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Recursion principles for syntax with bindings and substitution
 In ICFP
, 2011
"... We characterize the data type of terms with bindings, freshness and substitution, as an initial model in a suitable Horn theory. This characterization yields a convenient recursive definition principle, which we have formalized in Isabelle/HOL and employed in a series of case studies taken from the ..."
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Cited by 5 (4 self)
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We characterize the data type of terms with bindings, freshness and substitution, as an initial model in a suitable Horn theory. This characterization yields a convenient recursive definition principle, which we have formalized in Isabelle/HOL and employed in a series of case studies taken from the λcalculus literature.
Cardinals in Isabelle/HOL
"... Abstract. We report on a formalization of ordinals and cardinals in Isabelle/HOL. A main challenge we faced was the inability of higherorder logic to represent ordinals canonically, as transitive sets (as done in set theory). We resolved this into a “decentralized ” representation identifying ordin ..."
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Abstract. We report on a formalization of ordinals and cardinals in Isabelle/HOL. A main challenge we faced was the inability of higherorder logic to represent ordinals canonically, as transitive sets (as done in set theory). We resolved this into a “decentralized ” representation identifying ordinals with wellorders, with all concepts and results proved to be invariant under order isomorphism. We also discuss several applications of this general theory in formal developments. 1
Mechanizing the Metatheory of Sledgehammer
"... Abstract. This paper presents an Isabelle/HOL formalization of recent research in automated reasoning: efficient encodings of sorts in unsorted firstorder logic, as implemented in Isabelle’s Sledgehammer proof tool. The formalization provides the generalpurpose machinery to reason about formulas a ..."
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Cited by 2 (2 self)
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Abstract. This paper presents an Isabelle/HOL formalization of recent research in automated reasoning: efficient encodings of sorts in unsorted firstorder logic, as implemented in Isabelle’s Sledgehammer proof tool. The formalization provides the generalpurpose machinery to reason about formulas and models, emulating the theory of institutions. It also establishes classical metatheorems such as completeness, compactness, and downward Löwenheim–Skolem. Quantifiers are represented using a nominallike approach designed for interpreting syntax in semantic domains. 1
Towards SelfVerification of Isabelle’s Sledgehammer
"... Abstract. This paper presents an Isabelle/HOL formalisation of recent research in automated reasoning: efficient encodings of sorts in unsorted firstorder logic, as implemented in the Sledgehammer proof tool. The formalisation provides the machinery to reason about models as well as classical metat ..."
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Abstract. This paper presents an Isabelle/HOL formalisation of recent research in automated reasoning: efficient encodings of sorts in unsorted firstorder logic, as implemented in the Sledgehammer proof tool. The formalisation provides the machinery to reason about models as well as classical metatheorems, emulating the theory of institutions. Quantifiers are represented using an approach that avoids some of the tedium and restrictions associated with better known binder representations. Sledgehammer itself has been useful for discharging the proof obligations arising from its own metatheory. 1
TermGeneric Logic
"... We introduce termgeneric logic (TGL), a firstorder logic parameterized with terms defined axiomatically (rather than constructively), by requiring terms to only provide free variable and substitution operators satisfying some reasonable axioms. TGL has a notion of model that generalizes both first ..."
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We introduce termgeneric logic (TGL), a firstorder logic parameterized with terms defined axiomatically (rather than constructively), by requiring terms to only provide free variable and substitution operators satisfying some reasonable axioms. TGL has a notion of model that generalizes both firstorder models and Henkin models of the λcalculus. The abstract notions of term syntax and model are shown to be sufficient for obtaining the completeness theorem of a Gentzen system generalizing that of firstorder logic. Various systems featuring bindings and contextual reasoning, ranging from pure type systems to the picalculus, are captured as theories inside TGL. For two particular, but rather typical instances—untyped λcalculus and System F—the generalpurpose TGL models are shown to be equivalent with standard ad hoc models.