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On the Definition of the Etalong Normal Form in Type Systems of the Cube
 Informal Proceedings of the Workshop on Types for Proofs and Programs
, 1993
"... The smallest transitive relation ! on welltyped normal terms such that if t is a strict subterm of u then t ! u and if T is the normal form of the type of t and the term t is not a sort then T ! t is wellfounded in the type systems of the cube. Thus every term admits a jlong normal form. Introdu ..."
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The smallest transitive relation ! on welltyped normal terms such that if t is a strict subterm of u then t ! u and if T is the normal form of the type of t and the term t is not a sort then T ! t is wellfounded in the type systems of the cube. Thus every term admits a jlong normal form. Introduction In this paper we prove that the smallest transitive relation ! on welltyped normal terms such that ffl if t is a strict subterm of u then t ! u, ffl if T is the normal form of the type of t and the term t is not a sort then T ! t is wellfounded in the type systems of the cube [1]. This result is proved using the notion of marked terms introduced by de Vrijer [6]. A motivation for this theorem is to define the jlong form of a normal term in these type systems. In simply typed calculus, to define the jlong form of a normal term we first define the jlong form of a variable x of type P 1 ! ::: ! P n ! P (P atomic) as the term [y 1 : P 1 ]:::[y n : P n ](x y 0 1 ::: y 0 n ) w...
Type Classes With More HigherOrder Polymorphism
 In ACM SIGPLAN International Conference on Functional Programming
, 2002
"... We propose an extension of Haskell's type class system with lambda abstractions in the type language. Type inference for our extension relies on a novel constrained unification procedure called guided higherorder unification. This unification procedure is more general than Haskell's kind ..."
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We propose an extension of Haskell's type class system with lambda abstractions in the type language. Type inference for our extension relies on a novel constrained unification procedure called guided higherorder unification. This unification procedure is more general than Haskell's kindpreserving unification but less powerful than full higherorder unification.
The Coq Proof Assistant  Reference Manual Version 6.1
, 1997
"... : Coq is a proof assistant based on a higherorder logic allowing powerful definitions of functions. Coq V6.1 is available by anonymous ftp at ftp.inria.fr:/INRIA/Projects/coq/V6.1 and ftp.enslyon.fr:/pub/LIP/COQ/V6.1 Keywords: Coq, Proof Assistant, Formal Proofs, Calculus of Inductives Constru ..."
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: Coq is a proof assistant based on a higherorder logic allowing powerful definitions of functions. Coq V6.1 is available by anonymous ftp at ftp.inria.fr:/INRIA/Projects/coq/V6.1 and ftp.enslyon.fr:/pub/LIP/COQ/V6.1 Keywords: Coq, Proof Assistant, Formal Proofs, Calculus of Inductives Constructions (R'esum'e : tsvp) This research was partly supported by ESPRIT Basic Research Action "Types" and by the GDR "Programmation " cofinanced by MREPRC and CNRS. Unit'e de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) T'el'ephone : (33 1) 39 63 55 11  T'el'ecopie : (33 1) 39 63 53 30 Manuel de r'ef'erence du syst`eme Coq version V6.1 R'esum'e : Coq est un syst`eme permettant le d'eveloppement et la v'erification de preuves formelles dans une logique d'ordre sup'erieure incluant un riche langage de d'efinitions de fonctions. Ce document constitue le manuel de r'ef'erence de la version V6.1 qui est distribu 'ee par ftp ...
The Coq Proof Assistant  Reference Manual V 5.10
, 1995
"... ion All Axiom Begin Cd Chapter Check CheckGuard CoFixpoint Compute Defined Definition Drop Elimination End Eval Explain Extraction Fact Fixpoint Focus for Go Goal Hint Hypothesis Immediate Induction Inductive Infix Inspect Lemma Let Local Minimality ML Module Modules Mutual Node Opaque Parameter Par ..."
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ion All Axiom Begin Cd Chapter Check CheckGuard CoFixpoint Compute Defined Definition Drop Elimination End Eval Explain Extraction Fact Fixpoint Focus for Go Goal Hint Hypothesis Immediate Induction Inductive Infix Inspect Lemma Let Local Minimality ML Module Modules Mutual Node Opaque Parameter Parameters Print Proofs Prop Pwd Qed Remark Require Restart Resume Save Scheme Script Search Section Set Show Silent States Suspend Syntactic Theorem Token Transparent Tree Type TypeSet Undo Unfocus Variable Variables Write Other keywords and user's tokens The following sequences of characters are also keywords:  : := = ? ?? !? !! ! ? ; # * , ? @ :: / ! You can add new tokens with the command Token (see section 5.7.4). New tokens must be sequences, without blanks, of characters taken from the following list: ! ? / "  + = ; ,  ! @ # % & ? * : ~ $ a..z A..Z ' 0..9 that do not start with a character from $ a..z A..Z ' 0..9 Lexical ambiguities are resolved according to the "longest m...
Informal Proceedings Of The 1993 Workshop On Types For Proofs And Programs, Nijmegen
, 1993
"... Clauses : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 375 iii Foreword This document is the preliminary proceedings of the workshop of the Esprit Basic Research Project 6453 "Types for Proofs and Programs" held at the University of Nijmegen, the Netherla ..."
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Clauses : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 375 iii Foreword This document is the preliminary proceedings of the workshop of the Esprit Basic Research Project 6453 "Types for Proofs and Programs" held at the University of Nijmegen, the Netherlands, from May 24th until May 28th 1993. The workshop was organised by Henk Barendregt and Herman Geuvers. Local arrangements were made by Marielle van der Zandt, Erik Barendsen, Herman Geuvers and Mark Ruys. These proceedings have been collected from L a T E X sources, using email. It contains 22 papers from the 35 talks that were presented at the workshop. Very useful support in solving the L a T E X puzzles was provided by Erik Barendsen. This document can be obtained by anonymous ftp from the University of Nijmegen: Type ftp ftp.cs.kun.nl anonymous (as login) [your email address] (as password) cd /pub/csi/CompMath/Types bin get NijmegenTypes.ps.Z bye iv Workshop Programme Types for Proofs an...
Abstract Type Classes With More HigherOrder Polymorphism
"... We propose an extension of Haskell’s type class system with lambda abstractions in the type language. Type inference for our extension relies on a novel constrained unification procedure called guided higherorder unification. This unification procedure is more general than Haskell’s kindpreserving ..."
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We propose an extension of Haskell’s type class system with lambda abstractions in the type language. Type inference for our extension relies on a novel constrained unification procedure called guided higherorder unification. This unification procedure is more general than Haskell’s kindpreserving unification but less powerful than full higherorder unification. The main technical result is the soundness and completeness of the unification rules for the fragment of lambda calculus that we admit on the type level.