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Abstract: We present an approach to type theory in which the typing judgments do nothave explicit contexts. Instead of judgments of shape -Gamma |- A : B-, oursystems just have judgments of shape -A : B-. A key feature is that wedistinguish free and bound variables even in pseudo-terms.Specifically we give the rules of the -Pure Type System- class of typetheories in this style. We prove that the typing judgments of these systemscorrespond in a natural way with those of Pure Type Systems as traditionallyformulated. I.e., our systems have exactly the same well-typed terms astraditional presentations of type theory.Our system can be seen as a type theory in which all type judgments share anidentical, infinite, typing context that has infinitely many variables for eachpossible type. For this reason we call our system -Gamma infinity-. This namemeans 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-.



Autor: Herman Geuvers Radboud University Nijmegen, Robbert Krebbers Radboud University Nijmegen, James McKinna Radboud University Nijmeg

Fuente: https://arxiv.org/







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