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A Linear Logical Framework
, 1996
"... We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF c ..."
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Cited by 217 (44 self)
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We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of MiniML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cutelimination. 1 Introduction A logical framework is a formal system desig...
A Fixedpoint Approach to (Co)Inductive and (Co)Datatype Definitions
, 1997
"... This paper presents a fixedpoint approach to inductive definitions. Instead of using a syntactic test such as "strictly positive," the approach lets definitions involve any operators that have been proved monotone. It is conceptually simple, which has allowed the easy implementation of mutual re ..."
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Cited by 20 (2 self)
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This paper presents a fixedpoint approach to inductive definitions. Instead of using a syntactic test such as "strictly positive," the approach lets definitions involve any operators that have been proved monotone. It is conceptually simple, which has allowed the easy implementation of mutual recursion and iterated definitions. It also handles coinductive definitions: simply replace the least fixedpoint by a greatest fixedpoint. The method
A HeadtoHead Comparison of de Bruijn Indices and Names
 In Proc. Int. Workshop on Logical Frameworks and MetaLanguages: Theory and Practice
, 2006
"... Often debates about pros and cons of various techniques for formalising lambdacalculi rely on subjective arguments, such as de Bruijn indices are hard to read for humans or nominal approaches come close to the style of reasoning employed in informal proofs. In this paper we will compare four formal ..."
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Cited by 12 (1 self)
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Often debates about pros and cons of various techniques for formalising lambdacalculi rely on subjective arguments, such as de Bruijn indices are hard to read for humans or nominal approaches come close to the style of reasoning employed in informal proofs. In this paper we will compare four formalisations based on de Bruijn indices and on names from the nominal logic work, thus providing some hard facts about the pros and cons of these two formalisation techniques. We conclude that the relative merits of the different approaches, as usual, depend on what task one has at hand and which goals one pursues with a formalisation.
Tool Support for Logics of Programs
 Mathematical Methods in Program Development: Summer School Marktoberdorf 1996, NATO ASI Series F
, 1996
"... Proof tools must be well designed if they... ..."
Verification of Newman’s and Yokouchi Lemmas in PVS
 Local Proceedings of Logic and Theory of Algorithms, Fourth Conference on Computability in Europe  CiE 2008 (2008
, 2007
"... Abstract. This paper shows how a previously specified theory for Abstract Reduction Systems (ARSs) in which noetherianity was defined by the notion of wellfoundness over binary relations is used in order to prove results such as the wellknown Newman’s Lemma and the Yokouchi’s Lemma. The former one k ..."
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Cited by 2 (2 self)
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Abstract. This paper shows how a previously specified theory for Abstract Reduction Systems (ARSs) in which noetherianity was defined by the notion of wellfoundness over binary relations is used in order to prove results such as the wellknown Newman’s Lemma and the Yokouchi’s Lemma. The former one known as the diamond lemma and the later which states a property of commutation between ARSs. Thears theory was specified in the Prototype Verification System (PVS) for which to the best of our knowledge there are no available theory for dealing with rewriting techniques in general. In addition to proof techniques available in PVS the verification of these lemmas implies an elaborated use of natural as well as noetherian induction. 1.
Noname manuscript No. (will be inserted by the editor) A Solution to the PoplMark Challenge using de Bruijn indices in Isabelle/HOL
"... the date of receipt and acceptance should be inserted later Abstract We present a solution to the PoplMark challenge designed by Aydemir et al., which has as a goal the formalization of the metatheory of System F<:. The formalization is carried out in the theorem prover Isabelle/HOL using an encodi ..."
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the date of receipt and acceptance should be inserted later Abstract We present a solution to the PoplMark challenge designed by Aydemir et al., which has as a goal the formalization of the metatheory of System F<:. The formalization is carried out in the theorem prover Isabelle/HOL using an encoding based on de Bruijn indices. We start with a relatively simple formalization covering only the basic features of System F<:, and explain how it can be extended to also cover records and more advanced binding constructs. We also discuss different styles of formalizing the evaluation relation, and how this choice influences executability of the specification. 1
Author manuscript, published in "Second international conference on Certified Programs and Proofs (2012)" Proof Pearl: Abella Formalization of λCalculus Cube Property
, 2013
"... Abstract. In 1994 Gerard Huet formalized in Coq the cube property of λcalculus residuals. His development is based on a clever idea, a beautiful inductive definition of residuals. However, in his formalization there is a lot of noise concerning the representation of terms with binders. We reinterp ..."
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Abstract. In 1994 Gerard Huet formalized in Coq the cube property of λcalculus residuals. His development is based on a clever idea, a beautiful inductive definition of residuals. However, in his formalization there is a lot of noise concerning the representation of terms with binders. We reinterpret his work in Abella, a recent proof assistant based on higherorder abstract syntax and provided with a nominal quantifier. By revisiting Huet’s approach and exploiting the features of Abella, we get a strikingly compact and natural development, which makes Huet’s idea really shine. 1