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12
A unified approach to Type Theory through a refined λcalculus
, 1994
"... In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic. ..."
Abstract

Cited by 14 (13 self)
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In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic.
Canonical typing and Πconversion in the Barendregt Cube
, 1996
"... In this article, we extend the Barendregt Cube with \Piconversion (which is the analogue of betaconversion, on product type level) and study its properties. We use this extension to separate the problem of whether a term is typable from the problem of what is the type of a term. ..."
Abstract

Cited by 4 (3 self)
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In this article, we extend the Barendregt Cube with \Piconversion (which is the analogue of betaconversion, on product type level) and study its properties. We use this extension to separate the problem of whether a term is typable from the problem of what is the type of a term.
and
, 1996
"... In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic. There are moreover, many versions of calculi and type theories. In these versions, the presence of logic ranges from the nonexistant to the dominant. In fact, ..."
Abstract
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In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic. There are moreover, many versions of calculi and type theories. In these versions, the presence of logic ranges from the nonexistant to the dominant. In fact, the three subjects of calculus, logic and type theory, got separated due to the appearence of the paradoxes. Moreover, the existence of various versions of each topic is due to the need to get back to the lost paradise which allowed a great freedom in mixing expressivity and logic. In any case, the presence of such a variety of systems calls for a framework to unify them all. Barendregt's cube for example, is an attempt to unify various type systems and his associated logic cube is an attempt to nd connections between type theories and logic. We devise a new notation which enables categorising most of the known systems in a unied way. More precisely, we sketch the general structure of a system of typed lambda calculus and show that this system has enough expressive power for the description of various existing systems, ranging from Automathlike systems to singlytyped Pure Type Systems. The system We are grateful for Erik Poll who has read the paper carefully and for his productive comments. We are also grateful for discussions with Henk Barendregt, Inge Bethke, Tijn Borghuis and for the helpful remarks received from them. Furthermore, we are indebted to the anonymous referee for his/her useful suggestions and remarks. y
and
, 1996
"... In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic. There are moreover, many versions of calculi and type theories. In these versions, the presence of logic ranges from the nonexistant to the dominant. In fact, ..."
Abstract
 Add to MetaCart
(Show Context)
In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic. There are moreover, many versions of calculi and type theories. In these versions, the presence of logic ranges from the nonexistant to the dominant. In fact, the three subjects of calculus, logic and type theory, got separated due to the appearence of the paradoxes. Moreover, the existence of various versions of each topic is due to the need to get back to the lost paradise which allowed a great freedom in mixing expressivity and logic. In any case, the presence of such a variety of systems calls for a framework to unify them all. Barendregt's cube for example, is an attempt to unify various type systems and his associated logic cube is an attempt to nd connections between type theories and logic. We devise a new notation which enables categorising most of the known systems in a unied way. More precisely, we sketch the general structure of a system of typed lambda calculus and show that this system has enough expressive power for the description of various existing systems, ranging from Automathlike systems to singlytyped Pure Type Systems. The system We are grateful for Erik Poll who has read the paper carefully and for his productive comments. We are also grateful for discussions with Henk Barendregt, Inge Bethke, Tijn Borghuis and for the helpful remarks received from them. Furthermore, we are indebted to the anonymous referee for his/her useful suggestions and remarks. y
and
, 1996
"... First of all, we are very grateful to our colleague Bert van Benthem Jutting who has read draft versions of the manuscript, and who has made very useful suggestions. Furthermore, we are grateful for the discussions with Henk Barendregt, Roel Bloo, Tijn Borghuis, Herman Geuvers, Kevin Hammond, BartJ ..."
Abstract
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First of all, we are very grateful to our colleague Bert van Benthem Jutting who has read draft versions of the manuscript, and who has made very useful suggestions. Furthermore, we are grateful for the discussions with Henk Barendregt, Roel Bloo, Tijn Borghuis, Herman Geuvers, Kevin Hammond, BartJan de Leuw, Simon PeytonJones, Erik Poll and Phil Wadler, and for the helpful remarks received from them. Last but not least, we are grateful to the anonymous referees for their constructive comments and criticisms. y Kamareddine is grateful to the Department of Mathematics and Computing Science, Eindhoven University of Technology, for their nancial support and hospitality from October 1991 to September 1992, and during various short visits in 1993 and 1994. Furthermore, Kamareddine is grateful to the Department of Mathematics and Computer Science, University of Amsterdam, and in particular to Jan Bergstra and Inge Bethke for their hospitality during the preparation of this article, and to the Dutch organisation of research (NWO) for its nancial support. Last but not least, Kamareddine is grateful to the ESPRIT Basic Action for Research project \Types for Proofs and Programming " for its nancial support. 1
and
, 1996
"... First of all, we are very grateful to our colleague Bert van Benthem Jutting who has read draft versions of the manuscript, and who has made very useful suggestions. Furthermore, we are grateful for the discussions with Henk Barendregt, Roel Bloo, Tijn Borghuis, Herman Geuvers, Kevin Hammond, BartJ ..."
Abstract
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First of all, we are very grateful to our colleague Bert van Benthem Jutting who has read draft versions of the manuscript, and who has made very useful suggestions. Furthermore, we are grateful for the discussions with Henk Barendregt, Roel Bloo, Tijn Borghuis, Herman Geuvers, Kevin Hammond, BartJan de Leuw, Simon PeytonJones, Erik Poll and Phil Wadler, and for the helpful remarks received from them. Last but not least, we are grateful to the anonymous referees for their constructive comments and criticisms. y Kamareddine is grateful to the Department of Mathematics and Computing Science, Eindhoven University of Technology, for their nancial support and hospitality from October 1991 to September 1992, and during various short visits in 1993 and 1994. Furthermore, Kamareddine is grateful to the Department of Mathematics and Computer Science, University of Amsterdam, and in particular to Jan Bergstra and Inge Bethke for their hospitality during the preparation of this article, and to the Dutch organisation of research (NWO) for its nancial support. Last but not least, Kamareddine is grateful to the ESPRIT Basic Action for Research project \Types for Proofs and Programming " for its nancial support. 1
and
, 1996
"... First of all, we are very grateful to our colleague Bert van Benthem Jutting who has read draft versions of the manuscript, and who has made very useful suggestions. Furthermore, we are grateful for the discussions with Henk Barendregt, Roel Bloo, Tijn Borghuis, Herman Geuvers, Kevin Hammond, BartJ ..."
Abstract
 Add to MetaCart
First of all, we are very grateful to our colleague Bert van Benthem Jutting who has read draft versions of the manuscript, and who has made very useful suggestions. Furthermore, we are grateful for the discussions with Henk Barendregt, Roel Bloo, Tijn Borghuis, Herman Geuvers, Kevin Hammond, BartJan de Leuw, Simon PeytonJones, Erik Poll and Phil Wadler, and for the helpful remarks received from them. Last but not least, we are grateful to the anonymous referees for their constructive comments and criticisms. y Kamareddine is grateful to the Department of Mathematics and Computing Science, Eindhoven University of Technology, for their nancial support and hospitality from October 1991 to September 1992, and during various short visits in 1993 and 1994. Furthermore, Kamareddine is grateful to the Department of Mathematics and Computer Science, University of Amsterdam, and in particular to Jan Bergstra and Inge Bethke for their hospitality during the preparation of this article, and to the Dutch organisation of research (NWO) for its nancial support. Last but not least, Kamareddine is grateful to the ESPRIT Basic Action for Research project \Types for Proofs and Programming " for its nancial support. 1
and
, 1996
"... In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic. There are moreover, many versions of calculi and type theories. In these versions, the presence of logic ranges from the nonexistant to the dominant. In fact, ..."
Abstract
 Add to MetaCart
(Show Context)
In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic. There are moreover, many versions of calculi and type theories. In these versions, the presence of logic ranges from the nonexistant to the dominant. In fact, the three subjects of calculus, logic and type theory, got separated due to the appearence of the paradoxes. Moreover, the existence of various versions of each topic is due to the need to get back to the lost paradise which allowed a great freedom in mixing expressivity and logic. In any case, the presence of such a variety of systems calls for a framework to unify them all. Barendregt's cube for example, is an attempt to unify various type systems and his associated logic cube is an attempt to nd connections between type theories and logic. We devise a new notation which enables categorising most of the known systems in a unied way. More precisely, we sketch the general structure of a system of typed lambda calculus and show that this system has enough expressive power for the description of various existing systems, ranging from Automathlike systems to singlytyped Pure Type Systems. The system We are grateful for Erik Poll who has read the paper carefully and for his productive comments. We are also grateful for discussions with Henk Barendregt, Inge Bethke, Tijn Borghuis and for the helpful remarks received from them. Furthermore, we are indebted to the anonymous referee for his/her useful suggestions and remarks. y
and
, 1996
"... In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic. There are moreover, many versions of calculi and type theories. In these versions, the presence of logic ranges from the nonexistant to the dominant. In fact, ..."
Abstract
 Add to MetaCart
(Show Context)
In the area of foundations of mathematics and computer science, three related topics dominate. These are calculus, type theory and logic. There are moreover, many versions of calculi and type theories. In these versions, the presence of logic ranges from the nonexistant to the dominant. In fact, the three subjects of calculus, logic and type theory, got separated due to the appearence of the paradoxes. Moreover, the existence of various versions of each topic is due to the need to get back to the lost paradise which allowed a great freedom in mixing expressivity and logic. In any case, the presence of such a variety of systems calls for a framework to unify them all. Barendregt's cube for example, is an attempt to unify various type systems and his associated logic cube is an attempt to nd connections between type theories and logic. We devise a new notation which enables categorising most of the known systems in a unied way. More precisely, we sketch the general structure of a system of typed lambda calculus and show that this system has enough expressive power for the description of various existing systems, ranging from Automathlike systems to singlytyped Pure Type Systems. The system We are grateful for Erik Poll who has read the paper carefully and for his productive comments. We are also grateful for discussions with Henk Barendregt, Inge Bethke, Tijn Borghuis and for the helpful remarks received from them. Furthermore, we are indebted to the anonymous referee for his/her useful suggestions and remarks. y