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A Comparison of Formalizations of the MetaTheory of a Language with Variable Bindings in Isabelle
 Supplemental Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
, 2001
"... Abstract. Theorem provers can be used to reason formally about programming languages and there are various general methods for the formalization of variable binding operators. Hence there are choices for the style of formalization of such languages, even within a single theorem prover. The choice of ..."
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Abstract. Theorem provers can be used to reason formally about programming languages and there are various general methods for the formalization of variable binding operators. Hence there are choices for the style of formalization of such languages, even within a single theorem prover. The choice of formalization can affect how easy or difficult it is to do automated reasoning. The aim of this paper is to compare and contrast three formalizations (termed de Bruijn, weak HOAS and full HOAS) of a typical functional programming language. Our contribution is a detailed report on our formalizations, a survey of related work, and a final comparative summary, in which we mention a novel approach to a hybrid de Bruijn/HOAS syntax. 1
Completeness of Bisimilarity for Contextual Equivalence in Linear Theories
"... In this paper, we develop new variations of methods from operational semantics, and show how to apply these to a linear type theory which has a lazy operational semantics. In particular, we consider how one can establish contextual equivalences in a linear theory with function types and tensor types ..."
Abstract

Cited by 5 (1 self)
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In this paper, we develop new variations of methods from operational semantics, and show how to apply these to a linear type theory which has a lazy operational semantics. In particular, we consider how one can establish contextual equivalences in a linear theory with function types and tensor types by instead establishing bisimulations. Thus bisimilarity is sound for contextual equivalence. Further, we show that bisimilarity is complete for contextual equivalence.