Abstract

. Two-level #-calculi have been heavily utilised for applications such as partial evaluation, abstract interpretation and code generation. Each of these applications pose di#erent demands on the exact details of the two-level structure and the corresponding inference rules. We therefore formulate a number of existing systems in a common framework. This is done in such a way as to conceal those di#erences between the systems that are not essential for the multi-level ideas (like whether or not one restricts the domain of the type environment to the free identifiers of the expression) and thereby to reveal the deeper similarities and di#erences. In their most general guise the multi-level #-calculi defined here allow multi-level structures that are not restricted to (possibly finite) linear orders and thereby generalise previous treatments in the literature. 1 Introduction The concept of two-level languages is at least a decade old [7, 4] and the concept of multi-level languages at leas...

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