Elimination of Negation in a Logical Framework

Momigliano, Alberto

doi:10.1007/3-540-44622-2_28

Cited by 12 publications

(18 citation statements)

References 82 publications

(127 reference statements)

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“…The proof, by mutual induction on the derivation of Γ : ∆; ∇ ⇒ G and Γ : ∆; ∇ D −→ p(t), follows the lines in [30]. Completeness can be stated as follows: if a goal G finitely fails from a program D, then its complement NotG(G) should be provable from Not D (D).…”

Section: It Is Not the Case Thatmentioning

confidence: 99%

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Mechanized metatheory model-checking

Cheney

Momigliano

2007

Proceedings of the 9th ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming

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The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual problem of searching for errors in such formalizations has received comparatively little attention. In this paper, we consider the problem of bounded model-checking for metatheoretic properties of formal systems specified using nominal logic. In contrast to the current state of the art for metatheory verification, our approach is fully automatic, does not require expertise in theorem proving on the part of the user, and produces counterexamples in the case that a flaw is detected. We present two implementations of this technique, one based on negation-as-failure and one based on negation elimination, along with experimental results showing that these techniques are fast enough to be used interactively to debug systems as they are developed.

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Section: It Is Not the Case Thatmentioning

confidence: 99%

“…This approach is also possible (and seems likely to be helpful) in αProlog, but such analyses have not yet been adapted to the setting of nominal logic programming. Conversely, it may also be possible to implement counterexample search in Twelf via negation elimination along the lines of [30].…”

Section: Related Workmentioning

confidence: 99%

Mechanized metatheory model-checking

Cheney

Momigliano

2007

Proceedings of the 9th ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming

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“…This may explain why they restricted to linear terms and studied if these types of expressions have an equivalent representation using disjunctions. Actually, complementing non-linear terms was not very much addressed (except for disunification) and standard algorithms that computes complements are incorrect for non-linear terms, as mentioned in [18]. Complementing higher order patterns is also considered only in the linear case.…”

Section: Related Workmentioning

confidence: 99%

Anti-pattern Matching

Kirchner

Kopetz

Moreau

2007

Programming Languages and Systems

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Abstract. It is quite appealing to base the description of pattern-based searches on positive as well as negative conditions. We would like for example to specify that we search for white cars that are not station wagons.To this end, we define the notion of anti-patterns and their semantics along with some of their properties. We then extend the classical notion of matching between patterns and ground terms to matching between anti-patterns and ground terms. We provide a rule-based algorithm that finds the solutions to such problems and prove its correctness and completeness. Anti-pattern matching is by nature different from disunification and quite interestingly the anti-pattern matching problem is unitary. Therefore the concept is appropriate to ground a powerful extension to pattern-based programming languages and we show how this is used to extend the expressiveness and usability of the Tom language.

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“…In this paper we have provided algorithms to compute both. A full development for the higher-order case can be found in [Momigliano 2000a]. …”

Section: The Algebra Of Linear Simple Patternsmentioning

confidence: 99%

Higher-order pattern complement and the strict λ-calculus

Momigliano

Pfenning

2003

ACM Trans. Comput. Logic

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We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a finite set of patterns. We therefore generalize the simplytyped λ-calculus to include an internal notion of strict function so that we can directly express that a term must depend on a given variable. We show that, in this more expressive calculus, finite sets of patterns without repeated variables are closed under complement and intersection. Our principal application is the transformational approach to negation in higher-order logic programs.

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Elimination of Negation in a Logical Framework

Cited by 12 publications

References 82 publications

Mechanized metatheory model-checking

Mechanized metatheory model-checking

Anti-pattern Matching

Higher-order pattern complement and the strict λ-calculus

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