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Higher-Order Transformation of Logic Programs
2001It has earlier been assumed that a compositional approach to algorithm design and program transformation is somehow unique to functional programming. Elegant theoretical results codify the basic laws of algorithmics within the functional paradigm and with this paper we hope to demonstrate that some of the same techniques and results are applicable to ...
Silvija Seres, J. Michael Spivey
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1998
We now introduce the logical basis for program refinement, higher-order logic. This is an extension of the simply typed lambda calculus with logical connectives and quantifiers, permitting logical reasoning about functions in a very general way. In particular, it allows quantification over higher-order entities such as predicates and relations, a ...
Ralph-Johan Back, Joakim Wright
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We now introduce the logical basis for program refinement, higher-order logic. This is an extension of the simply typed lambda calculus with logical connectives and quantifiers, permitting logical reasoning about functions in a very general way. In particular, it allows quantification over higher-order entities such as predicates and relations, a ...
Ralph-Johan Back, Joakim Wright
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1983
What is nowadays the central part of any introduction to logic, and indeed to some the logical theory par excellence, used to be a modest fragment of the more ambitious language employed in the logicist program of Frege and Russell. ‘Elementary’ or ‘first-order’, or ‘predicate logic’ only became a recognized stable base for logical theory by 1930, when
Johan Van Benthem, Kees Doets
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What is nowadays the central part of any introduction to logic, and indeed to some the logical theory par excellence, used to be a modest fragment of the more ambitious language employed in the logicist program of Frege and Russell. ‘Elementary’ or ‘first-order’, or ‘predicate logic’ only became a recognized stable base for logical theory by 1930, when
Johan Van Benthem, Kees Doets
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On Higher-Order Description Logics.
2009We investigate an extension of Description Logics with higher-order capabilities, based on Henkin-style semantics. Our study starts from the observation that the various possibilities of adding higher-order constructs to a DL form a spectrum of increasing expressive power, including domain metamodeling, i.e., using concepts and roles as predicate ...
DE GIACOMO, Giuseppe +2 more
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2005
Abstract The philosophical literature contains numerous claims on behalf of and numerous claims against higher-order logic. Virtually all of the issues apply to second-order logic (vis-à-vis first-order logic), so this article focuses on that.
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Abstract The philosophical literature contains numerous claims on behalf of and numerous claims against higher-order logic. Virtually all of the issues apply to second-order logic (vis-à-vis first-order logic), so this article focuses on that.
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Abstraction and Refinement in Higher Order Logic
2001We develop within higher order logic (HOL) a general and flexible method of abstraction and refinement, which specifically addresses the problem of handling constraints. We provide a HOL interpretation of first-order Lax Logic, which can be seen as a modal extension of deliverables.
Matt Fairtlough +2 more
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1999
The approach presented in this chapter significantly differs from all formalisms presented before. Up to now, all approaches were fully automized based on simple formalisms like FSMs, close to the usual modeling methods of hardware ...
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The approach presented in this chapter significantly differs from all formalisms presented before. Up to now, all approaches were fully automized based on simple formalisms like FSMs, close to the usual modeling methods of hardware ...
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Higher-order abstract syntax in classical higher-order logic
Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice, 2009Higher-Order Abstract Syntax, or HOAS, is a technique for using a higher-order logic as a metalanguage for an object language with binding operators. It avoids formalizing syntactic details related to variable binding. This paper gives an extension to classical higher-order logic that supports HOAS.
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2002
Abstract We now turn from first-order logic to higher-order logic: the principal extra feature of this logic, compared with that which we studied in Chapter D1, is that we have variables running over types whose intended interpretation is the set of all subsets of (the set denoted by) some other type, or the set of all functions between ...
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Abstract We now turn from first-order logic to higher-order logic: the principal extra feature of this logic, compared with that which we studied in Chapter D1, is that we have variables running over types whose intended interpretation is the set of all subsets of (the set denoted by) some other type, or the set of all functions between ...
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1994
Abstract Higher order logics, long considered by many to be an esoteric subject, are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness.
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Abstract Higher order logics, long considered by many to be an esoteric subject, are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness.
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