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23
Pure type systems formalized
 Proceedings of the International Conference on Typed Lambda Calculi and Applications
, 1993
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The Conservation Theorem revisited
, 1993
"... This paper describes a method of proving strong normalization based on an extension of the conservation theorem. We introduce a structural notion of reduction that we call fi S , and we prove that any term that has a fi I fi Snormal form is strongly finormalizable. We show how to use this result ..."
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Cited by 32 (0 self)
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This paper describes a method of proving strong normalization based on an extension of the conservation theorem. We introduce a structural notion of reduction that we call fi S , and we prove that any term that has a fi I fi Snormal form is strongly finormalizable. We show how to use this result to prove the strong normalization of different typed calculi.
Modularity of Strong Normalization and Confluence in the algebraiclambdacube
, 1994
"... In this paper we present the algebraiccube, an extension of Barendregt's cube with first and higherorder algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraiccube, provided that the firstorder rewrite rules are nonduplicating and the hig ..."
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Cited by 25 (7 self)
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In this paper we present the algebraiccube, an extension of Barendregt's cube with first and higherorder algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraiccube, provided that the firstorder rewrite rules are nonduplicating and the higherorder rules satisfy the general schema of Jouannaud and Okada. This result is proven for the algebraic extension of the Calculus of Constructions, which contains all the systems of the algebraiccube. We also prove that local confluence is a modular property of all the systems in the algebraiccube, provided that the higherorder rules do not introduce critical pairs. This property and the strong normalization result imply the modularity of confluence. 1 Introduction Many different computational models have been developed and studied by theoretical computer scientists. One of the main motivations for the development This research was partially supported by ESPRIT Basic Research Act...
Implicit Syntax
 Informal Proceedings of First Workshop on Logical Frameworks
, 1992
"... A proof checking system may support syntax that is more convenient for users than its `official' language. For example LEGO (a typechecker for several systems related to the Calculus of Constructions) has algorithms to infer some polymorphic instantiations (e.g. pair 2 true instead of pair nat bo ..."
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Cited by 20 (2 self)
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A proof checking system may support syntax that is more convenient for users than its `official' language. For example LEGO (a typechecker for several systems related to the Calculus of Constructions) has algorithms to infer some polymorphic instantiations (e.g. pair 2 true instead of pair nat bool 2 true) and universe levels (e.g. Type instead of Type(4)). Users need to understand such features, but do not want to know the algorithms for computing them. In this note I explain these two features by nondeterministic operational semantics for "translating" implicit syntax to the fully explicit underlying formal system. The translations are sound and complete for the underlying type theory, and the algorithms (which I will not talk about) are sound (not necessarily complete) for the translations. This note is phrased in terms of a general class of type theories. The technique described has more general application. 1 Introduction Consider the usual formal system, !, for simp...
From HindleyMilner types to firstclass structures
 In Proceedings of the Haskell Workshop
, 1995
"... We describe extensions of the HindleyMilner type system to support higherorder polymorphism and firstclass structures with polymorphic components. The combination of these features results in a ‘core language ’ that rivals the expressiveness of the Standard ML module system in some respects and e ..."
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Cited by 14 (0 self)
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We describe extensions of the HindleyMilner type system to support higherorder polymorphism and firstclass structures with polymorphic components. The combination of these features results in a ‘core language ’ that rivals the expressiveness of the Standard ML module system in some respects and exceeds it in others. 1
Telescopic mappings in typed lambda calculus
 Information and Computation
, 1991
"... The paper develops notation for strings of abstracters in typed lambda calculus, and shows how to treat them more or less as single abstracters. 0 1991 Academic Press. Inc. 1. ..."
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Cited by 13 (0 self)
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The paper develops notation for strings of abstracters in typed lambda calculus, and shows how to treat them more or less as single abstracters. 0 1991 Academic Press. Inc. 1.
A Calculus of Transformation

, 1994
"... This paper presents the concepts and the semantics of a transformationcalculus TC that is generic wrt. concrete object languages. Built upon an object language description given by theory in higherorder logics (see [Andr 86]), TC provides contextsensitive rules in which requirements on the conte ..."
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Cited by 11 (7 self)
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This paper presents the concepts and the semantics of a transformationcalculus TC that is generic wrt. concrete object languages. Built upon an object language description given by theory in higherorder logics (see [Andr 86]), TC provides contextsensitive rules in which requirements on the context of a redex can be imposed, and integrates a restricted form of extended rewriting. Furthermore, rules may be higherorder in order to represent tactical combinators and to model "parametric transformations". This work can be seen as a specification of transformation systems and a foundation for correctnessproofs of transformations.
Monadic Type Systems: Pure Type Systems for Impure Settings (Preliminary Report)
 In Proceedings of the Second HOOTS Workshop
, 1997
"... Pure type systems and computational monads are two parameterized frameworks that have proved to be quite useful in both theoretical and practical applications. We join the foundational concepts of both of these to obtain monadic type systems. Essentially, monadic type systems inherit the parameteriz ..."
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Cited by 8 (2 self)
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Pure type systems and computational monads are two parameterized frameworks that have proved to be quite useful in both theoretical and practical applications. We join the foundational concepts of both of these to obtain monadic type systems. Essentially, monadic type systems inherit the parameterized higherorder type structure of pure type systems and the monadic term and type structure used to capture computational effects in the theory of computational monads. We demonstrate that monadic type systems nicely characterize previous work and suggest how they can support several new theoretical and practical applications. A technical foundation for monadic type systems is laid by recasting and scaling up the main results from pure type systems (confluence, subject reduction, strong normalisation for particular classes of systems, etc.) and from operational presentations of computational monads (notions of operational equivalence based on applicative similarity, coinduction proof techni...
Refining the Barendregt Cube using Parameters
, 2001
"... The Barendregt Cube (introduced in [3]) is a framework in which eight important typed calculi are described in a uniform way. Moreover, many type systems (like Automath [18], LF [11], ML [17], and system F [10]) can be related to one of these eight systems. Furthermore, via the propositionsastype ..."
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Cited by 8 (4 self)
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The Barendregt Cube (introduced in [3]) is a framework in which eight important typed calculi are described in a uniform way. Moreover, many type systems (like Automath [18], LF [11], ML [17], and system F [10]) can be related to one of these eight systems. Furthermore, via the propositionsastypes principle, many logical systems can be described in the Barendregt Cube as well (see for instance [9]). However, there are important systems (including Automath, LF and ML) that cannot be adequately placed in the Barendregt Cube or in the larger framework of Pure Type Systems. In this paper we add a parameter mechanism to the systems of the Barendregt Cube. In doing so, we obtain a re nement of the Cube. In this re ned Barendregt Cube, systems like Automath, LF, and ML can be described more naturally and accurately than in the original Cube.
Modularity of Strong Normalization in the Algebraicλcube
, 1996
"... In this paper we present the algebraicλcube, an extension of Barendregt's λcube with first and higherorder algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraicλcube, provided that the firstorder rewrite rules are nonduplicating and the ..."
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Cited by 8 (2 self)
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In this paper we present the algebraicλcube, an extension of Barendregt's λcube with first and higherorder algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraicλcube, provided that the firstorder rewrite rules are nonduplicating and the higherorder rules satisfy the general schema of Jouannaud and Okada. This result is proven for the algebraic extension of the Calculus of Constructions, which contains all the systems of the algebraicλcube. We also prove that local confluence is a modular property of all the systems in the algebraicλcube, provided that the higherorder rules do not introduce critical pairs. This property and the strong normalization result imply the modularity of confluence.