in the strictness of keeping the signaturesentence distinction. In each case, we briefly show the application to different logical frameworks. Section 4 concludes the paper. Due to lack of space, we omit proofs, which will appear elsewhere. 2 Preliminaries
Proving Semantical Equivalence of Data Specifications
 J. Pure and Applied Algebra
, 2005
"... More than two decades ago, Peter Freyd introduced essentially algebraic specifications, a wellbehaved generalization of algebraic specifications, allowing for equational partiality. These essentially algebraic specifications turn out to have a number of very interesting applications in computer ..."
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More than two decades ago, Peter Freyd introduced essentially algebraic specifications, a wellbehaved generalization of algebraic specifications, allowing for equational partiality. These essentially algebraic specifications turn out to have a number of very interesting applications in computer science.
Parameterized Recursion Theory  A Tool for the Systematic Classification of Specification Methods
 Proceedings of the Third International Conference on Algebraic Methodology and Software Technology, 1993, Workshops in Computing
"... We examine four specification methods with increasing expressiveness. Parameterized recursion theory allows to characterize the power of parameterization in the methods, using a computational model based on Moschovakis' search computability. The four specification methods can be characterized b ..."
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Cited by 3 (2 self)
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We examine four specification methods with increasing expressiveness. Parameterized recursion theory allows to characterize the power of parameterization in the methods, using a computational model based on Moschovakis' search computability. The four specification methods can be characterized by four different notions of semicomputable parameterized abstract data type, which differ in the availability of the parameter algebra and of nondeterminism. These characterizations further lead to different algebraic properties of specifiable PADTs. Together with example PADTs, they enable us to prove a hierarchy theorem. Given a sample PADT, the algebraic properties help to find out the lowest position (= most restricted method) in the hierarchy usable to specify it. This is important because the available tools may become weaker, if we choose a too general method.
Specification and Proof in Membership Equational Logic1
"... Abstract: This paper is part of a longterm effort to increase expressiveness of algebraic specification languages while at the same time having a simple semantic foundation on which efficient execution by rewriting and powerful theoremproving tools can be based. In particular, our rewriting techni ..."
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Abstract: This paper is part of a longterm effort to increase expressiveness of algebraic specification languages while at the same time having a simple semantic foundation on which efficient execution by rewriting and powerful theoremproving tools can be based. In particular, our rewriting techniques provide semantic foundations for Maude's functional sublanguage, where they have been efficiently implemented. This effort started in the late seventies, led by the ADJ group, who promoted equational logic and universal algebra as the semantic basis of program specification languages. An important later milestone was the work around ordersorted algebras and the OBJ family of languages developed at SRIInternational in the eighties. This effort has been substantially advanced in the midnineties with the development of Maude, a language based on membership equational logic. Membership equational logic is quite simple, and yet quite powerful. Its atomic formulae are equations and sort membership assertions, and its sentences are Horn clauses. It extends in a conservative way both (a version of) ordersorted equational logic and partial algebra approaches, while Horn logic with equality can be very easily encoded.