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Weak normalization implies strong normalization in a class of non-dependent pure type systems

Gilles Barthe, John Hatcliff, Morten Heine Sørensen
2001 Theoretical Computer Science  
This seems to be the ÿrst result giving a positive answer to the conjecture not merely for some concrete systems for which strong normalization is known to hold, but for a uniform class of systems in which  ...  The Barendregt-Geuvers-Klop conjecture states that every weakly normalizing pure type system is also strongly normalizing.  ...  in all generalized non-dependent pure type systems -that are also negatable and clean -weak normalization implies strong normalization.  ... 
doi:10.1016/s0304-3975(01)00012-3 fatcat:dibhh364vrbnzayj6j72tr7ri4

Author index volume 269 (2001)

2001 Theoretical Computer Science  
S+rensen, Weak normalization implies strong normalization in a class of non-dependent pure-type systems (1}2) 317}361 Bergstra, J.A. and A.  ...  Ponse, Non-regular iterators in process algebra (1}2) 203}229 Corradini, F., G. Ferrari and M. Pistore, On the semantics of durational actions (1}2) 47} 82 de Moor, O. and G.  ... 
doi:10.1016/s0304-3975(01)00335-8 fatcat:oxlsxh4dgnfoxbuq7wsipw4exm

Expanding the Cube [chapter]

Gilles Barthe
1999 Lecture Notes in Computer Science  
We prove strong normalization of -reduction+ -expansion for the Calculus of Constructions, thus providing the rst strong normalization result for -reduction+ -expansion in calculi of dependent types and  ...  As for strong normalization, Joachimski 18] has shown that a Pure Type System is strongly normalizing for -reduction+ -expansion if it is strongly normalizing for -reduction.  ...  In contrast to the -cube, neither weak normalization results nor strong normalization results are known for systems of dependent types.  ... 
doi:10.1007/3-540-49019-1_7 fatcat:zkxxtfxbmbblhkze3zsil5s6ei

A Notion of Classical Pure Type System (Preliminary version)

Gilles Barthe, John Hatcliff, Morten Heine Sørensen
1997 Electronical Notes in Theoretical Computer Science  
We present a notion of classical pure type system, which extends the formalism of pure type system with a double negation operator. c 1997 Published by Elsevier Science B. V.  ...  in a generic way standard notions from higher-order rewrite systems and type theories.  ...  Werner also considered in unpublished work, 1992 a classical variant of non-dependent logical pure type systems however his notion of reduction is extremely weak. subsection, we specify some important  ... 
doi:10.1016/s1571-0661(05)80170-7 fatcat:kugibpuzfvgcjkiasxdqeadsu4

Foundations of strong call by need

Thibaut Balabonski, Pablo Barenbaum, Eduardo Bonelli, Delia Kesner
2017 Proceedings of the ACM on Programming Languages  
More precisely, terms admitting a β-normal form in pure lambda calculus are typable, typability implies (weak) normalisation in the strong call-by-need calculus, and weak normalisation in the strong call-by-need  ...  The proof of completeness relies on two key tools: (1) the definition of a strong call-by-need calculus where reduction may be performed inside any context, and (2) the use of non-idempotent intersection  ...  A salient aspect of our proof is the use of non-idempotent intersection types to characterize needed normalisation: β-weakly normalising pure lambda terms are typable and moreover, typability implies weak  ... 
doi:10.1145/3110264 dblp:journals/pacmpl/BalabonskiBBK17 fatcat:5ryg5qtjprejhbmjaoukktlpz4

Page 8066 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
normalization implies strong normalization in a class of non-dependent pure type systems.  ...  This seems to be the first result giving a positive answer to the conjecture not merely for some concrete systems for which strong normalization is known to hold, but for a uniform class of systems in  ... 

Domain-free pure type systems [chapter]

Gilles Barthe, Morten Heine SØrensen
1997 Lecture Notes in Computer Science  
Domain-free pure type systems have a number of advantages over both pure type systems and so-called type assignment systems (they also have some disadvantages) and have been used in theoretical developments  ...  Pure type systems make use of domain-full -abstractions x : D : M. We present a variant of pure type systems, which we call domain-free pure type systems, with domain-free -abstractions x : M.  ...  Coquand for numerous discussions on the domain-free pure type systems, to R. Pollack for discussions on type-checking for domain-free pure type systems, and to J.  ... 
doi:10.1007/3-540-63045-7_2 fatcat:t6z2s6tnnfcq5m4v5ttcnsfvxa

Untyped Algorithmic Equality for Martin-Löf's Logical Framework with Surjective Pairs [chapter]

Andreas Abel, Thierry Coquand
2005 Lecture Notes in Computer Science  
An untyped algorithm to test βη-equality for Martin-Löf's Logical Framework with strong Σ-types is presented and proven complete using a model of partial equivalence relations between untyped terms.  ...  The first author is indebted to Frank Pfenning who taught him type-directed equality at Carnegie Mellon University in 2000, and to Carsten Schürmann for communication on LF Σ .  ...  We are grateful to Lionel Vaux whose clear presentation of models for this implicit calculus [Vau04] provided a guideline for our model construction. Thanks to Ulf Norell for proof-reading.  ... 
doi:10.1007/11417170_4 fatcat:2rtrhisy3rejppyltqd6gqufbi

Entropic entanglement criteria in phase space [article]

Stefan Floerchinger and Martin Gärttner and Tobias Haas and Oliver R. Stockdale
2021 arXiv   pre-print
We apply our entropic criteria to Gaussian states and show that they imply a pair of second-order criteria for moments.  ...  We exemplify the strengths of our entropic approach by considering several classes of non-Gaussian states where second-order criteria fail.  ...  Examples of non-Gaussian states-Finally, we consider a set of non-Gaussian entangled states that cannot be witnessed by second-order criteria to test the weak Eq. (14) and strong criteria Eq.  ... 
arXiv:2106.08788v1 fatcat:odcptgrxubbhdmppzumpsbpufe

Termination of algebraic type systems: The syntactic approach [chapter]

Gilles Baxthe, Femke van Raamsdonk
1997 Lecture Notes in Computer Science  
g R {the extension of the Calculus of Constructions with R. This is clearly a weakness of algebraic type systems for dependent type theories.  ...  They can be carried out in a weak system of arithmetic.  ... 
doi:10.1007/bfb0027010 fatcat:wrtsahg6zbbkphaw6juzgojawm

A combinatory logic approach to higher-order E-unification

Daniel J. Dougherty, Patricia Johann
1995 Theoretical Computer Science  
In fact, we treat a more general problem, in which the types of terms contain type variables.  ...  The case in which E admits presentation as a convergent term rewriting system is treated in detail: in this situation, a modification of ordinary narrowing is shown to be a complete method for enumerating  ...  unification in the presence of dependent function types in [13] .  ... 
doi:10.1016/0304-3975(94)00210-a fatcat:24row66nvngblegsxrbvffzfei

Superposition, transition probabilities and primitive observables in infinite quantum systems [article]

Detlev Buchholz, Erling Størmer
2015 arXiv   pre-print
The concepts of superposition and of transition probability, familiar from pure states in quantum physics, are extended to locally normal states on funnels of type I_∞ factors.  ...  Such funnels are used in the description of infinite systems, appearing for example in quantum field theory or in quantum statistical mechanics; their respective constituents are interpreted as algebras  ...  with the set of pure states in finite quantum systems.  ... 
arXiv:1411.2100v3 fatcat:f7tc7autxrdhplpv5yoamm25m4

The simple economics of bank fragility

C.G. De Vries
2005 Journal of Banking & Finance  
systemic risk is weak or strong.  ...  The similarity in exposures carries the potential for systemic breakdowns. This potential is either weak or strong, depending on whether the linkages remain or vanish asymptotically.  ...  potential for systemic risk is weak or strong.  ... 
doi:10.1016/j.jbankfin.2004.08.003 fatcat:yaf4agaccbh6nndla4mgooguku

The Refined Best Reply Correspondence and Backward Induction

Dieter Balkenborg, Josef Hofbauer, Christoph Kuzmics
2016 Social Science Research Network  
Fixed points of the (most) refined best-reply correspondence, introduced in Balkenborg, Hofbauer, and Kuzmics (2009), in the agent normal form of extensive form games have a remarkable, one might call  ...  They automatically induce fixed points of the same correspondence in the agent normal form of every subgame.  ...  Obviously very strong idio-justifiability implies strong idio-justifiability, which implies weak idio-justifiability, which, in turn, implies very weak idio-justifiability.  ... 
doi:10.2139/ssrn.2836853 fatcat:utyrbcvtqfc3fnrqlgedhu3exi

Host-pathogen interactions: redefining the basic concepts of virulence and pathogenicity

A Casadevall, L A Pirofski
1999 Infection and Immunity  
We thank Marta Feldmesser, Marcia Goldberg, and Reid Schwebach for critical reading of the manuscript.  ...  A.C. was supported by NIH grants RO1-AI33774, RO1-AI3342, and RO1-59842-01 and a Burroughs Wellcome Development Therapeutics Award. L.P. was supported by NIH grant RO1-AI35370.  ...  They can cause disease in normal hosts but are distinguished from class 2 microbes by their ability to cause significant damage in the setting of both weak or strong immune responses.  ... 
pmid:10417127 pmcid:PMC96643 fatcat:biynamqhezcmpem3hnyr5tpifq
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