|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4662874||1345202||2016||29 صفحه PDF||ندارد||دانلود کنید|
There are two versions of type assignment in the λ -calculus: Church-style, in which the type of each variable is fixed, and Curry-style (also called “domain free”), in which it is not. As an example, in Church-style typing, λx:A.xλx:A.x is the identity function on type A , and it has type A→AA→A but not B→BB→B for a type B different from A . In Curry-style typing, λx.xλx.x is a general identity function with type C→CC→C for every type C. In this paper, we will show how to interpret in a Curry-style system every Pure Type System (PTS) in the Church-style without losing any typing information. We will also prove a kind of conservative extension result for this interpretation, a result which implies that for most consistent PTSs of the Church-style, the corresponding Curry-style system is consistent. We will then show how to interpret in a system of the Church-style (a modified PTS, stronger than a PTS) every PTS-like system in the Curry style.
Journal: Journal of Applied Logic - Volume 18, November 2016, Pages 42–70