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An institutional view on categorical logic and the CurryHowardTaitisomorphism
"... We introduce a generic notion of propositional categorical logic and provide a construction of an institution with proofs out of such a logic, following the CurryHowardTait paradigm. We then prove logicindependent soundness and completeness theorems. The framework is instantiated with a number ..."
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We introduce a generic notion of propositional categorical logic and provide a construction of an institution with proofs out of such a logic, following the CurryHowardTait paradigm. We then prove logicindependent soundness and completeness theorems. The framework is instantiated with a number of examples: classical, intuitionistic, linear and modal propositional logics. Finally, we speculate how this framework may be extended beyond the propositional case.
Combining specification formalisms in the 'general logic' of multialgebras
, 2003
"... We recall basic facts about the institution of multialgebras, and introduce a new, quantifierfree reasoning system for deriving consequences of multialgebraic specifications. We then show how can be used for combining specifications developed in other algebraic frameworks. We spell out the defi ..."
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We recall basic facts about the institution of multialgebras, and introduce a new, quantifierfree reasoning system for deriving consequences of multialgebraic specifications. We then show how can be used for combining specifications developed in other algebraic frameworks. We spell out the definitions of embeddings of institution of partial algebras, and membership algebras, MA.
Modeling Partiality By Nondeterminism  From Specifications to Flexible Error Handling
, 1999
"... The paper presents a new way to model partial operations by use of nondeterminism: a partial operation is modeled as a nondeterministic operation returning, possibly, any value of the carrier. We introduce an institution of multialgebras MA (modelling nondeterministic operations by setvalued functi ..."
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The paper presents a new way to model partial operations by use of nondeterminism: a partial operation is modeled as a nondeterministic operation returning, possibly, any value of the carrier. We introduce an institution of multialgebras MA (modelling nondeterministic operations by setvalued functions) and illustrate the flexibility of our approach by examples showing uniform treatment of strictness, nonstrictness and various error handling. We present a methodology for specification development from an abstract specification to low level error handling. We also study the conditions for MA specifications to ensure the existence of initial models. Finally we relate MA to other institutions, in particular, we show embedding of partial algebras and membership algebras into MA. Applying institution transformation instead of embedding leads to the possibility of resuing partial algebra specifications in the proposed framework  a partial algebra specification can be conservatively (prese...
The Common Framework Initiative for algebraic specification and development of software
, 1999
"... . The Common Framework Initiative (CoFI) is an open international collaboration which aims to provide a common framework for algebraic specification and development of software. The central element of the Common Framework is a specification language called Casl for formal specification of functiona ..."
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. The Common Framework Initiative (CoFI) is an open international collaboration which aims to provide a common framework for algebraic specification and development of software. The central element of the Common Framework is a specification language called Casl for formal specification of functional requirements and modular software design which subsumes many previous algebraic specification languages. This paper is a brief summary of past and present work on CoFI. 1 Introduction Algebraic specification is one of the most extensivelydeveloped approaches in the formal methods area. The most fundamental assumption underlying algebraic specification is that programs are modelled as manysorted algebras consisting of a collection of sets of data values together with functions over those sets. This level of abstraction is commensurate with the view that the correctness of the input/output behaviour of a program takes precedence over all its other properties. Another common element is tha...
Algebraic System Specification and Development: Survey and Annotated Bibliography  Second Edition 
, 1997
"... Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . ..."
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Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.2 Action Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.7 Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.1 Early Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.2 Recent Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . 55 4.7.3 The Common Framework Initiative. . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5 Methodology 57 5.1 Development Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1 Applica...
Subsorted Partial HigherOrder Logic as an Extension of CASL
"... Casl provides constructs for writing structured requirement and design specifications as well as architectural specifications. Basic Casl specifications consist of declarations and axioms representing theories of a firstorder logic in which predicates, total as well as partial functions, and subsor ..."
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Casl provides constructs for writing structured requirement and design specifications as well as architectural specifications. Basic Casl specifications consist of declarations and axioms representing theories of a firstorder logic in which predicates, total as well as partial functions, and subsorts are allowed. Predicate and function symbols may be overloaded.
Specifying, Programming and Verifying with Equational Logic
"... 1 Introduction Programming is difficult, as shown by the fact that debugging a program usually takes more time than creating it; moreover, the difficulty of debugging increases nonlinearly with program size. One reason for such phenomena is the astonishing complexity and subtlety of the semantics o ..."
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1 Introduction Programming is difficult, as shown by the fact that debugging a program usually takes more time than creating it; moreover, the difficulty of debugging increases nonlinearly with program size. One reason for such phenomena is the astonishing complexity and subtlety of the semantics of most widely used programming languages, due mainly to the desire for high efficiency on conventional processors. But rapid increases in the power and flexibility of hardware, and in the need for greater reliability and security in applications, suggest that it may be valuable to consider alternative approaches, based on higher level languages with much simpler semantics, despite the undoubted inertia of tradition, and the difficulty of learning new languages and new paradigms. This paper focuses on the OBJ family of languages, which have semantics based on various extensions of (first order) equational logic. The OBJ languages are logical programming languages, in which programs are theories, and computation is deduction, which makes it possible to do specification, programming and verification in a unified framework. This paper is mainly intended to introduce and motivate the material that it covers, rather than to provide a thorough mathematical exposition. Consequently, there are many references and several examples, but all proofs and many technical details are omitted.