Using typed lambda calculus to implement formal systems on a machine

Much research has been devoted in building computer systems for checking proofs or for developing interactively correct proofs in specific logical systems. However, implementing a proof environment for a specific logical system is both complex and time-consuming, this-together with the proliferation of logics-suggests that a uniform and reliable alternative is desirable. One such alternative is the Edinburgh Logical Framework (LF), developed in the late eighties at the LFCS (Laboratory for Foundations of Computer Science). The LF is a logic-independent tool which, given a specification for a logical system, synthesizes a proof editor and checker for that system. Its specification language is based on a general theory of logics, which enables one to capture uniformities and idiosyncrasies of a large class of logics without sacrificing generality for tractability. Peculiarities (such as side conditions on rule application, variable occurrence or formula formation) are expressed at the level of the specification. In this paper we are going to provide a broad illustration of its applicability and discuss to what extent it is successful. The analysis (of the formal presentation) of a system carried out through encoding often illuminates the system itself. This paper will also deal with this phenomenon.