Herman Geuvers (Radboud University Nijmegen) |
Robbert Krebbers (Radboud University Nijmegen) |
James McKinna (Radboud University Nijmegen) |
Freek Wiedijk (Radboud University Nijmegen) |

We present an approach to type theory in which the typing judgments do not have explicit contexts. Instead of judgments of shape "Gamma |- A : B", our systems just have judgments of shape "A : B". A key feature is that we distinguish free and bound variables even in pseudo-terms.
Specifically we give the rules of the "Pure Type System" class of type theories in this style. We prove that the typing judgments of these systems correspond in a natural way with those of Pure Type Systems as traditionally formulated. I.e., our systems have exactly the same well-typed terms as traditional presentations of type theory. Our system can be seen as a type theory in which all type judgments share an identical, infinite, typing context that has infinitely many variables for each possible type. For this reason we call our system "Gamma_infinity". This name means to suggest that our type judgment "A : B" should be read as "Gamma_infinity |- A : B", with a fixed infinite type context called "Gamma_infinity". |

Published: 11th September 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.34.6 | bibtex | |

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