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12
Relating CASL with Other Specification Languages: the Institution Level
, 2000
"... In this work, we investigate various specification languages and their relation to Casl, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3, CafeOBJ, ACT ONE, ASF, and HEPtheories, as well as various sublanguages of Casl that more or ..."
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Cited by 34 (16 self)
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In this work, we investigate various specification languages and their relation to Casl, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3, CafeOBJ, ACT ONE, ASF, and HEPtheories, as well as various sublanguages of Casl that more or less directly correspond to these. All these languages are translated to an appropriate sublanguage of Casl. The translation mainly concerns the level of specification inthesmall: the logics underlying the languages are formalized as institutions, and representations among the institutions are developed. However, it is also considered how these translations interact with specification inthelarge. Thus, we obtain one hand translations of any of the abovementioned specification languages to an appropriate sublanguage of Casl. This allows us to take libraries and case studies that have been developed for other languages and reuse them in Casl. On the other hand, we set up institution repre...
Static Semantic Analysis and Theorem Proving for CASL
 In F. ParisiPresicce (Ed.): Recent Trends in Algebraic Development Techniques
, 1998
"... . This paper presents a static semantic analysis for CASL, the Common Algebraic Specification Language. Abstract syntax trees are generated including subsorts and overloaded functions and predicates. The static semantic analysis, through the implementation of an overload resolution algorithm, checks ..."
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Cited by 22 (12 self)
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. This paper presents a static semantic analysis for CASL, the Common Algebraic Specification Language. Abstract syntax trees are generated including subsorts and overloaded functions and predicates. The static semantic analysis, through the implementation of an overload resolution algorithm, checks and qualifies these abstract syntax trees. The result is a fully qualified CASL abstract syntax tree where the overloading has been resolved. This abstract syntax tree corresponds to a theory in the institution underlying CASL, subsorted partial firstorder logic with sort generation constraints (SubPCFOL). Two ways of embedding SubPCFOL in higherorder logic (HOL) of the logical framework Isabelle are discussed: the first one from SubPFOL to HOL via PFOL (partial firstorder logic) first drops subsorting and then partiality, and the second one is the counterpart via SubFOL (subsorted firstorder logic). The C in SubPCFOL stands for sort generation constraints, which are translated separat...
Relating Semantic and ProofTheoretic Concepts for Polynomial Time Decidability of Uniform Word Problems
 In Proceedings 16th IEEE Symposium on Logic in Computer Science, LICS'2001
, 2001
"... In this paper we compare three approaches to polynomial time decidability for uniform word problems for quasivarieties. Two of the approaches, by Evans and Burris, respectively, are semantical, referring to certain embeddability and axiomatizability properties. The third approach is more prooftheor ..."
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Cited by 22 (2 self)
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In this paper we compare three approaches to polynomial time decidability for uniform word problems for quasivarieties. Two of the approaches, by Evans and Burris, respectively, are semantical, referring to certain embeddability and axiomatizability properties. The third approach is more prooftheoretic in nature, inspired by McAllester's concept of local inference. We define two closely related notions of locality for equational Horn theories and show that both the criteria by Evans and Burris lie in between these two concepts. In particular, the variant we call stable locality will be shown to subsume both Evans' and Burris' method.
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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Cited by 17 (7 self)
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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...
Using Limits of Parchments to Systematically Construct Institutions of Partial Algebras
 Recent Trends in Data Type Specifications. 11th Workshop on Specification of Abstract Data Types, volume 1130 of Lecture Notes in Computer Science
, 1996
"... this paper, so we leave them out here. Thus we can apply the idea of combining things via colimits to institutions themselves, with the special point that we have to take limits here instead of colimits. Taking limits in CAT results in categories of "amalgamated objects", i. e. we put signatures an ..."
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Cited by 15 (5 self)
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this paper, so we leave them out here. Thus we can apply the idea of combining things via colimits to institutions themselves, with the special point that we have to take limits here instead of colimits. Taking limits in CAT results in categories of "amalgamated objects", i. e. we put signatures and models together at the level of single objects. In contrast to this, sentences are combined with colimits in Set (due to the contravariant direction of the sentence component). That is, sets of sentences are combined. To show how this works, we introduce some wellknown institutions and morphisms between them.
Combining and Representing Logical Systems
, 1997
"... The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the modeltheoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic ..."
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Cited by 12 (3 self)
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The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the modeltheoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic way of presenting institutions). We propose a modified notion of parchment together with a notion of parchment morphism and representation, respectively. We lift formal properties of the categories of institutions and their representations to this level: the category of parchments is complete, and parchment representations may be put together using categorical limits as well. However, parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessary invention for proper combination of various logical features may be introduced either on an ad hoc basis (when putting parchments together using limits in the cat...
Moving Specification Structures Between Logical Systems
 13th WADT’98
, 1998
"... The conditions under which a formal system for reasoning about structural specifications, built over one logical system could be reused for reasoning about structured specifications built over another logical system are formulated and studied. Following Goguen and Burstall, the notion of a logical s ..."
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Cited by 10 (1 self)
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The conditions under which a formal system for reasoning about structural specifications, built over one logical system could be reused for reasoning about structured specifications built over another logical system are formulated and studied. Following Goguen and Burstall, the notion of a logical system is formalized as an institution and extended to a Dinstitution. A new function between classes of specifications, inspired by a similar function from [HST 94], is defined as a natural extension of institution representations to structured specifications. 1
Representations, Hierarchies, and Graphs of Institutions
, 1996
"... For the specification of abstract data types, quite a number of logical systems have been developed. In this work, we will try to give an overview over this variety. As a prerequisite, we first study notions of {\em representation} and embedding between logical systems, which are formalized as {\em ..."
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Cited by 5 (4 self)
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For the specification of abstract data types, quite a number of logical systems have been developed. In this work, we will try to give an overview over this variety. As a prerequisite, we first study notions of {\em representation} and embedding between logical systems, which are formalized as {\em institutions} here. Different kinds of representations will lead to a looser or tighter connection of the institutions, with more or less good possibilities of faithfully embedding the semantics and of reusing proof support. In the second part, we then perform a detailed ``empirical'' study of the relations among various wellknown institutions of total, ordersorted and partial algebras and firstorder structures (all with Horn style, i.e.\ universally quantified conditional, axioms). We thus obtain a {\em graph} of institutions, with different kinds of edges according to the different kinds of representations between institutions studied in the first part. We also prove some separation results, leading to a {\em hierarchy} of institutions, which in turn naturally leads to five subgraphs of the above graph of institutions. They correspond to five different levels of expressiveness in the hierarchy, which can be characterized by different kinds of conditional generation principles. We introduce a systematic notation for institutions of total, ordersorted and partial algebras and firstorder structures. The notation closely follows the combination of features that are present in the respective institution. This raises the question whether these combinations of features can be made mathematically precise in some way. In the third part, we therefore study the combination of institutions with the help of socalled parchments (which are certain algebraic presentations of institutions) and parchment morphisms. The present book is a revised version of the author's thesis, where a number of mathematical problems (pointed out by Andrzej Tarlecki) and a number of misuses of the English language (pointed out by Bernd KriegBr\"uckner) have been corrected. Also, the syntax of specifications has been adopted to that of the recently developed Common Algebraic Specification Language {\sc Casl} \cite{CASL/Summary,Mosses97TAPSOFT}.
Generalized Interpolation in CASL
 Information Processing Letter, 76:19–24
, 2000
"... In this paper we consider the partial manysorted firstorder logic and its extension to the subsorted partial manysorted firstorder logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not h ..."
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Cited by 4 (0 self)
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In this paper we consider the partial manysorted firstorder logic and its extension to the subsorted partial manysorted firstorder logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not hold for these logics in general (i.e., with respect to arbitrary signature morphisms). Then we formulate conditions under which the generalization of the Craig Interpolation Property holds for the first logic.
A Hierarchy of Institutions Separated By Properties of Parameterized Data Types
, 1995
"... A hierarchy of institutions ranging form equational logic to partial conditional existenceequational logic with relations is built. The different levels of the hierarchy can be separated by properties of parameterized abstract data types. A sample parameterized abstract data type, bounded stacks, i ..."
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Cited by 4 (1 self)
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A hierarchy of institutions ranging form equational logic to partial conditional existenceequational logic with relations is built. The different levels of the hierarchy can be separated by properties of parameterized abstract data types. A sample parameterized abstract data type, bounded stacks, is located within the hierarchy.