This paper formalises within first-order logic some common practices in computer science to do with representing and reasoning about syntactical structures involving named bound variables (as opposed to nameless terms, explicit substitutions, or higher order abstract syntax). It introduces Nominal Logic, a version of first-order many-sorted logic with equality containing primitives for renaming via name-swapping and for freshness of names, from which a notion of binding can be derived. Its axioms express...

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

. This paper describes the design of a meta-logical framework that supports the representation and verication of deductive systems which are prevalent in the areas of programming languages, type theory, and logics. It extends the logical framework LF [HHP93] by a meta-logic M + 2 whose soundness follows from a realizability argument. The metalogical framework is implemented in the Twelf system [PS99]. 1 Introduction The logical framework LF [HHP93] has been designed as a meta-language for representing deductive systems. It allows concise encodings of many inference systems, such as natural deduction, sequent calculi, type systems, operational semantics, compilers, etc. The logical framework derives its expressive power from dependent types together with higher-order representation techniques which directly support common concepts in deductive systems such as variable binding, capture-avoiding substitutions, parametric and hypothetical judgments and substitution properties. Th...