Abstract
Logical frameworks and meta-languages are intended as a common substrate for representing and implementing a wide variety of logics and formal systems. Their definition and implementation have been the focus of considerable work over the last decade. At the heart of this work is a quest for generality: A logical framework provides a basis for capturing uniformities across deductive systems and support for implementing particular systems. Similarly a meta-language supports reasoning about and using languages.Logical frameworks have been based on a variety of different languages including higher-order logics, type theories with dependent types, linear logic, and modal logic. Techniques of representation of logics include higher-order abstract syntax, inductive definitions or some form of equational or rewriting logic in which substitution is explicitly encoded.Examples of systems that implement logical frameworks include Alf, Coq, NuPrl, HOL, Isabelle, Maude, lambda-Prolog and Twelf. An active area of research in such systems is the study of automated reasoning techniques. Current work includes the development of various automated procedures as well as the investigation of rewriting tools that use reflection or make use of links with systems that already have sophisticated rewriting systems. Program extraction and optimization are additional topics of ongoing work.
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