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DomainFree Pure Type Systems
 JOURNAL OF FUNCTIONAL PROGRAMMING
, 1993
"... Pure type systems make use of domainfull λabstractions λx:D.M . We present a variant of pure type systems, which we call domainfree pure type systems, with domainfree λabstractions λx.M. Domainfree pure type systems have a number of advantages over both pure type systems and socalled type ass ..."
Abstract

Cited by 34 (8 self)
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Pure type systems make use of domainfull λabstractions λx:D.M . We present a variant of pure type systems, which we call domainfree pure type systems, with domainfree λabstractions λx.M. Domainfree pure type systems have a number of advantages over both pure type systems and socalled type assignment systems (they also have some disadvantages) and have been used in theoretical developments as well as in implementations of proofassistants. We study the basic properties of domainfree pure type systems, establish their formal relationship with pure type systems and type assignment systems, and give a number of applications of these correspondences.
Typechecking Safe Process Synchronization
, 2004
"... Session types describe the interactions between two parties within multiparty communications. They constitute a communication protocol in the sense that the order and type of interactions between two parties are specified. For their part, correspondence assertions provide a mechanism for synchroniz ..."
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Cited by 19 (4 self)
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Session types describe the interactions between two parties within multiparty communications. They constitute a communication protocol in the sense that the order and type of interactions between two parties are specified. For their part, correspondence assertions provide a mechanism for synchronization. When session types and correspondence assertions are combined, they are able to describe synchronization across different communication sessions, yielding a rich language for imposing expressive interaction patterns in multiparty communications. This paper studies the typechecking problem for Iris, a typed πcalculus that combines session types and correspondence assertions. We define a typechecking algorithm and prove that it is sound and complete with respect to the typing rules. Furthermore, we show that the typing system satisfies the minimum effects property. Although session types have been extensively studied in the past few years, to our knowledge this is the first proof of decidability of typechecking for a type system with session types.
Type Preservation as a Confluence Problem ∗
"... This paper begins with recent work by Kuan, MacQueen, and Findler, which shows how standard type systems, such as the simply typed lambda calculus, can be viewed as abstract reduction systems operating on terms. The central idea is to think of the process of typing a term as the computation of an ab ..."
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This paper begins with recent work by Kuan, MacQueen, and Findler, which shows how standard type systems, such as the simply typed lambda calculus, can be viewed as abstract reduction systems operating on terms. The central idea is to think of the process of typing a term as the computation of an abstract value for that term. The standard metatheoretic property of operational semantics, viewed as abstract reduction systems (ARSs). In this paper, we build on the work of Kuan et al. by showing show how modern ARS theory, in particular the theory of decreasing diagrams, can be used to establish type preservation via confluence. We illustrate this idea through several examples of solving such problems using decreasing diagrams. We also consider how automated tools for analysis of termrewriting systems can be applied in testing type preservation. 1
Under consideration for publication in J. Functional Programming 1 Pure Type System conversion is always typable
, 2011
"... Pure Type Systems are usually described in two different ways, one that uses an external notion of computation like betareduction, and one that relies on a typed judgment of equality, directly in the typing system. For a long time, the question was open to know whether both presentations described ..."
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Pure Type Systems are usually described in two different ways, one that uses an external notion of computation like betareduction, and one that relies on a typed judgment of equality, directly in the typing system. For a long time, the question was open to know whether both presentations described the same theory. A first step towards this equivalence has been made by Adams for a particular class of Pure Type Systems (PTS) called functional. Then, his result has been relaxed to all semifull PTSs in previous work. In this paper, we finally give a positive answer to the general question, and prove that equivalence holds for any Pure Type System. 1
unknown title
"... Session types describe the interactions between two parties within multiparty communications. They constitute a communication protocol in the sense that the order and type of interactions between two parties are specified. For their part, correspondence assertions provide a mechanism for synchroniz ..."
Abstract
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Session types describe the interactions between two parties within multiparty communications. They constitute a communication protocol in the sense that the order and type of interactions between two parties are specified. For their part, correspondence assertions provide a mechanism for synchronization. When session types and correspondence assertions are combined, they are able to describe synchronization across different communication sessions, yielding a rich language for imposing expressive interaction patterns in multiparty communications. This paper studies the typechecking problem for Iris, a typed πcalculus that combines session types and correspondence assertions. We define a typechecking algorithm and prove that it is sound and complete with respect to the typing rules. Furthermore, we show that the typing system satisfies the minimum effects property. Although session types have been extensively studied in the past few years, to our knowledge this is the first proof of decidability of typechecking for a type system