Pure type system

Pure type system

In proof and type theory, a pure type system is a form of typed lambda calculus that obscures the distinction between "types" and "terms" and collapses the type hierarchy. It can be seen as a generalisation of Barendregt's lambda cube, and therefore serves as a uniform logical framework for studying type systems. Intuitionistic pure type systems were first described by Barendregt, [cite book|editor=S. Abramsky, D. Gabbay and T. Maibaum|author=H. Barendregt|chapter=Lambda calculi with types|chapterurl=ftp://ftp.cs.ru.nl/pub/CompMath.Found/HBK.ps|title=Handbook of Logic in Computer Science|publisher=Oxford Science Publications|year=1992] and the formalism was extended to classical logics via control operators by Barthe "et al". [cite journal|author=G. Barthe|coauthors=J. Hatcliff; M. H. Sørensen|title=A Notion of Classical Pure Type System|url=ftp://ftp-sop.inria.fr/everest/personnel/Gilles.Barthe/mfps97.ps.gz|journal=Mathematical Foundations of Programming Semantics|volume=6|year=1997|editor=S. Brookes, M. Main, A. Melton and M. Mislove]

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