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On Formalised Proofs of Termination of Recursive Functions
 In Proceedings of the Int. Conf. on Principles and Practice of Declarative Programming, volume 1702 of LNCS
, 1999
"... In proof checkers and theorem provers (e.g. Coq [4] and ProPre [13]) recursive de nitions of functions are shown to terminate automatically. ..."
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In proof checkers and theorem provers (e.g. Coq [4] and ProPre [13]) recursive de nitions of functions are shown to terminate automatically.
Types complets dans une extension du système AF2
"... In this paper, we extend the system AF2 in order to have the subject reduction for the βηreduction. We prove that the types with positive quantifiers are complete to models stable by weakheadexpansion. 1 ..."
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Cited by 3 (0 self)
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In this paper, we extend the system AF2 in order to have the subject reduction for the βηreduction. We prove that the types with positive quantifiers are complete to models stable by weakheadexpansion. 1
Church numerals, twice!
, 2002
"... This paper explains Church numerals, twice. The first explanation links Church numerals to Peano numerals via the wellknown encoding of data types in the polymorphic λcalculus. This view suggests that Church numerals are folds in disguise. The second explanation, which is more elaborate, but also ..."
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This paper explains Church numerals, twice. The first explanation links Church numerals to Peano numerals via the wellknown encoding of data types in the polymorphic λcalculus. This view suggests that Church numerals are folds in disguise. The second explanation, which is more elaborate, but also more insightful, derives Church numerals from first principles, that is, from an algebraic specification of addition and multiplication. Additionally, we illustrate the use of the parametricity theorem by proving exponentiation as reverse application correct. 1
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...
Least and Greatest Fixed Points in Intuitionistic Natural Deduction
, 2002
"... This paper is a comparative study of a number of (intensionalsemantically distinct) least and greatest fixed point operators that naturaldeduction proof systems for intuitionistic logics can be extended with in a prooftheoretically defendable way. Eight pairs of such operators are analysed. The e ..."
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This paper is a comparative study of a number of (intensionalsemantically distinct) least and greatest fixed point operators that naturaldeduction proof systems for intuitionistic logics can be extended with in a prooftheoretically defendable way. Eight pairs of such operators are analysed. The exposition is centered around a cubeshaped classification where each node stands for an axiomatization of one pair of operators as logical constants by intended proof and reduction rules and each arc for a proof and reductionpreserving encoding of one pair in terms of another. The three dimensions of the cube reflect three orthogonal binary options: conventionalstyle vs. Mendlerstyle, basic (``[co]iterative'') vs. enhanced (``primitive[co]recursive''), simple vs. courseofvalue [co]induction. Some of the axiomatizations and encodings are wellknown; others, however, are novel; the classification into a cube is also new. The differences between the least fixed point operators considered are illustrated on the example of the corresponding natural number types.
LogiCal Project
, 2004
"... This document is the Reference Manual of version 8.0 of the COQ proof assistant. A companion volume, the COQ Tutorial, is provided for the beginners. It is advised to read the Tutorial first. A new book [13] on practical uses of the COQ system will be published in 2004 and is a good support for both ..."
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This document is the Reference Manual of version 8.0 of the COQ proof assistant. A companion volume, the COQ Tutorial, is provided for the beginners. It is advised to read the Tutorial first. A new book [13] on practical uses of the COQ system will be published in 2004 and is a good support for both the beginner and the advanced user.