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Abstract: Injective Pure Type Systems form a large class of Pure Type Systems for which one can compute by purely syntactic means two sorts elmt(\GammajM ) and sort(\GammajM ), where \Gamma is a pseudo-context and M is a pseudo-term, and such that for every sort s, \Gamma ` M : A \Gamma ` A : s ) elmt(\GammajM ) = s \Gamma ` M : s ) sort(\GammajM ) = s By eliminating the problematic clause in the (abstraction) rule in favor of constraints over elmt(:j:) and sort(:j:), we provide a sound and complete... (Update)
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...rules is an open problem. For a full analysis of the problems with a proof of the completeness of Pollack s rules see [17] Barthe s [4] solution to Pollack s problem is to formulate a new (abs) rule, based on the so called classification algorithm, and to distribute the (conv)...
...completeness of the algorithm. Finally there are other algorithms that are concerned with the smaller class of (weakly) injective PTSs [2, 6]. These algorithms are simpler but do not cover all existing systems. For example some of the languages of the Automath family [4] and...
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BibTeX entry: (Update)
Gilles Barthe. Type-checking injective pure type systems. Journal of Functional Programming, 9(6):675--698, November 1999. http://citeseer.ist.psu.edu/barthe93typechecking.html More
@article{ barthe99typechecking,
author = "Gilles Barthe",
title = "Type-checking injective pure type systems",
journal = "Journal of Functional Programming",
volume = "9",
number = "6",
pages = "685-698",
year = "1999",
url = "citeseer.ist.psu.edu/barthe93typechecking.html" }
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