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 1. The Lattice Of Lambda Theories -- Lusin And Salibra 14 (3): 373 -- Journal Of Lo lambda theories are equational extensions of the untyped lambda calculus that are closed under derivation. The set of lambda theories is naturally equippedhttp://logcom.oxfordjournals.org/cgi/content/abstract/14/3/373?ck=nck

2. [cs/0211011] Intersection Types And Lambda Theories
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy
http://arxiv.org/abs/cs/0211011
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##### Title: Intersection Types and Lambda Theories
Authors: M.Dezani-Ciancaglini S.Lusin (Submitted on 12 Nov 2002) Abstract: We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation of an arbitrary simple easy term is any filter which can be described in an uniform way by a predicate. This allows us to prove the consistency of a well-know lambda theory: this consistency has interesting consequences on the algebraic structure of the lattice of lambda theories. Subjects: Logic in Computer Science (cs.LO) ACM classes: F.3.2 Cite as: arXiv:cs/0211011v1 [cs.LO]
##### Submission history
From: Mariangiola Dezani [ view email
Tue, 12 Nov 2002 21:33:33 GMT (13kb)

 3. JSTOR Degrees Of Sensible Lambda Theories DEGREES OF SENSIBLE lambda theories 47 Clearly, ~ Fn = I if R (n). Now suppose -n R (n). Then it is easily checked that there is an infinite reductionhttp://links.jstor.org/sici?sici=0022-4812(197803)43:1<45:DOSLT>2.0.CO;2-6

4. Degrees Of Sensible Lambda Theories
A $\lambda$theory $T$ is a consistent set of equations between $\lambda$-terms closed under derivability. The degree of $T$ is the degree of the set of
http://projecteuclid.org/handle/euclid.jsl/1183740105

 5. UBLCS-2003-7 Abstract In this thesis by using filter models (i.e. intersection types) and methods of universal algebra we investigate some properties of lambda theorieshttp://www.cs.unibo.it/pub/TR/UBLCS/ABSTRACTS/2003.bib?ncstrl.cabernet//BOLOGNA-

6. Fundamenta Informaticae Vol. 45 Abstracts
In this paper we prove that the lattice of lambda theories is not modular and that the variety generated by the term algebra of a semisensible lambda
http://fi.mimuw.edu.pl/abs45.html
 Preface PaweÂ³ Urzyczyn and Jean-Ives Girard Elementary Complexity and Geometry of Interaction Patrick Baillot and Marco Pedicini We introduce a geometry of interaction model given by an algebra of clauses equipped with resolution (following [10]) into which proofs of Elementary Linear Logic can be interpreted. In order to extend geometry of interaction computation (the so called execution formula ) to a wider class of programs in the algebra than just those coming from proofs, we define a variant of execution (called weak execution ). Its application to any program of clauses is shown to terminate with a bound on the number of steps which is elementary in the size of the program. We establish that weak execution coincides with standard execution on programs coming from proofs. Counting a Type's (Principal) Inhabitants Sabine Broda and LuÃ­s Damas We present a Counting Algorithm that computes the number of l-terms in b-normal form that have a given type t as a principal type and produces a list of these terms. The design of the algorithm follows the lines of Ben-Yelles' algorithm for counting normal (not necessarily principal) inhabitants of a type t. Furthermore, we show that one can use similar algorithms with adequate limits to count normal and principal normal inhabitants in the lI-calculus.

Theories 16. Sensible Theories 17. Other lambda theories Part V. Models 18. Construction of Models 19. Local Structure of Models
##### Theory of Computation
L ast updated 2003-02-10-22:35 -0800 (pst)
Barendregt, Hendrik Pieter. The Lambda Calculus: Its Syntax and Semantics . North-Holland (Amsterdam, 1981). ISBN 0-444-85490-8. Studies in Logic and the Foundations of Mathematics, vol. 103.
This is one of my fundamental sources on the lambda calculus. I want to pay particular attention to combinatory logic (CL) and combinatory algebra (CA). My notes on this book focus on that.
Content
Preface
Part I. Towards the Theory
1. Introduction
2. Conversion
3. Reduction
4. Theories 5. Models Part II. Conversion 6. Classical Lambda Calculus 7. The Theory of Combinators 8. Classical Lambda Calculus (continued) I -Calculus Part III.

8. CoMeta - Computational Metamodels - Publications
GSÂ·lambda theories enrich gs theories by requiring the existence of a right adjoint a _ to .. Intersection types and lambda theories. In WIT 2002, 2002.
http://cometa.dimi.uniud.it/publications.shtml
##### CoMeta - Computational Metamodels
Home Meetings Documents and Reports Publications ... Tools
##### Publications
[ABB L. Andrade, P. Baldan, H. Baumeister, R. Bruni, A. Corradini, R. De Nicola, J. L. Fiadeiro, F. Gadducci, S. Gnesi, P. Hoffman, N. Koch, P. Kosiuczenko, A. Lapadula, D. Latella, A. Lopes, M. Loreti, M. Massink, F. Mazzanti, U. Montanari, C. Oliveira, R. Pugliese, A. Tarlecki, M. Wermelinger, M. Wirsing, and A. Zawlocki. AGILE: Software architecture for mobility. In M. Wirsing, D. Pattinson, and R. Hennicker, editors, Proceedings of WADT'02 , volume 2755 of Lecture Notes in Computer Science , pages 1-33. Springer, 2003.
bib
.pdf F. Alessi, F. Barbanera, and M. Dezani-Ciancaglini. Intersection types and computational rules. In WoLLIC '03 , volume 84 of Electronic Notes in Theoretical Computer Science . Elsevier, August 2003.
bib
.pdf The invariance of the meaning of a lambda term by reduction/expansion w.r.t. the considered computational rules is one of the minimal requirements one expects to hold for a lambda model. Being the intersection type systems a general framework for the study of semantic domains for the Lambda-calculus, the present paper provides a characterisation of meaning invariance'' in terms of characterisation results for intersection type systems enabling typing invariance of terms w.r.t. various notions of reduction/expansion, like beta, eta and a number of relevant restrictions of theirs. Christopher Anderson, Franco Barbanera, and Mariangiola Dezani-Ciancaglini. Alias and Union types for Delegation.

9. Peter Selinger Papers
Our second result is a syntactical characterization, in terms of socalled generalized Mal cev operators, of those lambda theories which cannot be induced
http://www.mscs.dal.ca/~selinger/papers.html
Papers
##### Proceedings of the Eleventh International Conference on Foundations of Software Science and Computation Structures (FOSSACS 2008), Budapest

10. Front: [cs.LO/0211011] Intersection Types And Lambda Theories
Abstract We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of
http://front.math.ucdavis.edu/0211.6011
 Front for the arXiv Fri, 21 Dec 2007 Front cs LO cs.LO/0211011 search register submit journals ... iFAQ cs.LO/0211011 Title: Intersection Types and Lambda Theories Authors: M. Dezani-Ciancaglini , S. Lusin Categories: cs.LO Logic in Computer Science ACM: F.3.2 Abstract: We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation of an arbitrary simple easy term is any filter which can be described in an uniform way by a predicate. This allows us to prove the consistency of a well-know lambda theory: this consistency has interesting consequences on the algebraic structure of the lattice of lambda theories. Owner: Mariangiola Dezani Version 1: Tue, 12 Nov 2002 21:33:33 GMT - for questions or comments about the Front arXiv contact page - for questions about downloading and submitting e-prints

11. HAL :: [hal-00149556, Version 1] Graph Lambda Theories
Berline, is whether, given a class of lambda models, there are a minimal lambdatheory and a minimal sensible lambda-theory represented by it.
http://hal.archives-ouvertes.fr/hal-00149556/en/
 Home Submit Login Register ... [information] .:. hal-00149556, version 1 .:. Detailed view Graph Lambda Theories Antonio Bucciarelli Antonino Salibra Preuves, Programmes et SystÃ¨mes (PPS) Dipartimento di Informatica UniversitÃ  "CÃ  Foscari", Venezia Subject Computer Science/Logic in Computer Science Attached file list to this document: PDF graphlt.pdf (201.4 KB) hal-00149556, version 1 http://hal.archives-ouvertes.fr/hal-00149556/en/ oai:hal.archives-ouvertes.fr:hal-00149556_v1 From: Antonio Bucciarelli str_unrot('','wPxxDvsKKNtEPNNDzPtAM',''); Saturday, 26 May 2007 19:18:46 all articles on CCSd database...

12. Seminaires De Logique En Region Parisienne: Seminaire Du Vendredi
A general introduction to the theory of lambda theories will be attempted, and recent results concerning semantical and syntactical properties of theories
http://pauillac.inria.fr/cdrom/www/coq/mailing-lists/GTlogique/0059.html
##### Seminaire du vendredi
Paul Roziere roziere@logique.jussieu.fr
Mon, 25 May 1998 09:40:03 +0200
Date: Mon, 25 May 1998 09:40:03 +0200
roziere@logique.jussieu.fr

To: semlambda@logique.jussieu.fr
Subject: Seminaire du vendredi
Universite de Paris VII, UFR de Mathematiques
et Ecole Normale Superieure, DMI
Preuves, Programmes et ModÃ¨les
Organisateurs: Berline, di Cosmo, Danos, Krivine, Roziere
Vendredi 10h30.
Universite Paris 7 couloir 45-55, 5ieme etage salle 13 29/5/98: deux seances 10h30 Furio Honsell (Udine) A Cook's tour of Lambda theories 11h30 Marina Lenisa (Udine) Semantique finale Resumes : A Cook's tour of Lambda theories A general introduction to the theory of lambda theories will be attempted, and recent results concerning semantical and syntactical properties of theories and models of untyped lambd calculus will be discussed. In particular, we shall focus on

 13. The Lambda Calculus - Elsevier Other lambda theories. Models. Construction of Models. Local Structure of Models. Global Structure of Models. Combinatory Groups. Appendices Typed Lambdahttp://www.biolc.com/wps/find/bookdescription.cws_home/501727/description?navope

 14. CARNEGIE MELLON UNIVERSITY PROGRAM IN PURE AND APPLIED LOGIC LOGIC Toward this end certain material on lambda theories will be excluded. @ Topics covered include (1)Basic properties of reduction and conversion (2)Reductionhttp://logic.cmu.edu/pal-courses-s06.txt

15. DSpace At RU: Degrees Of Sensible Lambda Theories
Title, Degrees of sensible lambda theories. Authors, Barendregt, HP Bergstra, JA Klop, JW Volken, H. Issue Date, 1978. URI, http//hdl.handle.net/2066/
http://hdl.handle.net/2066/17248
 About DSpace Software Search DSpace Advanced Search Home Browse Communities Titles Authors Subjects ... By Date Sign on to: Receive email updates My DSpace authorized users Edit Profile Help About DSpace DSpace at RU ... Cream of Science Please use this identifier to cite or link to this item: http://hdl.handle.net/2066/17248 Title: Degrees of sensible lambda theories Authors: Barendregt, H.P. Bergstra, J.A. Klop, J.W. Volken, H. Issue Date: URI: http://hdl.handle.net/2066/17248 Appears in Collections: Cream of Science Electronic documents Radboud University Files in This Item: File Size Format 13265.pdf Adobe PDF View/Open DSpace Software MIT and Hewlett-Packard Feedback

 16. Citebase - Lambda Theories Of Effective Lambda Models The sensible graph theories of lambda calculus. 19th Annual IEEE Symposium on Logic in Computer Science (LICS 2004), IEEE Computer Society Press, 2004.http://www.citebase.org/abstract?identifier=oai:arXiv.org:math/0701684&action=ci

17. Scientific Commons The Lattice Of Lambda Theories (2002), 2002-01
The lattice lambdaT of lambda theories is isomorphic to the congruence lattice of the term algebra of the minimal lambda theory lambdabeta.
http://de.scientificcommons.org/623559
 ÃµÂ¸-#Ãp,Â¯0 #Ã¯ÂÃÃ¯Ãº)$Ãr <ÂÂPÂJÂ 18. Intersection Types And Lambda Theories Intersection Types and lambda theories. Mariangiola DezaniCiancaglini, Stefania Lusin. Journal Title CoRR Logic in Computer Science. Date 2002 http://wotan.liu.edu/docis/dbl/xxcslo/0211011.html  The Digital Librarian's Digital Library search D O CISÃÂ Do cumentsÃÂ inÃÂ C omputing and I nformationÃÂ S cience Home Journals and Conference Proceedings CoRR: Logic in Computer Science Intersection Types and Lambda Theories Mariangiola Dezani-Ciancaglini, Stefania Lusin Journal Title: CoRR: Logic in Computer Science Date: 2002 Full Text Version: http://xxx.arxiv.org/pdf/cs.LO/0211011 For further information about this item go to: http://arxiv.org/abs/cs.LO/0211011 This data comes from DBLP This page is maintained by Angela Cornwell and Thomas Krichel It was last updated on 2006-04-12 19. British Library Direct: Order Details Order from the British Library lambda theories of Effective Lambda Models. http://direct.bl.uk/research/23/28/RN215434538.html  This is an article from British Library Direct, a new service that allows you to search across 20,000 journals for free and order full text using your credit card. Article details Article title Lambda Theories of Effective Lambda Models Author Berline, C. Manzonetto, G. Salibra, A. Journal title LECTURE NOTES IN COMPUTER SCIENCE Bibliographic details 2007, NUMB 4646, pages 268-282 Publisher SPRINGER-VERLAG Country of publication Germany ISBN ISSN Language English Pricing To buy the full text of this article you pay: service charge Abstract: By using this site you agree to our Terms and Conditions Privacy policy We welcome your comments  20. ODOBS - Publication Page: Degrees Of Sensible Lambda Theories. Degrees of Sensible lambda theories. Authors. Henk BARENDREGT; Jan A. BERGSTRA; Jan Willem KLOP; Henri VOLKEN. Year, 1978. Journal, J. Symb. Log.http://lupus.cs.uni-dortmund.de:8080/odobs/publication;jsessionid=7D6D5E35073902 21. Cookies Required A comparison with the f\Theta R\lambda theories is immediate. It is striking to notice that modified Friedmann equations are once more first order field http://link.aps.org/doi/10.1103/PhysRevD.70.103503 What is Scitation? News Contact Us Help MyScitation: Sign In Register Home MyScitation ... Usage Reports Welcome! Sign In Sign up for free Send Feedback ... Learn more about our new features! ##### Cookies Required ALERT! This service requires a web browser and/or firewall/network configuration that supports and accepts cookies. You may have been redirected to this page for one or more of the following reasons: • You are using a browser that supports cookies, but cookie acceptance is disabled. You are using an older browser that does not support cookies. You are utilizing a personal firewall that is configured to override your browser settings and reject cookies. You are accessing Scitation from a network or proxy that is configured to reject cookies. • (1) Browsers that support cookies: You may be using a browser that does support cookies, but you have cookies disabled. Setting up your browser to accept cookies is straightforward in most current versions of Scitation's recommended browsers . Once you have enabled cookies, you may continue to the URL you requested or return to the previous page (2) Browsers that do not support cookies: If you are using a browser that does not support cookies, you must upgrade to a cookie-capable browser. Consult the Scitation 22. LDP : SÃ©minaire RÃ©sumÃ© We show how to solve the word problem for simply typed lambda calculus and various lambda theories, using elementary properties of presheaves and http://iml.univ-mrs.fr/ldp/Seminaire/SemLog99.html ##### LOGIQUE DE LA PROGRAMMATION Organisatrice Lieu • Mardi 30 Novembre 1999 Vincent DANOS et Russ HARMER (CNRS- Paris VII) 2) semantique des jeux probabilistes • Mardi 19 Octobre 1999 Rick BLUTE (University of Ottawa). Hopf Algebras and non-commutative logic. • Mitsu OKADA (Keio University, visiting IML, Marseille). Some analysis on predicativity and impredicativity in phase model constructions. : We analyze two impredicative constructions of phase models, one for intuitionistic phase model constructions, the other for higher order (but, of course, non-standard) phase model constructions. (2)As for the second, we analyze the nature of impredicativity and of non-standardness of the higher order phase-models construction, and we relate it to a (strongly) uniform phase-semantic higher order cut-elimination proof, which works not only for linear logic but also for all reasonable higher order logics uniformly. We also give some relationships between the linear logic proof-search method and some phase-semantic model constructions, (and give their application to a concurrent process calculus). The first part of this work is on-going work with my Ph.D student, Kazushige Terui, and Max Kanovitch.  23. Libra: The Lattice Of Lambda Theories Intersection Types and lambda theories(2002) (citation2). Mariangiola DezaniCiancaglini Stefania Lusin. We illustrate the use of intersection types as ahttp://libra.directtaps.net/papercited.aspx?id=2276738 24. McTafi - Goals - Specific Goals - Torino We plan also to characterise the lambda theories whose consistency can be shown using filter models, and the domain operators which can be equated to the http://www.mctafi.math.unipd.it/english/goals_specific-goals_To.htm ##### McTafi - Metodi Costruttivi in Topologia Algebra Fondamenti dell'Informatica • home project methods topics ... specific goals ##### The goals of Torino The goal of our research project is to use topologies over ordered structures in order to study typed programming language s, in the broadest sense, including parallel computations and learning processes. ##### Constructive completion of the integer line We plan to study several classical proof as test case, to see if we may analyze the program hidden in each of them using the constructive completion of the integer line we have in our scientifical base • In 1989, Stolzenberg found an anomaly in the existing program extraction methods in Proof Theory. By "program extraction" we mean a method taking any (classical) proof of the existence of an object satisfying a decidable property, and returning an algorithm finding such object. We also require that the algorithm we get is implicit in the original proof, and that it is no blind search in general.  25. Libra: P. K. Agarwal And M. Sharir, Planar Geometric Location Problems, Tech. Re Relying on the notion of easy intersection type theory we successfully build a lambda;model in which the interpretation of an arbitrary simple easy termhttp://libra.msra.cn/papercited.aspx?id=1382497 26. Scientific Commons Degrees Of Sensible Lambda Theories (1978 Degrees of sensible lambda theories (1978). Bergstra, JA,; Barendregt, HP,; Klop, JW,; Volken, H. Publication details http://en.scientificcommons.org/15877012  <Â(2YpÂ _ÃÂÃÃ¥XÃ©Ã 27. ICTCS 2007 Can a proper lambdamodel have an r.e. equational theory? 11.00-11.30, Coffee Break Proving the range property for lambda theories and models http://www.disp.uniroma2.it/ictcs07/program.html ##### ICTCS 2007 Tenth Italian Conference on Theoretical Computer Science ##### Final Program ##### ICTCS'07 ##### Types and Computations: Colloquium in Honor of Coppo, Dezani-Ciancaglini, Ronchi Della Rocca ##### October 3, 2007 Registration and Opening Invited Talk, Corrado Boehm. The scientific works of Coppo, Dezani and Ronchi Invited Talk, Chantal Berline. Can a proper lambda-model have an r.e. equational theory? Coffee Break Invited Talk, Furio Honsell. TBA Lunch Invited Talk, Giuseppe Longo. Symmetries in Foundations Coffee Break Invited Talk, Henk Barendregt. Proving the range property for lambda theories and models Invited Talk, Pawel Urzyczyn. Proof search in propositional intuitionistic logic Social Dinner ##### ICTCS 2007 - Conference Program ##### October 4, 2007 Registration and Opening Chair Eugenio Moggi Invited Talk, Rocco De Nicola. Session Centered Calculi for Service Oriented Computing Session 1: Chair Alberto Marchetti-Spaccamela Mathias Hauptmann. 28. [Pao04] Lambda-theories: Some Investigations On the other hand, we are able to show that some property on theories hold for each$\lambda\Delta$calculus.\\ The notion of solvability in the http://www.di.unito.it/~lambda/biblio/entry-paolini04phd.html  Chronological Overview Type-Hierarchical Overview Semantics and Logics of Computation (Most of the papers antecedent to 1995 are not included in the list) FRAMES NO FRAME (PhD thesis) Author(s) Luca Paolini Title School Year Abstract In this thesis we present somes investigations on -calculi, both untyped and typed. The first two parts concerning some pure untyped calculi, while the last concerns PCF and an extension of its syntax. In the first part, a -calculus is defined, which is parametric with respect to a set of input values and subsumes all the different (pure and untyped) -calculi given in the literature, in particular the classical one and the call-by-value -calculus of Plotkin. It is proved that it enjoys the confluence property, and a necessary and sufficient condition is given, under which it enjoys the standardization property. Hence, we extended some basic syntactical notion of the classical -calculus to the parametric -calculus such as solvability, separability, theory. We have studied the notions of solvability and separability in the call-by-value setting; unfortunately, there is no evidence on how treat this kind of notions in an unified way for our parametric -calculus. On the other hand, we are able to show that some property on theories hold for each  29. Re: Huge Hole Found In The Lambda-CDM And Big Bang Theories - Forums Powered By One of the most important predictions of lambda theory (and inflation) is that the inflation phase of the expansion process created a nearly homogeneoushttp://uplink.space.com/showthreaded.php?Board=sciastro&Number=799447 30. Scott: Relating Theories Of The Lambda-Calculus The correspondence is made complete by noting we can start with a (typed) lambdatheory and form a (syntactic) CCC representing the same theory of functions http://mathgate.info/cebrown/notes/scott80.php The Omega Group TPS A higher-order theorem proving system This page was created and is maintained by Chad E Brown ##### Scott, Dana S. "Relating Theories of the Lambda-Calculus." (1980) Section 1. Theories of Functions. The lambda-calculus is a theory of functions. We can relate this theory to other theories of functions. General category theory provides a much purer theory of functions than set theory. Category theory gives a theory of functions under composition and is also a theory of types. Category theory is extensional in the sense that functions (arrows) defined in different ways may be identical and that identical functions (arrows) can always replace one another. Some intensional theories of functions do not provide categories. The axioms of category theory do not imply the existence of anything (there is an empty category)it has no "existential import" and was not meant to. Set theory on the other had has "too much existential import" and was meant to. We would like a "middle way": cartesian closed categories. Section 2. A Theory of Types. 31. DBLP: Antonino Salibra 18, Antonino Salibra A Continuum of theories of lambda Calculus without Semantics. LICS 2001 334346. 17 EE, Antonino Salibra Towards lambda Calculus http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/s/Salibra:Antonino.htm ##### Antonino Salibra List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... Giulio Manzonetto , Antonino Salibra: Lambda Theories of Effective Lambda Models. CSL 2007 EE Giulio Manzonetto , Antonino Salibra: Boolean Algebras for Lambda Calculus. LICS 2006 EE Chantal Berline , Antonino Salibra: Easiness in graph models. Theor. Comput. Sci. 354 EE Antonio Bucciarelli , Antonino Salibra: The Sensible Graph Theories of Lambda Calculus. LICS 2004 EE Stefania Lusin , Antonino Salibra: The Lattice of Lambda Theories. J. Log. Comput. 14 EE Antonio Bucciarelli , Antonino Salibra: The Minimal Graph Model of Lambda Calculus. MFCS 2003 EE Antonino Salibra: Topological incompleteness and order incompleteness of the lambda calculu. ACM Trans. Comput. Log. 4 EE Stefania Lusin , Antonino Salibra: A Note on Absolutely Unorderable Combinatory Algebras. J. Log. Comput. 13 Antonino Salibra: A Continuum of Theories of Lambda Calculus without Semantics. LICS 2001 EE Antonino Salibra: Towards Lambda Calculus Order-Incompleteness. Electr. Notes Theor. Comput. Sci. 50 32. [cs/0609080] Solution Of A Problem Of Barendregt On Sensible Lambda-Theories Solution of a Problem of Barendregt on Sensible lambdatheories. Authors Benedetto Intrigila, Richard Statman Comments 17 pages http://aps.arxiv.org/abs/cs.LO/0609080 ##### aps.arXiv.orgcs Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Full-text links: Download: Citations p revious n ... ext ##### Computer Science > Logic in Computer Science ##### Title: Solution of a Problem of Barendregt on Sensible lambda-Theories Authors: Benedetto Intrigila Richard Statman (Submitted on 14 Sep 2006 ( ), last revised 18 Oct 2006 (this version, v2)) Abstract: Comments: 17 pages Subjects: Logic in Computer Science (cs.LO) ACM classes: F.4.1 Journal reference: LMCS 2 (4:5) 2006 DOI 10.2168/LMCS-2(4:5)2006 Cite as: arXiv:cs/0609080v2 [cs.LO] ##### Submission history From: Benedetto Intrigila [ view email Thu, 14 Sep 2006 16:01:52 GMT (17kb) Wed, 18 Oct 2006 10:48:10 GMT (28kb) Which authors of this paper are endorsers? Link back to: arXiv form interface contact 33. Domains And Lambda Calculi (book Announcement) Book announcement DOMAINS AND lambda CALCULI by Roberto AMADIO and 4.3 Interpretation of lambdacalculi 4.4 From CCC s to lambda-theories and back 4.5 http://www.seas.upenn.edu/~sweirich/types/archive/1997-98/msg00317.html [Prev] [Next] [Index] [Thread] ##### Domains and Lambda Calculi (book announcement) Book announcement: DOMAINS AND LAMBDA CALCULI by Roberto AMADIO and Pierre-Louis CURIEN Cambridge Tracts in Theoretical Computer Science 46, ISBN 0-521-62277-8, Cambridge University Press We are pleased to announce that the book is now available. Order informations can be found at http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521622778 and for North-America at http://www.cup.org/Titles/62/0521622778.html  34. @article {LassenJanuary 20041571-06611, Author = Lassen S.B. The paper surveys notions of bisimulation and trees for sensible IMG SRC= /isoents/isogrk32/lambda-s.gif ALT= lambda -theories based on reduction tohttp://www.ingentaconnect.com/content/els/15710661/2004/00000020/00000001/art000 35. LICS - Index Of Papers And Short Presentations By Authors : W Conditional lambdatheories and the verification of static properties of programs A Theory of Recursive Domains with Applications to Concurrency (LICS http://www.lfcs.inf.ed.ac.uk/events/lics/papers/W.html ##### IEEE Symposium on Logic in Computer Science ##### Papers and Short Presentations by Authors : W LICS website Main Page All Conferences Papers by Author Newsletters Authors on this page: ##### Philip Wadler ##### Richard J. Waldinger ##### Uwe Waldmann ##### D. J. Walker ##### David Walker 36. Pugs, Practicing The Theories. | Lambda The Ultimate A lot of language theory goes past here on lambda the Ultimate, but we rarely see that theory directly impacting commercial programmers. http://lambda-the-ultimate.org/node/620 @import "misc/drupal.css"; @import "themes/chameleon/ltu/style.css"; ##### Lambda the Ultimate Home Feedback FAQ ... Archives ##### User login Username: Password: ##### Navigation Home ##### Pugs, Practicing the Theories. A lot of language theory goes past here on Lambda the Ultimate, but we rarely see that theory directly impacting commercial programmers. I'm a great fan of theoretical concepts like arrows, but at the same time I'm a self-employed programmer interested in solving my clients' problems. Pugs is notable in that it profitably uses recent developments such as GADTs and Template Haskell for an implementation of Perl6. I recently became a regular on the #perl6 irc channel and soon after joined the list of committers. In just a few days I've seen a lot. I've seen enthusiastic members of the Perl community learning Haskell. I've seen myself learning Perl. I've also seen how daily Perl programmers work with abstractions like monad transformers. I've seen how some structures are easy to extend for programmers new to both the Pugs codebase and Haskell. The Pugs project was started 64 days ago by Autrijus Tang , as an exercise while reading TaPL. Pugs already includes network and threading primitives. New tests and code are add at an amazing rate, as evidenced by the 37. Cs/0609080 Solution Of A Problem Of Barendregt On Sensible Lambda-Theories title= Solution of a Problem of Barendregt on Sensible lambdatheories , year= 2006 , eprint= cs/0609080 , doi= 10.2168/LMCS-2(45)2006 http://eprintweb.org/S/article/cs/0609080/bibtex  Username: Password: Main Archive Authors Personalization ... About astro-ph cond-mat cs gr-qc hep-ex hep-lat hep-ph hep-th math math-ph nlin nucl-ex nucl-th physics q-bio quant-ph stat January February March April May June July August September October November December Apr 07 -> astro-ph cond-mat cs gr-qc hep-ex hep-lat hep-ph hep-th math math-ph nlin nucl-ex nucl-th physics q-bio quant-ph stat Previous Next Computer Research Repository (CoRR) Abstract ... Citations author="Benedetto Intrigila and Richard Statman", title="Solution of a Problem of Barendregt on Sensible lambda-Theories", year="2006", eprint="cs/0609080", doi="10.2168/LMCS-2(4:5)2006" 38. Papers On Analysis-Based Transformation Conditional lambdatheories and the Verification of Static Properties of Programs. Information and Computation, 113(2)253277, 1994. http://www.ccs.neu.edu/home/wand/semantics/analysis-papers.html For up-to-date information, check the bibliography ##### Papers on Analysis-Based Transformation and Related Topics Programming Languages and Systems, 11th European Symposium on Programming, ESOP 2002, held as Part of the Joint European Conference on Theory and Practice of Software, ETAPS 2002, Grenoble, France, April 8-12, 2002, Proceedings , volume 2305 of Lecture Notes in Computer Science , pages 213227, Berlin, Heidelberg, and New York, 2002. Springer-Verlag. Abstract: We introduce a new proof technique for showing the correctness of 0CFA-like analyses with respect to small-step semantics. We illustrate the technique by proving the correctness of 0CFA for the pure lambda-calculus under arbitrary beta-reduction. This result was claimed by Palsberg in 1995; unfortunately, his proof was flawed. We provide a correct proof of this result, using a simpler and more general proof method. We illustrate the extensibility of the new method by showing the correctness of an analysis for the Abadi-Cardelli object calculus under small-step semantics. Mitchell Wand. Analyses that Distinguish Different Evaluation Orders, or, Unsoundness Results in Control-Flow Analysis. submitted for publication, July 2002. 39. Solution Of A Problem Of Barendregt On Sensible Lambda-Theories - Science-adviso Scienceadvisor.net is a free scientific search engine and online forum for scientific discussions, short reviews and ranking of research articles. http://science-advisor.net/article/cs/0609080 register info/FAQ sitemap donations Sign in username password forgot password? register here for free... Research articles search articles ... reviews guidelines My Science-advisor my alerts my messages my reviews my favorites Google search Web Science-advisor Statistics Members: Articles: Articles rated: 22 December 2007 cs/0609080 ##### Article overview Solution of a Problem of Barendregt on Sensible lambda-Theories Benedetto Intrigila Richard Statman Date 14 Sep 2006 Subject Logic in Computer Science Abstract Source arXiv, cs/0609080 Services Article forum Review this article Full Text PDF Add to favorites Visitor rating : did you like this article? no yes No review found. Did you like this article? This article or document is ... important: Select One (no value) 1.0 (Poor) 2.0 (Fair) 3.0 (Good) 4.0 (Very Good) 5.0 (Excellent) of broad interest: Select One (no value) 1.0 (Poor) 2.0 (Fair) 3.0 (Good) 4.0 (Very Good) 5.0 (Excellent) readable: Select One (no value) 1.0 (Poor) 2.0 (Fair) 3.0 (Good) 4.0 (Very Good) 5.0 (Excellent) new: Select One (no value) 1.0 (Poor) 40. Alessandro Berarducci - Home Page Alessandro Berarducci and Benedetto Intrigila, ChurchRosser$\lambda$-theories, infinite$\lambda$-terms and consistency problems, in Logic from http://www.dm.unipi.it/~berardu/pubblicazioni.html ##### Alessandro Berarducci ##### Dipartimento di Matematica Universita' di Pisa Home Curriculum Papers Didattica Links ##### PAPERS The documents available on this server are the preprint versions of my papers, not the published ones. If you don't succeed to download a paper please write to the author. A. Berarducci, Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup Nov. 15, 2007 , Download here: arXiv:0711.2502v1 [math.LO] , or if you don't succeed here: PDF A. Berarducci and A. Fornasiero, O-mininal cohomology: finiteness and invariance results 26 May 2007 , Download here: ArXiv:0705.3425 , or if you don't succeed here: PDF dvi A. Berarducci, O-minimal spectra, infinitesimal subgroups and cohomology Preprint April 9, 2006, 21 pp. ArXiv.org, math.LO/0604186. Revised April 29, 2007, To appear in: Journal of Symbolic Logic 72, n. 4 (2007) 1177-1193. PDF A. Berarducci, Zero-groups and maximal tori , in: Logic Colloquium 2004. Editors: A. Andretta, K. Kearnes, D. Zambella, ASL Lecture Notes in Logic, Vol. 29 (2006) 33-45  41. EULER Record Details It shows that the addition of the GirardReynolds system$F$to algebraic theories (and even simply typed$\lambda\$ theories) is conservative.http://www.emis.de/projects/EULER/detail?ide=1993breaconsequatheo&matchno=206&ma

42. CSL'04: AcceptedÂ papers
Provably Total Primitive Recursive Functions theories with Induction A natural .. exploiting an equivalence between partial lambdatheories and partial
http://www.csl04.ii.uni.wroc.pl/accepted.html
 Home Programme Timetable Venue ... Registration Accepted papers Andreas Abel and Ralph Matthes Fixed Points of Type Constructors and Primitive Recursion Roberto M. Amadio, Solange Coupet-Grimal, Silvano Dal Zilio, and Line Jakubiec A Functional Scenario for Bytecode Verification of Resource Bounds We consider a scenario where (functional) programs in pre-compiled form are exchanged among untrusted parties. Our contribution is a system of annotations for the code that can be verified at load time so as to ensure bounds on the time and space resources required for its execution, as well as to guarantee the usual integrity properties. Specifically, we define a simple stack machine for a first-order functional language and show how to perform type, size, and termination verifications at the level of the bytecode of the machine. In particular, we show that a combination of size verification based on quasi-interpretations and of termination verification based on lexicographic path orders leads to an explicit bound on the space required for the execution. Marcelo Arenas, Pablo BarcelÃ³, and Leonid Libkin

43. Takeuti Izumi: Abstracts
This paper defines the theories of parametricity for the system lambdaP-omega in lambda cube, and shows some of its application. These theories are defined
http://www.m.is.sci.toho-u.ac.jp/~takeuti/abs-e.html
Top page: [NIHONGO] [English] [francais]
##### Transition Systems over Continuous Time-Space
Abstract: This paper gives transition systems over continuous time-space, which are systems of functions of continuous time-space into descrete states. These systeme are situated between the cellular automata and the partial differential equations. This paper shows the reasonable sufficient condition of the uniquness of the solution. ps file [290KB] ps.gz file [101KB] pdf file [256KB] pdf.gz file [119KB]
##### Effective Limit in Computable Analysis
Abstract: This paper introduce the notion of effective limit, which gives an alternative definition of effective uniform topology. The aim of this paper is to combine the precedent works of algebraic structure and of limit structure, which have appeared in studies of computable analysis. This paper also compares the definition of computable functions based on representations and that based on computability structure, and shows that both of them are essentially equivalent to each other. ps file [200KB] ps.gz file [70KB]

44. The Sensible Graph Theories Of Lambda Calculus
Sensible theories are equational extensions of the untyped lambda calculus that equate all the unsolvable -terms and are closed under derivation.
http://csdl.computer.org/comp/proceedings/lics/2004/2192/00/21920276abs.htm

45. Classical Equivalence Of Lambda R Phi 2 Theories
Classical equivalence of lambda R phi 2 theories. A J Accioly et al 1993 Class. Quantum Grav. 10 L215L219 doi10.1088/0264-9381/10/12/001
http://www.iop.org/EJ/abstract/0264-9381/10/12/001
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##### Classical equivalence of lambda R phi theories
A J Accioly et al Class. Quantum Grav. L215-L219 doi:10.1088/0264-9381/10/12/001 PDF (214 KB) References Articles citing this article
A J Accioly
... S F Kwok and N L P Pereira da Silva
Inst. de Fisica Teorica, Univ. Estadual Paulista, Sao Paulo, Brazil Abstract. It is shown that the action functional S(g, phi )= integral d x square root (-g)((R/K)(1+k lambda phi )+ delta u phi delta mu phi ) describes, in general, one and the same classical theory whatever may be the value of the coupling constant lambda . Print publication: Issue 12 (December 1993)
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46. Curried Lambda: Geoff Wozniak’s Weblog Â· Beauty, Theories And Equations
Curried lambda Geoff WozniakÂs weblog. Musings on just about anything Beauty, theories and equations. Thursday, December 6th, 2007 in Opinion,
http://wozniak.ca/2007/12/06/beauty-theories-and-equations/
##### Beauty, theories and equations
Thursday, December 6th, 2007 in Opinion Research by Geoff Wozniak I really enjoyed the following talk by Murray Gell-Mann.
• ##### Monkeys perform arithmetic as well as college students
Wednesday, December 19th in Asides Monkeys perform arithmetic as well as college students. No comment. Monday, December 17th in General
##### The Golden Compass
Saturday, December 8th in Movie Reviews
##### Beauty, theories and equations
Thursday, December 6th in Opinion Research
##### Squirrels!
Saturday, December 1st in General Acrobatic little things, they are. And tricky, to boot.

47. FLoC 2006 - LICS
We call this coinductive syntactic theory extensional head normal form bisimilarity and in this paper we extend it to the lambda-pi calculus (the lambda
http://www.easychair.org/FLoC-06/LICS-day225.html
LICS 2006 Twenty First Annual IEEE Symposium on Logic in Computer Science
Seattle, August 12 - 15, 2006 FLoC Home About FLoC MEETINGS CAV ICLP IJCAR LICS ... Workshops (by conf.) PROGRAM Room Assignments FLoC at a glance Social Events Invited Talks ... Workshop Proceedings FACILITIES Conference Hotel Event Space Internet Access SEATTLE Travel to/in Seattle Dining Guide Sightseeing in Seattle ORGANIZATION Steering Committee Program Committee Organizing Committee Sponsors MISCELLANEOUS Related Events Site Design OUT-OF-DATE Registration Visa Information Student Travel Support
##### Chair: Patrice Godefroid Location: Metropolitan A
Orna Kupferman (Hebrew University, Israel)
Avoiding Determinization [ppt]
Automata on infinite objects are extensively used in system specification, verification, and synthesis. While some applications of the automata-theoretic approach have been well accepted by the industry, some have not yet been reduced to practice. Applications that involve determinization of automata on infinite words have been doomed to belong to the second category. This has to do with the intricacy of Safra's optimal determinization construction, the fact that the state space that results from determinization is awfully complex and is not amenable to optimizations and a symbolic implementation, and the fact that determinization requires the introduction of acceptance conditions that are more complex than the Buchi acceptance condition. Examples of applications that involve determinization and belong to the unfortunate second category include model checking of omega-regular properties, decidability of branching temporal logics, and synthesis and control of open systems.

48. Atlas: Boolean Algebra And Lambda Calculus By Antonino Salibra
This implies that, if the term model of a lambda theory T is decomposible in a nontrivial way, then every model of T can be also decomposible in a
http://atlas-conferences.com/cgi-bin/abstract/caug-81
 Atlas home Conferences Abstracts about Atlas ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III (TANCL'07) August 5-9, 2007 St Anne's College, University of Oxford Oxford, England Organizers Mai Gehrke and Hilary Priestley View Abstracts Conference Homepage Boolean algebra and lambda calculus by Antonino Salibra University of Venice One of the milestones of modern algebra is the Stone representation theorem for Boolean algebras. In [1] Manzonetto and Salibra have shown that Comer's generalization of the Stone representation theorem holds also for combinatory algebras: any combinatory algebra is isomorphic to a weak Boolean product of directly indecomposable combinatory algebras. The proof of the representation theorem for combinatory algebras is based on the fact that every combinatory algebra has central elements, i.e., elements which define a direct decomposition of the algebra as the Cartesian product of two other combinatory algebras. Central elements in a combinatory algebra constitute a Boolean algebra, whose Boolean operations can be defined by suitable combinators. Then it is natural to investigate the semantics of lambda calculus given in terms of models, which are directly indecomposable as combinatory algebras (indecomposable semantics, for short). The indecomposable semantics includes all known models of lambda calculus (i.e., the continuous, stable and strongly stable semantics), and the term models of all semisensible lambda theories (theories which do not equate solvable and unsolvable terms). The class of indecomposible combinatory algebras is a universal class, so that it is closed under subalgebras and ultraproducts. This implies that, if the term model of a lambda theory T is decomposible in a non-trivial way, then every model of T can be also decomposible in a non-trivial way. It follows that the indecomposable semantics is incomplete because there exist lambda theories whose term models admit non-trivial central elements.

49. Hans Aberg
I have made a computer semantics, successfully implemented, that can be used to produce both functional (Church lambdatheory based) and imperative
http://www.matematik.su.se/~haberg/
##### Hans Aberg
I am a member of the American Mathematical Society (AMS); my address and telephone number can be searched at the AMS member search . I also have an AMS member email address
##### Algebra, Geometry and Topology
My first research concerned finiteness properties of metabelian groups: For example, among the set of arithmetic groups with invertible primes, this is the first non-trivial case. Among other things, I proved a difficult conjecture by Robert Bieri and Ralph Strebel , relating the finiteness properties to number theory. The proof made heavy use of algebra, such as group theory, ring theory, commutative algebra, number theory, homological algebra and category theory, but also relied on topology, algebraic topology, homotopy theory, and geometry. These latter topics became a part by work originated by Kenneth S. Brown
##### Intrinsic Spin Manuscript
I discovered a formula (equation (1.16) in the manuscript) that suggests that in order to perform the metric variations of the GR Lagrangian when including QM statistical waves, then this kind of intrinsic spin theory is necessary. I then developed the intrinsic spin theory, so that it can be used for translating QM formulas into Lorentz coordinate independent formulas. This is what is described in the manuscript. Recently, I put the intrinsic spin theory to work, and made additional findings relating GR and QM, a construction of a wave based Fock space on a suitably modified Lorentz cotangent bundle manifold. The intrinsic spin makes it possible to construct a coordinate independent, Lorentz-covariant positive definite metric on this Fock space. (If one, for example, converts the formula (1-57) in the Streater-Wightman book on PCT, that scalar product will be Lorentz covariant and positive definite, but not coordinate independent.) Other parts of the construction correspond to QFT axioms. In principle, by supplying a suitable wave equation, one could extract QFT via Sobolev spaces by such a construction. (To be written up.)

50. Luke Ong's Selected Publications
A. D. Ker, H. Nickau and C.H. L. Ong, Adapting innocent game models for the Boehm tree lambda-theory. In Theoretical Computer Science 308, pp.
http://users.comlab.ox.ac.uk/luke.ong/publications/index.html
##### Dr. C.-H. L. Ong: Selected Publications
W. Blum and C.-H. L. Ong. The Safe Lambda Calculus . In Proceedings of Typed Lambda Calculus and Applications , Springer-Verlag LNCS Vol. ?, 2007. M. Hague, A. S. Murawski, C.-H. L. Ong and O. Serre. Collapsible pushdown automata and recursion schemes . 13 pages, preprint, November 2006. M. Hague and C.-H. L. Ong. Symbolic backwards-reachability analysis of higher-order pushdown systems . To appear in Proceedings of Tenth International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2007), 24 March - 1 April, 2007, Braga, Portugal. Long version , 59 pages, October 2006. S. Sanjabi and C.-H. L. Ong. Fully abstract semantics of additive aspects by translation . To appear in Proceedings of Sixth International Conference on Aspect-Oriented Software Development (AOSD 2007), Vancouver, British Columbia March 12-16, 2007. S. Abramsky and C.-H. L. Ong. Algorithmic Game Semantics and its Application: Final Report of an EPSRC Project . 6 pages. January 2006. C.-H. L. Ong.

51. Categories And Computation | The N-Category CafÃ©
and these are fullfledged models of nCob as a quantum lambda theory, because they But nCob isnÂt closed, so it canÂt be a quantum lambda theory,
http://golem.ph.utexas.edu/category/2006/08/cartesian_closed_categories_an.html
@import url("/category/styles-site.css"); A group blog on math, physics and philosophy
Enough, already! Skip to the content. Note: These pages make extensive use of the latest XHTML and CSS Standards only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser. Main
##### Posted by John Baez
My student Mike Stay and I are working on category theory and quantum computation. But, I still have some catching up to do when it comes to category theory and ordinary computation! If anyone else wants to learn about this, here are some fun, easy places to start:
Good Math, Bad Math JB wrote: I talked to Jim some more and we figured out what it is. You get programs for free in a lambda theory. As soon as you have one type, you get a whole bunch of programs as morphisms in the category, everything you can write using typed S and K combinators. These programs are proofs in intuitionistic logic.

52. CSL07
Session lambda Calculus 1 Chair JeanPierre Jouannaud. 1600-1630, The Theory of Calculi with Explicit Substitutions Revisited; Delia Kesner
http://www2.unil.ch/csl07/programme.html
 Programme CSL 07 Tuesday 11 September (joint day with GAMES 07 Registration Opening Ceremony (Chair: Erich Graedel) Invited Tutorial: Anuj Dawar (Cambridge) Model Checking First-Order Logic: Automata and Locality Coffee Break Session: Logic and Games Chair: Tom Henzinger Omega-Regular Half-positional Winning Conditions; Eryk Kopczynski Clique-Width and Parity Games; Jan Obdrzalek Alexander Rabinovich and Wolfgang Thomas The Power of Counting Logics on Restricted Classes of Finite Structures; Anuj Dawar and David Richerby LUNCH (Chair: Wolfgang Thomas) Invited Tutorial: Luca de Alfaro (Santa Cruz); The Symbolic Approach to Repeated Games Session: Expressiveness Chair: Wolfgang Thomas Comparing the Expressive Power of Well-structured Transition Systems; Giorgio Delzanno, Parosh Aziz Abdulla and Laurent Van Begin Olivier Finkel and Dominique Lecomte Coffee Break Session: Games and Trees Chair: Damian Niwinski Satisfiability of a Spatial Logic with Tree Variables; Emmanuel Filiot, JeanMarc Talbot and Sophie Tison Forest Expressions; Mikolaj Bojanczyk MSO on the Infinite Binary Tree: Choice and Order;

53. Lambda-Renormalized Einstein-Schrodinger Theory
In general though, there has not been much interest in the EinsteinSchrodinger theory for 50 years. lambda-renormalized Einstein-Schrodinger theory
http://www.einstein-schrodinger.com/
 The Einstein-Schrodinger theory without a cosmological constant was originally proposed by Einstein and Straus in 1946. In this form it is also known as "Einstein's Unified Field Theory", or the "Einstein-Straus Theory", or the "Hermitian Theory of Relativity", or the "Nonsymmetric Gravitational Theory", or the "Generalized Theory of Gravitation", or the "Relativistic Theory of the Non-symmetric Field". Schrodinger made an important contribution to the theory in 1947 by generalizing it to include a cosmological constant, and by showing that the theory can be derived from a very simple Lagrangian density if this cosmological constant is assumed to be non-zero. This more general theory is usually called "Schrodinger's Affine Field Theory" or the "Einstein-Schrodinger Theory". Here are a few of Einstein's and Schrodinger's original papers on this topic. The Einstein-Schrodinger theory is a generalization of ordinary general relativity which allows a non-symmetric fundamental tensor. When Einstein and Schrodinger developed the theory they suspected that this fundamental tensor might contain both the metric and electromagnetic field, and they hoped that the theory would unify gravitation and electromagnetism. However, it was shown way back in 1953 that the original theory apparently does not predict a Lorentz force between charged particles. Since then there has been some interest in the theory by a few researchers who dispute the proof of the missing Lorentz force. Other researchers have assumed that the theory is correct but represents something other than gravity and electromagnetism. Still others have investigated theories which are significantly modified versions of the original theory. In general though, there has not been much interest in the Einstein-Schrodinger theory for 50 years.

54. Type Theory - Wikipedia, The Free Encyclopedia
Alonzo Church, inventor of the lambda calculus, developed a higherorder logic commonly called Church s Theory of Types, in order to avoid the Kleene-Rosser
http://en.wikipedia.org/wiki/Type_theory
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
##### Type theory
Jump to: navigation search In mathematics logic and computer science type theory is any of several formal systems that can serve as alternatives to naive set theory , or the study of such formalisms in general. In programming language theory , a branch of computer science type theory can refer to the design, analysis and study of type systems , although some computer scientists limit the term's meaning to the study of abstract formalisms such as typed ÃÂ»-calculi Bertrand Russell invented the first type theory in response to his discovery that Gottlob Frege 's version of naive set theory was afflicted with Russell's paradox . This type theory features prominently in Whitehead and Russell 's Principia Mathematica . It avoids Russell's paradox by first creating a hierarchy of types, then assigning each mathematical (and possibly other) entity to a type. Objects of a given type are built exclusively from objects of preceding types (those lower in the hierarchy), thus preventing loops. Alonzo Church , inventor of the lambda calculus , developed a higher-order logic commonly called Church's Theory of Types , in order to avoid the Kleene-Rosser paradox afflicting the original pure lambda calculus. Church's type theory is a variant of the lambda calculus in which expressions (also called formulas or ÃÂ»-terms) are classified into types, and the types of expressions restrict the ways in which they can be combined. In other words, it is a

55. Summer School And Workshop On Proof Theory, Computation And Complexity
The course will not strictly assume knowledge of the lambda calculus but participants who are already familiar with its syntactic theory will gain most from
http://www.ki.inf.tu-dresden.de/~guglielm/WPT2/
 Summer School and Workshop on Proof Theory, Computation and Complexity June 23-July 4, 2003 Call for Participation (Dresden) and For attending courses, we ask for a fee of 100 EUR (to be paid in cash at the school). Registration is requested before May 25, 2003; please send an email to PTEvent@Janeway.Inf.TU-Dresden.DE , making sure you include a very brief bio (5-10 lines) stating your experience, interests, home page, etc. We select applicants in case of excessive demand. A limited number of grants covering all expenses is available. Applications for grants must include an estimate for travel costs and they should be sent together with the registration. We provide assistance in finding an accommodation in Dresden. Week 1, June 23-27: courses on Denotational Semantics of Lambda Calculi Achim Jung (Birmingham, UK) Proof Theory with Deep Inference Alessio Guglielmi (Dresden, Germany) Semantics and Cut-elimination for Church's (Intuitionistic) Theory of Types, with Applications to Higher-order Logic Programming Jim Lipton (Wesleyan, USA)

56. Bibliography For Intersection Types And Related Systems
An extension of the basic functionality theory for the lambda calculus. Notre Dame J. Formal Logic , 21(4)685-693, 1980.
http://www.macs.hw.ac.uk/~jbw/itrs/bibliography.html
##### Bibliography for Intersection Types and Related Systems
This bibliography is woefully incomplete. It will be greatly appreciated if people send me additional entries. These entries should preferably be in BibTeX format. It helps if the entry includes a brief (e.g., one sentence) note giving the main topics of the item. 187 references, last updated Wed Dec 19 18:05:07 2007
Alexander S. Aiken and Edward L. Wimmers. Type inclusion constraints and type inference. In FPCA '93, Conf. Funct. Program. Lang. Comput. Arch. , pages 31-41. ACM, 1993.
Alexander S. Aiken , Edward L. Wimmers, and T. K. Lakshman. Soft typing with conditional types. In Conf. Rec. 21st Ann. ACM Symp. Princ. of Prog. Langs. , pages 163-173, 1994.
F. Alessi and F. Barbanera . Strong conjunction and intersection types. In A. Tarlecki, editor, Proc. 16th Int'l Symp. Mathematical Foundations Computer Science (MFCS '91) , volume 520 of Lecture Notes in Computer Science , pages 64-73. Springer, 1991.
Fabio Alessi and Mariangiola Dezani-Ciancaglini . Type preorders and recursive terms. In ITRS '04 , pages 3-21. The ITRS '04 proceedings appears as vol. 136 (2005-07-19) of

57. RE: Lambda (was: Refactoring In Tunes)
The usual meaning of the word notation is a mathematical device, which has to include the theory. lambda theory is about modelling function calls via
http://osdir.com/ml/os.tunes/2000-01/msg00037.html