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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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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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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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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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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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A First-order Logic with Frames
ACM Transactions on Programming Languages and Systems, 2023Adithya Murali +2 more
exaly
The representation of logics in higher-order logic
1987Intuitionistic higher-order logic — the fragment comtaining implication, universal quantification, and equality — can serve as a meta-logic for formalizing various logics. As an example, axioms formalizing first-order logic are presented, and proved sound and complete by induction on proof trees.
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