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1. The Church-Rosser Theorem For The Lambda Calculus For many years the churchrosser theorem has been a milestone in the treatment of the lambda calculus. It describes the confluence property, http://www.cis.upenn.edu/~hol/lamcr/

The Church-Rosser Theorem for the Lambda Calculus A Proof in Higher Order Logic For many years the Church-Rosser theorem has been a milestone in the treatment of the lambda calculus. It describes the confluence property, that if an expression may be evaluated in two different ways, both will lead to the same result. This paper describes a formulation of the proof within the Higher Order Logic (HOL) theorem prover. This follows the proof by This page gives information about this proof of the Church-Rosser theorem. It contains postscript and PDF versions of the paper. It also contains the full source code for the Higher Order Logic theorem prover to perform all proofs described in the paper. In addition, this page describes packages of supporting software, which supply needed tools to support the automated proof in the Higher Order Logic theorem prover. Papers A Proof of the Church-Rosser Theorem for the Lambda Calculus in Higher Order Logic PDF Briefing charts in postscript and PDF Given as a Category B paper at TPHOLs'2001,

2. Church-Rosser Theorem -- From Wolfram MathWorld The churchrosser theorem states that lambda calculus as a reduction system with lambda conversion rules satisfies the Church-Rosser property. http://mathworld.wolfram.com/Church-RosserTheorem.html

Search Site Algebra Applied Mathematics Calculus and Analysis ... Sakharov Church-Rosser Theorem The Church-Rosser theorem states that lambda calculus as a reduction system with lambda conversion rules satisfies the Church-Rosser property SEE ALSO: Church-Rosser Property Church's Theorem Church-Turing Thesis Lambda Calculus ... [Pages Linking Here] This entry contributed by Alex Sakharov author's link REFERENCES: Baader, F. and Nipkow, T. Term Rewriting and All That. Cambridge, England: Cambridge University Press, 1999. LAST MODIFIED: June 1, 2003 CITE THIS AS: Sakharov, Alex . "Church-Rosser Theorem." From MathWorld A Wolfram Web Resource, created by Eric W. Weisstein http://mathworld.wolfram.com/Church-RosserTheorem.html Wolfram Research, Inc. Other Wolfram Sites: Wolfram Research Demonstrations Site Integrator Tones Functions Site Wolfram Science Download Mathematica Player Complete Mathematica Show off your math savvy with a MathWorld T-shirt

3. Church-Rosser Theorem From FOLDOC churchrosser theorem. theory A property of a reduction system that states that if an expression can be reduced by zero or more reduction steps to either http://foldoc.org/?Church-Rosser Theorem

4. Church-rosser Theorem - OneLook Dictionary Search churchrosser theorem FOLDOP - Free On Line Dictionary Of Philosophy home, info Additional searches for church-rosser theorem. http://www.onelook.com/?loc=rescb&w=church-rosser theorem

5. Church-Rosser Theorem From FOLDOC foldoc.doc.ic.ac.uk/foldoc/ foldoc.cgi?ChurchRosser+Theorem - Similar pages A Proof of the church-rosser theorem and its Representation in a We give a detailed, informal proof of the Church-Rosser property for the untyped A-calculus and show its representation in LF. The proof is due to Tait and http://foldoc.doc.ic.ac.uk/foldoc/foldoc.cgi?Church-Rosser Theorem

6. JSTOR A New Proof Of The Church-Rosser Theorem. In effect, the churchrosser theorem demonstrated a strong form of consistency for a certain system for analyzing the behavior of functions; this was done http://links.jstor.org/sici?sici=0022-4812(195612)21:4<377:ANPOTC>2.0.CO;2-P

7. A Church-Rosser Theorem For Graph Grammars 7 Rosen, B. K., Treemanipulating systems and church-rosser theorems. J. ACM 20 (1973), 160187. 8 Rosen, B. K. Correctness of parallel programs the http://portal.acm.org/citation.cfm?id=1008343.1008344

8. Hardly Accessible Publications In Theoretical Computer Science A General churchrosser theorem by Peter Aczel and its corrections, (July 1978). The last section of this paper introduces contraction schemes that were http://perso.ens-lyon.fr/pierre.lescanne/not_accessible.html

A COLLECTION OF HARDLY ACCESSIBLE PUBLICATIONS IN THEORETICAL COMPUTER SCIENCE WITH A HISTORICAL INTEREST On type theory, lambda calculus and explicit substitutions On termination of term rewrite systems On confluence On syntax On type theory, lambda calculus and explicit substitutions The Decision of Equality in Recursive Types, an early proof Concerning the Syntax of ALGOL 68 by Claude Pair , in Algol Bulletin n. 31, March 1970 . This file contains copies of a paper written in 1969 by Claude Pair that shows that the equality in recursive types is decidable. The first calculus of explicit substitutions A namefree lambda calculus with facilities for internal definition of expressions and segments by N. G. de Bruijn Technological University Eindhoven, Netherlands, Department of Mathematics, (1978), (TH-Report), Number 78-WSK-03 . This report is probably the first presentation ever of a calculus of explicit substitutions. A generalization of type theory in lambda-calcul ) by , in On termination of term rewrite systems On the termination of Markov algorithms Zohar Manna and Steven Ness , Proc. of the Third Hawaii International Conference on System Science, Honolulu, HI, pp. 789-792 (January 1970)

9. Church-Rosser Theorem @ Computer-Dictionary-Online.org churchrosser theorem @ Computer Dictionary Online. Computer terminology definitions including hardware, software, equipment, devices, jargon abbreviations http://www.computer-dictionary-online.org/Church-Rosser Theorem.htm?q=Church-Ros

10. Barendregt: Lambda Calculus The churchrosser theorem states that if two terms are beta-convertible to one another, then there is a common term to which they both reduce. http://mathgate.info/cebrown/notes/barendregt.php

The Omega Group TPS A higher-order theorem proving system This page was created and is maintained by Chad E Brown Barendregt, H. P. The Lambda Calculus: Its Syntax and Semantics. North Holland, Amsterdam (1984). Part I: TOWARDS THE THEORY Chapter 1: Introduction. Chapter 2: Conversion. Chapter 3: Reduction. Chapter 4: Theories. ... Chapter 5: Models. Part II: CONVERSION Chapter 6: Classical Lambda Calculus. Chapter 7: The Theory of Combinators. Chapter 8: Classical Lambda Calculus (Continued) Chapter 10: Bohm Trees. Part III: REDUCTION Chapter 11: Fundamental Theorems. Chapter 13: Reduction Strategies. Appendix A: Typed Lambda Calculus. Part I: TOWARDS THE THEORY Chapter 1: Introduction. Lambda calculus is a theory of functions as rules instead of graphs. The objects of study (type free lambda terms) can be used as both function and argument. Lambda calculus was originally invented to provide a general theory of functions which could be extended to provide a foundation for mathematics. Church's original system [1932/33] was inconsistent due to the Kleene-Rosser paradox [1935]. One response by Church [1941] was to study the subsystem given by the lambda-I calculus. [Another response was to study a system based on typed lambda calculus.] Curry proposed to extend pure combinatory logic by illative notions to give a foundation for mathematics. This program has not been completed. Another foundational approach related to lambda calculus is Feferman's [1975/80] systems for constructive mathematics based on partial application. These systems are related to Wagner [1969] and Strong's [1968] Uniformly Reflexive Structures. Also, there are relationships between typed lambda calculus, proof theory and category theory.

11. Church-Rosser Theorem@Everything2.com A theorem of the lambda calculus. It states, basically, that each lambda expression with a terminating betareduction has a unique normal form, http://everything2.com/index.pl?node_id=609140

12. Church-Rosser Theorem churchrosser theorem. There is no more than one normal form. The normal form. Order of reductions doesn t matter. The normal form is the value of a - http://perl.plover.com/yak/lambda/samples/slide014.html

September 22, 1999 Strong Typing Slide #14 Church-Rosser theorem There is no more than one normal form: The normal form Order of reductions doesn't matter The normal form is the value of a -expression (Alonzo Church and J. Barkley Rosser) Next

13. Lecture22 - CS 330 This was proven by two people named Church and Rosser and is thus called the churchrosser theorem. Another name for this property is confluence. http://classes.eclab.byu.edu/330/wiki/index.cgi?Lecture22

14. Church-Rosser Theorem - Computing Reference - ELook.org Previous Terms, Terms Containing churchrosser theorem, Next Terms . chug chunker Church, Alonzo Church integer Church of the SubGenius http://www.elook.org/computing/church-rosser-theorem.htm

eLook Home eLook Computing Reference Search Computing Reference By Letter: Non-alphabet A B C ... Email this page to a friend Church-Rosser Theorem This property of a reduction system states that if an expression can be reduced by zero or more reduction steps to either expression M or expression N then there exists some other expression to which both M and N can be reduced. This implies that there is a unique normal form for any expression since M and N cannot be different normal forms because the theorem says they can be reduced to some other expression and normal forms are irreducible by definition. It does not imply that a normal form is reachable, only that if reduction terminates it will reach a unique normal form. Terms Containing Church-Rosser Theorem chug chunker Church, Alonzo Church integer ... Contact

15. Church-Rosser Theorem - Definitions From Dictionary.com Definitions of churchrosser theorem at Dictionary.com. http://dictionary.reference.com/browse/Church-Rosser Theorem

var pid = 113832; var nid = 113874; var mid = 679788; var word = 'Church-Rosser%20Theorem'; SafeAddOnload(init_near); Premium Content Register Log In Help ... The Web Advertisement 16 results for: Church-Rosser Theorem Browse Nearby Entries church tower church triumphant church visible ... Share This Church-Rosser Theorem theory A property of a reduction system that states that if an expression can be reduced by zero or more reduction steps to either expression M or expression N then there exists some other expression to which both M and N can be reduced. This implies that there is a unique normal form for any expression since M and N cannot be different normal forms because the theorem says they can be reduced to some other expression and normal forms are irreducible by definition. It does not imply that a normal form is reachable, only that if reduction terminates it will reach a unique normal form. U.S. Gazetteer Cite This Source Share This Church Creek, MD (town, FIPS 17050) Location: 38.50531 N, 76.15473 W Population (1990): 113 (52 housing units) Area: 0.8 sq km (land), 0.0 sq km (water)

16. Copyright (C) 1994 By Natarajan Shankar. All Rights Reserved. This (BOOTSTRAP THM) ;An Annotated Script of A MECHANICAL PROOF OF THE church-rosser theorem. ; by ; N. Shankar ; ;What follows is a list of events (definitions http://www.cs.utexas.edu/users/boyer/ftp/nqthm/nqthm-1992/examples/shankar/churc

17. Church-rosser Theorem - Definition Of Church-rosser Theorem By The Online Dictio Definition of churchrosser theorem in the Online Dictionary. Multiple meanings, detailed information and synonyms for church-rosser theorem. http://onlinedictionary.datasegment.com/word/church-rosser theorem

Online Dictionary C : church-rosser theorem church-rosser theorem 1 definition found church-rosser theorem Free On-line Dictionary of Computing (26 May 2007) : reduction system that states that if an expression can be reduced by zero or more reduction steps to either expression M or expression N then there exists some other expression to which both M and N can be reduced. This implies that there is a unique normal form for any expression since M and N cannot be different normal forms because the theorem says they can be reduced to some other expression and normal forms are irreducible by definition. It does not imply that a normal form is reachable, only that if reduction terminates it will reach a unique normal form. (1995-01-25)

18. Readings: Theory Of Computation The churchrosser theorem is treated in here, also. And a treatment of FP, the John Backus approach to functional programming. http://miser-theory.info/readings/theory.htm

Miser Project Readings Theory of Computation L ast updated 2003-02-10-22:35 -0800 (pst) see also Readings in Logic Readings in Mathematics Readings in Philosophy 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.

19. CiteULike: A Proof Of The Church-Rosser Theorem And Its Representation In A Logi A Proof of the churchrosser theorem and its Representation in a Logical Proofs of meta-theorems are represented as higher-level judgments which relate http://www.citeulike.org/user/msakai/article/1639223

Register Log in FAQ CiteULike News Discussion Journals Browse current issues Groups Search groups Profile Library Watchlist ... Import A Proof of the Church-Rosser Theorem and its Representation in a Logical Framework Authors Pfenning F Online Article CiteSeer (at Penn State): View article online CiteSeer (at MIT): View article online CiteSeer (at Zurich): View article online CiteSeer (at Singapore): View article online Note: You or your institution must have access rights to this article. CiteULike will not help you view an online article which you aren't authorized to view. Copy-and-Pasteable Citation Journal of Automated Reasoning Citation format: Plain APA Chicago Elsevier Harvard MLA Nature Oxford Science Turabian Vancouver msakai's tags for this article type-theory Everyone's tags for this article type-theory Abstract We give a detailed, informal proof of the Church-Rosser property for the untyped -calculus and show its representation in LF. The proof is due to Tait and Martin-Lof and is based on the notion of parallel reduction. The representation employs higher-order abstract syntax and the judgments-as-types principle and takes advantage of term reconstruction as it is provided in the Elf implementation of LF. Proofs of meta-theorems are represented as higher-level judgments which relate sequences of... BibTeX Note: You may cite this page as: http://www.citeulike.org/user/msakai/article/1639223

20. Church-Rosser Theorem - Wikipedia The churchrosser theorem states that, in the lambda calculus, a term has at most one normal form. Specifically, if two different reductions of a term both http://www.facetroughgemstones.com/wikipedia/ch/Church-Rosser_theorem.html

Contents Church-Rosser theorem The Church-Rosser theorem states that, in the lambda calculus , a term has at most one normal form . Specifically, if two different reductions of a term both terminate in normal forms, then the two normal forms will be identical. It is the Church-Rosser theorem that justifies references to " the normal form" of a certain term. The theorem was discovered in 1937 by Alonzo Church and J. Barkley Rosser[?] See also lambda calculus wikipedia.org dumped 2003-03-17 with terodump

21. Powell's Books - Cambridge Tracts In Theoretical Computer Science #0038: Metamat Derived inference rules; 4. The representability of metatheory; 5. The undecidable sentence; 6. A mechanical proof of the churchrosser theorem; 7. http://www.powells.com/biblio?isbn=9780521585330

22. Church-Rosser Theorem From FOLDOC Nearby terms Christianity « Chrysippus « Church Alonzo « churchrosser theorem » Church s theorem » Church s thesis » Cicero Marcus Tullius. http://lgxserver.uniba.it/lei/foldop/foldoc.cgi?Church-Rosser Theorem

23. Church-Rosser Theorem For A Rewriting System On Categorical Combinators churchrosser theorem for a Rewriting System on Categorical Combinators. Hirofumi Yokouchi. Journal Title Theoretical Computer Science. Date 1989 http://wotan.liu.edu/docis/show?doc=dbl/tcstcs/1989_65_3_271_CTFARS.htm&query=

24. Definition Of Church-Rosser Theorem In Computing Vietnamese English French Chinese online dictionary. Tu dien tieng Viet truc tuyen. Free Vietnamese online translation. http://vdict.com/Church-Rosser Theorem,6.html

Dictionary Translation Community Tools ... Firefox search plugin For Webmasters VDict on your site VDict search form Company information Press release ... Community support forum Language English Vietnamese Search history History size Delete history View history tabdropdown.init("colortab", "auto") English - Vietnamese dictionary Vietnamese - English dictionary Vietnamese - Vietnamese Dictionary French - Vietnamese Dictionary Vietnamese - French Dictionary Computing English - English Dict (Wordnet) Chinese - Vietnamese dictionary Vietnamese keyboard On Off Search in Name Definition Match type Chinese character Exact Pinyin trans. Broad Vietnamese trans. Fuzzy Computing Church-Rosser Theorem This property of a reduction system states that if an expression can be reduced by zero or more reduction steps to either expression M or expression N then there exists some other expression to which both M and N can be reduced. This implies that there is a unique normal form for any expression since M and N cannot be different normal forms because the theorem says they can be reduced to some other expression and normal forms are irreducible by definition. It

25. Online Otter-λ The churchrosser theorem. A term of the form Ap(lambda (i.e. one that matches the left side of the beta axiom) is said to permit beta reduction, http://michaelbeeson.com/research/otter-lambda/index.php?include=LambdaCalculus

26. [Some Citations For Lambda Calculus Books From MathSciNet Djr He then gives the simplest known proof of the churchrosser theorem, which shows the consistency of both systems. Next follows a discussion of completeness, http://www.math.niu.edu/~rusin/known-math/99/lambdacalc_refs

27. Miscellaneous churchrosser theorem I If E1 \leftrightarrow E2 then there is an expression E, church-rosser theorem II If E1 E2, and E2 is in normal form, http://cs.wwc.edu/~aabyan/PLBook/HTML/Misc.html

28. Masterclass Typed Lambda Calculus Untyped theory second fixedpoint theorem (6 Thm. 6.5.9), Scott s theorem (6 Thm. 6.6.2);. church-rosser theorem (1 Ch 4). Typed theory Church typed http://www.cs.ru.nl/~henk/Masterclass.html

Masterclass Typed Lambda Calculus by Henk Barendregt assisted by Wil Dekkers and Venanzio Capretta Fall Semester 2006, Wednesdays 10.00-13.00. Radboud University, Huygens Building 3.054, Toernooiveld 1, Nijmegen Behind the content of the lectures the numbers refer to the references below. 20.09.2006 Week 1 Excercises Untyped theory: conversion, reduction, Church numerals, A_+, A_*, A_exp. (5: Sct. 2.2 Typed theory: Typing a la Curry (1: Ch. 5 Sct. 1.1 27.09.2006 Week 2 Excercises Untyped theory: Representing arbitrary computable functions (5: Sct. 2.2 ). Fixed-points. (5: Sct. 2.1 Typed theory: Typing algorithm. (2: ; it is less difficult than it looks!) Inhabitation algorithm for typing a la Curry (2: Sct. 1.2 04.10.2006 Week 3 Excercises Untyped theory: eta-reduction (2: ). Coding and reflection (4: Sct. 5 Typed theory: eta-expansion (2: Sct. 1.2 11.10.2006 Week 4 test 1 Untyped theory: second fixed-point theorem (6: Thm. 6.5.9), Scott's theorem (6: Thm. 6.6.2); Church-Rosser theorem (1: Ch 4 Typed theory: Church typed terms. (2: Sct 1.1

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30. J Roger Hindley : Research MR0693047 J R Hindley, The completeness theorem for typing lambda terms, MR0302434 J R Hindley, An abstract form of the churchrosser theorem, I, http://www-maths.swan.ac.uk/staff/jrh/JRHresearch.html

Swansea University Physical Sciences Mathematics Department J Roger Hindley J Roger Hindley : Research fields of interest main publications career Fields of Interest Mathematical logic; particularly lambda-calculus, combinatory logic and type-theories, with a current bias towards historical aspects. Lambda-calculus and combinatory logic are formal systems, to some extent rivals, used in the construction and study of programming languages which are higher-order (i.e. in which programs may change other programs). These two systems were invented in the 1920s by mathematicians for use in higher-order logic, and came to be applied in programming theory from the 1970s onward, when that theory expanded to cover higher-order computations. In a type-theory, types are labels which may be attached to certain programs to show what other programs they can change. A type-system is a particular set of rules for attaching types; the rules themselves are usually reasonably simple, but such questions as what programs are typable, what set of types a program may receive, and whether a typable computation can continue indefinitely, are not always easy to answer and have occupied many researchers. Main Publications J R Hindley, J P Seldin

31. A Proof Of The Church-Rosser Theorem And Its Representation In A Title, A Proof of the churchrosser theorem and its Representation in a Logical Framework. Author, Pfenning, Frank. Abstract, We give a detailed, http://www.ncstrl.org:8900/ncstrl/servlet/search?formname=detail&id=oai:ncstrlh:

32. CSc 520 Principles Of Programming Languages : 29 churchrosser theorem. Question. If there is more than one reduction strategy, does each one lead to the same normal form expression? http://www.cs.arizona.edu/~collberg/Teaching/520/2005/Html/Html-24/index.html

CSc 520 Principles of Programming Languages Christian Collberg Department of Computer Science University of Arizona Functional Programming Languages 1 Functional Programming In contrast to procedural languages, functional programs don't concern themselves with state and memory locations. Instead, they work exclusively with values , and expressions and functions which compute values. Functional programming is not tied to the von Neumann machine. It is not necessary to know anything about the underlying hardware when writing a functional program, the way you do when writing an imperative program. Functional programs are more declarative than procedural ones; i.e. they describe what is to be computed rather than how it should be computed. 2 Functional Languages Common characteristics of functional programming languages: Simple and concise syntax and semantics. Repetition is expressed as recursion rather than iteration. Functions are first class objects . I.e. functions can be manipulated just as easily as integers, floats, etc. in other languages.

33. Church-Rosser Theorem - Mathematics Dictionary And Research Guide churchrosser theorem - The Church–Rosser theorem states that if there are two distinct reductions starting from the same term in la. http://www.123exp-math.com/t/01704107984/

The Language of Mathematics - Dictionary and Research Guide Provided by Search: Add to Favorites Church-Rosser theorem The Church–Rosser theorem states that if there are two distinct reductions starting from the same term in lambda calculus, then there exists a term that is reachable via a (possibly empty) sequence of reductions from both reducts. As a consequence, a term in the lambda calculus has at most one normal form. Wikipedia and Wikis Church-Rosser theorem - Wikipedia http://en.wikipedia.org/wiki/Church-Rosser_theorem Keywords and Synonyms Church-Rosser theorem, Church-Rosser More topics about: Church-Rosser theorem Edit this page Add new links, rate and edit existing links, or make suggestions. - Staff Explore related topics: Eager evaluation Lazy evaluation Gordon Plotkin J Barkley Rosser ... Lambda calculus Some descriptions may have been derived in part from Princeton University WordNet or Wikipedia Last update: December 19, 2007

34. The Church-Rosser Theorem II The churchrosser theorem II. The church-rosser theorem II. If E1 - * E2 and E2 is in normal form, then there exists a normal-order reduction from E1 to http://www.exso.com/courses/cs101a/slides/lambda/node11.html

Next: Recursive functions Up: No Title Previous: Different reduction strategies The Church-Rosser Theorem II If E1 ->* E2 and E2 is in normal form, then there exists a normal-order reduction from E1 to E2. Alan Bond

35. Church-Rosser Theorem Definition - Computer Dictionary Online churchrosser theorem definition Computer Dictionary, Computer Terms Dictionary online. http://www.hobbyprojects.com/computer-terms-dictionary/computer-dictionary-c/def

36. FOLDOP Search churchrosser theorem. logic This property of a reduction system states that Nearby terms Chrysippus « Church Alonzo « church-rosser theorem » Cicero http://www.swif.it/foldop/dizionario.php?find=Church-Rosser Theorem

37. Rewrite Rules, Reduction, And Normal Forms The first churchrosser theorem. Rewriting with beta and eta conversions The last result is a direct consequence of the second church-rosser theorem. http://www.cs.aau.dk/~normark/prog3-03/html/notes/eval-order_themes-reduction-se

The Order of Evaluation 20. Rewrite rules, reduction, and normal forms At this point in the material it will be assumed that the reader is motivated to study evaluation order in some detail. An evaluation of an expression can be understood as a transformation of the expressions which preserves its meaning. In this chapter we will see that transformations can be done incrementally in rewriting steps . A rewriting of an expression gives a new expression which is semantically equivalent to the original one. Usually, we go for rewritings which simplify an expression. In theory, however, we could also rewrite an expression to more complicated expression. In this chapter we will formally characterize the value of an expression , using the concept of a normal form. We will see that the value of an expression is an expression in itself that cannot be rewritten to simpler forms by use of any rewriting rules. As a key insight in this chapter, we will also see that an expression can be reduced to a value (a normal form) in many different ways. We will identify and name a couple of these, and we will discuss which of the evaluation strategies is the 'best'. Rewrite rules An example of normal versus applicative evaluation The alpha rewrite rule Theoretical results ... The ordering of reductions 20.1. Rewrite rules

38. A Mechanical Proof Of The Church-Rosser Theorem. D2R Server A mechanical proof of the churchrosser theorem. Resource URI http//www4.wiwiss.fu-berlin.de/dblp/resource/record/journals/jacm/Shankar88 http://www4.wiwiss.fu-berlin.de/dblp/resource/record/journals/jacm/Shankar88

39. The Church-Rosser Theorem In Isabelle: A Proof Porting Experiment This paper describes a proof of the churchrosser theorem for the pure -calculus formalised in the Isabelle theorem prover. The initial version of the proof http://nsdl.org/resource/2200/20061123082842405T

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40. Church-Rosser Theorem - Wikiosity Topic churchrosser theorem, = one degree of separation. Boston Interior Design Rankings 2007 An unofficial guide to Greater Boston http://www.maxtility.com/scgi-bin/wikiosity.cgi?q=Church-Rosser_theorem

41. Bibliography Of LF - The Twelf Project A proof of the churchrosser theorem and its representation in a logical framework. Journal of Automated Reasoning, 1993. To appear. http://twelf.plparty.org/wiki/Bibliography_of_LF

var skin = 'monobook';var stylepath = '/w/skins'; Bibliography of LF From The Twelf Project Jump to: navigation search This page needs some work: The links haven't all been taken over from the old page , and after that happens, they should be tested as many are dead links. This is a bibliography collected by Frank Pfenning on the LF logical framework, the logic programming language Elf which is based on LF, and the Twelf meta-logical framework (which includes an implementation of Elf). It is a selection of papers from a more general bibliography on logical frameworks. Papers with known URLs in the World-Wide Web have been annotated with their location and can be previewed or retrieved directly. Corrections, additions, and new URL's for papers and implementations are welcome. edit Basic References For the LF logical framework : R. Harper, F. Honsell, and G. Plotkin, A Framework for Defining Logics For the Elf language: F. Pfenning, Logic Programming in the LF Logical Framework For the Twelf implementation: System description: Twelf - a meta-logical framework for deductive systems edit Full Bibliography Penny Anderson. Program Derivation by Proof Transformation. PhD thesis, Carnegie Mellon University, October 1993. Available as Technical Report CMU-CS-93-206.

42. Seminars Of The CENTRE De RECHERCHE En THEORIE Des CATEGORIES The constant \Label can be defined as a closed term, so that the labelled syntax is ultimately interpreted in a syntax for which the churchrosser theorem http://www.math.mcgill.ca/rags/seminar/seminar.listings.93

is category equivalent to the variety W generated by some known algebra ; this equivalence induces a lattice isomorphism between the sets of closed sets containing G and G' which enables us to determine if G is maximal in F. We present several examples and certain extensions of this method.

43. Foundations Of Computer Science The notion of parallel reduction is extracted from the simple proof of the churchrosser theorem by Tait and Martin-Löf. Intuitively, this means to reduce a http://tcs.uj.edu.pl/csfs

Theoretical Computer Science Faculty of Mathematics and Computer Science Jagiellonian University Foundations of Computer Science guest TCS - home algorithmics cs foundations news ... links events: computer science on trail (pl) UZI - January 12, 2008(pl) CLA 2007 past events seminars: Computer Science Foundations faculty: Jakub Kozik Stanisà ‚aw Sędziwy Edward Szczypka Paweà ‚ Waszkiewicz ... Marek Zaionc secretary: Monika Gillert phd students: Katarzyna Grygiel Jarosà ‚aw Karpiak Mikoà ‚aj Pudo graduates: phd thesis msc thesis login: password: Computer Science Foundations Seminar Wednesday: 12:15 - 14:00, room 117 Research seminar devoted to problems related to asymptotic densities in logic, computability theory, computational logic, typed lambda calculus, logic programming, logics of programs, functional programming. table edited by: Marek Zaionc Szymon W³jcik Parallel reductions in lambda calculus The notion of parallel reduction is extracted from the simple proof of the Church-Rosser theorem by Tait and Martin-L¶f. Intuitively, this means to reduce a number of redexes (existing in a lambda term) simultaneously. During the talk, after reevaluating the significance of the notion of parallel reduction in Tait-and-Martin-L¶f type proofs of the Church-Rosser theorems, we show that the notion of parallel reduction is also useful in giving short and direct proofs of some other fundamental theorems in reduction theory of lambda calculus. Dominika Majsterek UJ Behavioural differential equations: a coinductive calculus (czÄ™à ›Ä‡ 2)

44. A Notation For Deterministic Cooperating Processes The ideas in this paper are derived from the churchrosser theorem about systems that obey the diamond property 7, 20 and from the concept of http://doi.ieeecomputersociety.org/10.1109/71.406962

var sc_project=2763585; var sc_invisible=0; var sc_partition=28; var sc_security="3c678009"; var addtoLayout=0; var addtoMethod=0; var AddURL = escape(document.location.href); // this is the page's URL var AddTitle = escape(document.title); // this is the page title Advanced Search CS Search Google Search Home Digital Library Podcasts Site Map ... Table of Contents Abstract August 1995 (Vol. 6, No. 8) pp. 863-871 A Notation for Deterministic Cooperating Processes K. Mani Chandy Ian Foster Full Article Text: DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.406962 Send link to a friend Abstract About References Back to Top References [1] American National Standards Institute Inc., The Programming Language Ada Reference Manual, Springer-Verlag, 1983. Proc. ASPLOS-IV, Apr. 1991. Tech. Report, Computer Science, UCLA, Los Angeles, Calif., 1990. [4] J. Boyle,R. Butler,T. Disz,B. Glickfield,E. Lusk,R. Overbeek,J. Patterson,, and R. Stevens

45. Awesome Library - Mathematics Proving theorems is a central activity of mathematics. Chebotarev s density theorem, Chinese remainder theorem, churchrosser theorem, Closed and exact http://www.awesomelibrary.org/Classroom/Mathematics/College_Math/College_Math.ht

Search Spelling Here: Home Classroom Mathematics > College Math College Math Sub-Topics Algebra Calculus Geometry Graphing ... Trigonometry Lesson Plans Algorithms (Math Forum) Provides sources. 6-02 Common Errors in College Math (Vanderbilt University) Provides a description of the most common errors by undergraduate students in algebra, calculus, reasoning, and more. 6-02 Discrete Math (Math Forum) Provides sources. 6-02 Exponents (Math Forum) Provides sources of lessons. 6-02 Imaginary and Complex Numbers (Math Forum) Provides sources. 6-02 Logic and Set Theory (Math Forum) Provides sources. 6-02 Number Theory (Math Forum) Provides sources. 6-02 Papers -Articles by Topic (Wikipedia.org) Provides dozens of topics. 1-07 -Mathematical Notation (Wikipedia.org) Includes Big O notation, Blackboard bold, Bra-ket notation, Bracket, Del, Ellipsis, Equality (mathematics), Index set, Infix, Infix notation, Internet shorthand notation, Kronecker delta, Mathematical alphanumeric symbols, Mathematical notation, Operator, Parenthesis, Plus and minus signs, Plus-minus sign, Polish notation, Positional notation, Prefix, Reverse Polish notation, Set-builder notation, Table of mathematical symbols, and Vinculum. 10-04 Chaos Theory (Wikipedia.org)

46. Projects Tobias Nipkow has proved the churchrosser theorem for the lambda-calculus using a novel formalization, covering both the beta and the eta rules. Isabelle http://isabelle.in.tum.de/projects.html

Projects Navigation Home Overview Download Installation ... Community Site Mirrors: Cambridge (.uk) Munich (.de) Sydney (.au) Introduction Researchers are applying Isabelle to a broad range of problems. Further work has been presented at the 2007 Isabelle Workshop and at many conferences, such as FME, CADE and TPHOLs. Formalized Mathematics (including semantics) Logical Investigations Program Development Specification Languages Verification (of programs or systems) « means the material is included in the Isabelle distribution This page is based upon information supplied by the researchers themselves. Comments and corrections are welcome at Formalized Mathematics Simon Ambler and Roy Crole have used a deep encoding of syntax based on de Bruijn indices to formalize the operational semantics of a small functional programming language. This has enabled standard concepts of program equivalence to be presented uniformly through inductive and coinductive definitions. It is proved formally that applicative bisimulation is a congruence, and that it coincides with Morris-style contextual equivalence. A preliminary report is available as compressed postscript.

47. QG Seminar: Winter 2007 The churchrosser theorem. Surface diagrams showing the process of computation. -reduction as a fold catastrophe. Thom s ideas on catastrophe theory. http://math.ucr.edu/home/baez/qg-winter2007/

Quantum Gravity Seminar - Winter 2007 John Baez and Derek Wise This quarter's seminar will be a continuation of the Fall 2006 seminar . So, we will again discuss two subjects: Quantization and Cohomology (Tuesdays) Classical versus Quantum Computation (Thursdays) As usual, John Baez lectured and Derek Wise took beautiful notes which you can see here. If you discover any errors in these notes, please email me, and we'll try to correct them. We'll keep a list of errors that haven't been fixed yet. These courses are also available via my blog at the n . This is a new experiment, and I hope you try it. Each week's notes comes with a blog entry where you can ask questions, make comments, and chat with other people following the course. The week numbers for these notes continue where last quarter's notes leave off. The course continues in the Spring There are also LaTeX, encapsulated PostScript and xfig files to download if for some bizarre reason you want them. However, we reserve all rights to this work. Quantization and Cohomology In last Fall's lectures , we discussed the Lagrangian and Hamiltonian approaches to the classical mechanics of point particles, and sketched how these could be generalized to strings and higher-dimensional membranes by a process that we'll ultimately see as categorification . You can read what we did here: John Baez and Apoorva Khare, with figures by Christine Dantas

48. ODOBS - Publication Page A Mechanical Proof Of The Church-Rosser A mechanical proof of the churchrosser theorem. Authors. Natarajan SHANKAR. Year, 1988. Journal, J. ACM. Volume, 35. Number, 3. Pages, 475-522 http://odobs.cs.uni-dortmund.de:8080/odobs/publication;jsessionid=B834D22721815E

49. Annotated Bibliography - POPLmark 1992, Frank Pfenning A proof of the church-rosser theorem and its representation in a logical framework (via citeseer) Elf, HOAS. http://alliance.seas.upenn.edu/~plclub/cgi-bin/poplmark/index.php?title=Annotate

50. DBLP: J. Roger Hindley 4, J. Roger Hindley The Discrimination Theorem Holds for Combinatory Weak Reduction 2, J. Roger Hindley An Abstract Form of the churchrosser theorem. http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/h/Hindley:J=_Roger.htm

J. Roger Hindley List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... EE , J. Roger Hindley: Combinatory Weak Reduction in Lambda Calculus. Theor. Comput. Sci. 198 EE Martin W. Bunder , J. Roger Hindley: Two beta-Equal lambda-I-Terms with no Types in Common. Theor. Comput. Sci. 155 P. Trigg , J. Roger Hindley, Martin W. Bunder : Combinatory Abstraction Bsing B, B' and Friends. Theor. Comput. Sci. 135 J. Roger Hindley: BCK and BCI Logics, Condensed Detachment and the 2-Property. Notre Dame Journal of Formal Logic 34 J. Roger Hindley: Types with Intersection: An Introduction. Formal Asp. Comput. 4 Mariangiola Dezani-Ciancaglini , J. Roger Hindley: Intersection Types for Combinatory Logic. Theor. Comput. Sci. 100 J. Roger Hindley, David Meredith : Principal Type-Schemes and Condensed Detachment. J. Symb. Log. 55 Martin W. Bunder , J. Roger Hindley, Jonathan P. Seldin : On Adding (xi) to Weak Equality in Combinatory Logic. J. Symb. Log. 54 J. Roger Hindley: BCK-Combinators and Linear lambda-Terms have Types. Theor. Comput. Sci. 64

51. Practical Foundations Of Mathematics FACT 2.3.3 The churchrosser theorem says that the pure l-calculus (without d-rules) is confluent (Definition 1.2.5). The simply typed pure l-calculus is http://www.cs.man.ac.uk/~pt/Practical_Foundations/html/s23.html

Practical Foundations of Mathematics Paul Taylor Sums, Products and Function-Types We begin our reassessment of the constructions needed in mathematics by considering the function-type and sum. The system of types which is freely generated by the binary symbols x and + from , 1 and a given collection of base types or sorts will be called simple type theory . Applied to sets, x , + and refer to the constructions of Section . Recall that these were accompanied by operations such as p i n i and ev , which we shall now discuss. Later we shall show how certain other mathematical objects admit directly analogous structures. Function ( l ) abstraction Sections discussed how functions act , but they must also be considered as entities in themselves . Early in the history of the integral calculus problems arose in which the unknown was a function as a whole , rather than its value at particular or even all points: the Sun's light takes that path through the variable density of the atmosphere which minimises the time of travel; the motion of a stretched string depends on its initial displacement along its whole length. R EMARK 2.3.1 In order to consider a function

52. Quals: Programming Languages - SEWiki The churchrosser theorem says that if there is more than one possible way of evaluating an expression in a functional language, then it does not matter http://www.cs.wm.edu/~coppit/wiki/index.php/Quals:_Programming_Languages

Quals: Programming Languages From SEWiki edit MacLennan's Design Principles Abstraction Avoid requiring something being stated more than once. (Factor out the repeating pattern, such as with functions or abstract data types.) Automation Automate mechanical, tedious or error-prone activities. (No need to code offsets, let the machine do it. Looping, macros, garbage collection, type inferencing, implicit coercion, automatic declaration of variables, compiler optimizations.) Defense in Depth Have a series of defenses such that if an error isn't caught by one defense, then it probably will be caught by another. (That is if the syntax checker doesn't spot an illegal type assignment, then the type checker will. Array bounds checking, types on parameters to functions, GOTOs violate.) Information Hiding The languages should permit modules designed such that (1) the user has all of the information needed to use the module correctly, and (2) the implementor has all of the information needed to implement the module and nothing more. (Classes, modularity.) Labeling Avoid arbitrary sequences more than a few lines long. (Do not require the user to know the absolute position of an item in a list. Instead, associate a meaningful label with each item and allow the item to occur in any order. Case statements, position independent parameters, enumerated types.)

53. Church’s Thesis And Functional Programming The two most important technical results are churchrosser theorem If A . The rules for reduction remain unchanged, as does the church-rosser theorem. http://www.scribd.com/doc/35191/Churchs-Thesis-and-Functional-Programming

Login Home Browse Groups ... Upload utmx_section("View Redirect") document.write(''); Type in Email Addresses Your Name Send Doc to (one email address per line): Personal Message (optional): OR Import Email Addresses to Send to Choose your email provider: Sign into your account: Username Password Church’s Thesis and Functional Programming utmx_section("Top of Right Bar Ad") Related Documents Views: From: god Yet another Haskell tutorial Views: From: beautiphu developing-applications-w ith-ocaml Views: From: anon-42121 radical Views: From: god onlisp Views: From: snowmaker Programming Languages and Lambda Calculi Views: From: knv csharp 3 specification Views: From: anon-255668 Church's Thesis and Functional Programming Views: From: knv Views: From: anon-527597 cmu Views: From: anon-782398 KrsticConchon Views: From: anon-387258 Views: From: anon-716316 picklercombinators Views: From: anon-81777 2002-10-28-lc Views: From: anon-164262 Views: From: anon-648394 Views: From: anon-822776 Views: From: anon-544326 Views: From: anon-987674 aspect traceability through invertible wea... Views: From: anon-798030 lecture-03 Views: From: anon-301084 lecture-08 Views: From: anon-18462 static Views: From: anon-671214 talk Views: From: college Views: From: college Views: From: college wed Views: From: college Views: From: college Views: From: college onlisp Views: From: stark Yet Another Haskell Tutorial + Haskell Wik...

54. I. Why Study The Theory Of Programming Languages? A. Arguments For C. churchrosser theorems - CHURCH ROSSER THEOREMS 1. If X Y, then there is some Z such that X * Z and Y * Z (this http://www.cs.iastate.edu/~leavens/ComS541Fall03/meeting-outlines/lambda-calculu

inc - 4. convertability relation denoted =, cnv, or Y, then there is some Z such that X >* Z and Y >* Z (this property is called *confluence*) - - 2. If X has a normal form Y, there is a normal order reduction from X to Y. corollary: if want to find normal form, use normal order eval. - D. Normalization, comparison of simply typed and untyped calculus - NORMALIZATION def: a system is * weakly normalizing (or church-rosser, confluent): if only one normal form for a term * strong normalizing (terminating): if every term has a normal form -

55. Church–Rosser Theorem - Wikipedia, The Free Encyclopedia The Church–Rosser theorem states that if there are two distinct reductions starting from the same term in lambda calculus, then there exists a term that is http://en.wikipedia.org/wiki/Church–Rosser_theorem

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Church–Rosser theorem From Wikipedia, the free encyclopedia Jump to: navigation search The Church–Rosser theorem states that if there are two distinct reductions starting from the same term in lambda calculus , then there exists a term that is reachable via a (possibly empty) sequence of reductions from both reducts. As a consequence, a term in the lambda calculus has at most one normal form . It is thus the Church–Rosser theorem that justifies references to " the normal form" of a certain term. The theorem was proved in 1936 by Alonzo Church and J. Barkley Rosser The Church–Rosser theorem also holds for many variants of the lambda calculus, such as the simply-typed lambda calculus , many calculi with advanced type systems, and Gordon Plotkin 's beta-value calculus. Plotkin also used a Church–Rosser theorem to prove that the evaluation of functional programs (for both lazy evaluation and eager evaluation ) is a function from programs to values (a subset of the lambda terms). In the 1980s, the Church–Rosser theorem was established for extensions of the lambda calculus with features from imperative programming languages edit See also Confluence (term rewriting) edit References Alonzo Church and J. Barkley Rosser.