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1. "Archives: Re: Problems And Suggestions For Coq
de bruijn indexes. So does Coq when it works on my formalization of CoC, i.e. it has to execute my implementations of xi and beta conversion.
Re: Problems and suggestions for Coq
Mon, 19 Sep 94 18:59:42 +0200
Subject: Re: Problems and suggestions for Coq
Date: Mon, 19 Sep 94 18:59:42 +0200
Sorry for being so long time about answering your letters on
my problem with and my suggestions for Coq. I did not
want to answer before I could make my source available for
FTP. My thesis advisor asked me to complete a report that
answers many of your questions before replying. Werner, Murphy and Pollack have send me answers. I will try answering all three by this letter. I wrote: Werner answered: Murthy answered: I have now worked a bit more with the examples. I think Murthy is right. I have made two definitions of CoC that are both placed in the directory for FTP. The first definition is called formcoc10.v and the second formcoc12.v. I changed

2. Calculus Of Inductive Constructions
In the expressions lambda xT, U and for all xT, U the occurrences of x in U are bound. They are represented by de bruijn indexes in the internal structure
Chapter 4 Calculus of Inductive Constructions
The underlying formal language of Coq is a Calculus of Constructions with Inductive Definitions . It is presented in this chapter. For Coq version V7, this Calculus was known as the Calculus of (Co)Inductive Constructions Cic in short). The underlying calculus of Coq version V8.0 and up is a weaker calculus where the sort Set satisfies predicative rules. We call this calculus the Predicative Calculus of (Co)Inductive Constructions (p Cic in short). In section we give the extra-rules for Cic . A compiling option of Coq allows to type-check theories in this extended system.
In p Cic all objects have a type . There are types for functions (or programs), there are atomic types (especially datatypes)... but also types for proofs and types for the types themselves. Especially, any object handled in the formalism must belong to a type. For instance, the statement ``for all x, P'' is not allowed in type theory; you must say instead: ``for all x belonging to T, P'' . The expression ``x belonging to T'' is written ``x:T'' . One also says: ``x has type T'' . The terms of p Cic are detailed in section
In p Cic there is an internal reduction mechanism. In particular, it allows to decide if two programs are

3. @article {Ohori19970892-463561, Author = Ohori A. , Author
Different from de bruijn indexes, our integer representation of a variable corresponds to the actual offset to the value in a runtime environment;j

4. A Question On Free Variable Capture. | Lambda The Ultimate
The upshot of alpha conversion is simply that the labels don t matter, the bindings do, and there are a number of formal tricks, such as de bruijn indexes
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A question on free variable capture.
I've been studying the lambda calculus by reading the available texts found doing your basic google search. A question has come up that I have not found a sufficient answer to. When doing variable substitution in an application ((E1 E2)) it is fairly straight forward if E2 is a variable. When E2 is something more complex, like an abstraction, how do things work with regards to alpha conversion? Do you first find all the free variables in E2, then rename those that exist free in E1? Or since E2 isn't a variable do not do an alpha conversion stage? Anyone out there too familiar with lambda calculus, I'd appreciate a little assist. -Chris By cjh LtU Forum previous forum topic next forum topic ... other blogs
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5. Abstracts Of The Workshops At The School In Logic And Computation
There are several well known approaches, e.g. nameless variables (de bruijn indexes) and quotienting by alphaconversion, but these have their own drawbacks

6. MySQL AB :: Index Usage In 4.1.7
If something did change in the new version 4.1.7 can someone tell me how the indexes are used by MySQL now ? With kind regards, F. de bruijn,8135,8135

7. EULER Record Details
Forwarding indexes are calculated for cube networks and generalized de bruijn networks. General bounds are derived which show that de bruijn networks are

8. Rewriting.Term.SimpleType.TermsLifting
Operation of lifting (increasing indexes of variables) and lowering (decreasing them) on of terms using de bruijn indices) is defined in this file.
Library Rewriting.Term.SimpleType.TermsLifting
  • Adam Koprowski, 2006-04-27
Operation of lifting (increasing indexes of variables) and lowering (decreasing them) on terms of simply typed lambda-calculus (which is an equivalent of renaming of variables for the representation of terms using de Bruijn indices) is defined in this file. Require Import RelExtras Require Import ListExtras Require TermsManip Require Import Require Import Arith. Require Omega. Module TermsLifting (Sig : TermsSig.Signature). Module TB := TermsManip.TermsManip Sig. Export TB. Fixpoint prelift_aux (n: nat ) (P: Preterm ) (k: nat Preterm match P with Fun Var match ( k i) with left Var (i + n) right Var i end App App (prelift_aux n M k) (prelift_aux n N k) Abs Abs A (prelift_aux n M ( S k)) end. Definition prelift P n := n P 0. Definition liftedEnv (n: nat ) (E: Env ) (k: nat Env initialSeg E k ++ copy n None finalSeg E k. Lemma liftedEnv_next : forall A E n k, liftedEnv n ( decl A E) ( S k) = decl A ( liftedEnv n E k). Hint Rewrite : terms. Lemma liftedEnv Lemma liftedEnv Lemma var_liftedEnv_var_lifted : forall E x A k n

9. De Bruijn Index - Wikipedia, The Free Encyclopedia
In mathematical logic, the de bruijn index is a notation invented by the Dutch mathematician Nicolaas Govert de bruijn (IPA d b œyn) for representing
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de Bruijn index
From Wikipedia, the free encyclopedia
Jump to: navigation search In mathematical logic , the de Bruijn index is a notation invented by the Dutch mathematician Nicolaas Govert de Bruijn (pronounced help [dɪˈbʁœyn] ) for representing terms in the λ calculus Terms written using these indexes are invariant with respect to α conversion , so the check for α-equivalence is the same as that for syntactic equality. Each de Bruijn index is a natural number that represents an occurrence of a variable in a λ-term, and denotes the number of binders that are in scope between that occurrence and its corresponding binder. The following are some examples:
  • The term λ x y x , sometimes called the K combinator , is written as λ λ 2 with de Bruijn indexes. The binder for the occurrence x is the second λ in scope. The term λ x y z x z y z ) (the S combinator ), with de Bruijn indexes, is λ λ λ 3 1 (2 1). The term λ z y y x x x z x ) is λ (λ 1 (λ 1)) (λ 2 1). See the following illustration, where the binders are coloured and the references are shown with arrows.

10. De Bruijn
De bruijn indices are a method of proving two programs are what is called alphaequivalent. Imagine that you had two programs like this

11. Submission By Arthur Charguéraud (de Bruijn Indices) - POPLmark
Encoding techniques De bruijn indices, variable labelling, Retrieved from http//

12. Archives Of The Caml Mailing List > Message From John R Harrison
It s been interesting for me to see a discussion of de bruijn versus a variable must be substituted for a de bruijn index throughout the body.
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13. Inge De Bruijn Biography, Bio, Profile, Pictures, Photos From
Inge De bruijn Index, Inge De bruijn Filmography, Inge De bruijn Photogallery, Inge De bruijn Awards, Inge De bruijn Links. Inge De bruijn Biography
Home News Holidays Movies ... Contact Us Search Celebrity / Movie Inge De Bruijn - Biography Inge De Bruijn Biography Name : Inge De Bruijn Birth date : 24 Aug 1973 Birth place : Barendrecht, Netherlands Height : 1.78 m / 5'10 Weight : 60 kg / 132 lbs Education : Sports Management - Schoevers: Rotterdam, NED Occupation : Swimmer Debut : 1991 for NED, European Championships, Athens, GRE Coach : Hans Elzerman Club : PSV Eindhoven, Eindhoven, North Brabant, NED Videos
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14. De Bruijn Indices
de bruijn s index representation eliminates the need for arrows associating leaf nodes with nodes through a numbering scheme. The numbers at the leaf nodes
Next: Binding Up: classnote 14 Previous: Equality Definition
de Bruijn indices
Standard presentations of the -calculus begin with some surface syntax (usually defined by a context-free grammar). The -terms and are abbreviated by and respectively. A convention is also adopted where:
  • parentheses are omitted
  • function application associates to the left: abbreviates
  • abbreviates
It can be difficult at times to determine the structure of an abbreviated -term. In such instances, it is useful to give a pictorial depiction. One way of doing so is by using de Bruijn indices. eg. abbreviates pictorial form of de Bruijn's index representation of de Bruijn's index representation eliminates the need for arrows associating leaf nodes with -nodes through a numbering scheme. The numbers at the leaf nodes of the representation indicate the number of -nodes to count up.

15. The Handling Of Variable Binding: De Bruijn Levels And The Formal Definition Of
The disadvantage of de bruijn levels (which de bruijn indices do not have) is thus its index must be changed from n to nl1+l2 (while the indices of
Next: Abstraction and reduction by Up: Implementing stratified abstraction in Previous: Implementing stratified abstraction in
The handling of variable binding: de Bruijn levels and the formal definition of substitution
As we noted above, the term construction using brackets represents -abstraction. There is nothing in Watson's notation corresponding to the component of the notation ; the variable bound in a bracket is determined by the syntax of its context using a scheme due to deBruijn (but differing from the most familiar name-free binding scheme due to deBruijn). The variable bound in an outermost set of brackets is always ; the variable bound in a set of brackets which is in the scope of one set of brackets is ; in general, the variable bound in a set of brackets which is enclosed in n-1 further brackets is ?n . For example, the constant function is written , but its constant function is written (because the bound variable in this term is bound by the inner of the two sets of brackets). The use of de Bruijn levels creates a complication of the definition of substitution in a much more pervasive way than the similar problem that arises with the numbering of hypothesis tactics. On the other hand, the complication is simpler than the one that would be occasioned by use of the usual variable binding schemes. For users the system adopted is certainly better than de Bruijn indices, but admittedly less readable than the usual schemes of variable binding when there is enough nesting of abstraction terms (but, as noted above, there is a tactic which converts such terms to a more readable form).

16. Concrete Representation - The Twelf Project
Next, we translate the Church boolean operator Not, p.p( x. y.y)( x. y.x) from a bruijn index to a HOAS representation.
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Concrete representation
From The Twelf Project
Jump to: navigation search This is Literate Twelf Code: here
Status: %% OK %%
Output: here The use of higher-order abstract syntax , using Twelf's binding structure to represent binding structure in an encoded language, is one of the more unique and convenient aspects of using Twelf. However, the fundamental nature of the binding structure has been troubling to some, because it is not obvious that everything you might ever want to do to a lambda term is doable within the framework of HOAS. One way to deal with this question is to show that there is a bijection between HOAS terms in Twelf and some concrete representation of terms with bound variables. In that case, any arbitrary operation on the concrete representation can be related to an operation in the HOAS representation by translating the HOAS term into concrete form, performing the operation on the concrete term, and translating it back into HOAS. That said, we do not know of any practical proof that has required this technique. The technique of de Bruijn indices, described fully

17. Inge De Bruijn - Tag Story Index -
Petria Thomas of Australia upset defending Olympic champion Inge de bruijn in the 100meter butterfly Sunday night, while American Jenny Thompson was once de Bruijn

18. Re: Directory Documents In Konqueror SOLVED
On Saturday 02 November 2002 945 am, Leo de bruijn wrote On Saturday 02 November 2002 0058, I got the error after copiing a file named index.html.
var addthis_pub = 'comforteagle'; kde.linux Top All Lists Date Thread
Re: Directory Documents in Konqueror SOLVED
Subject Re: Directory Documents in Konqueror SOLVED List-id On Saturday 02 November 2002 00:58, James Richard Tyrer wrote: all files from Documents to doc. (in a Konsole as user) When I tried to open doc in konqueror I got the same error. I emptied doc and copied all files from Documents to doc one at the time and tried each time to open doc in Konqueror. I got the error after copiing a file named index.html. In this file it tried to open home.html and top.html and this caused the errors. So after deleting this file all is well again. The index .html file came from trying to save a web page with frames. Interesting question remains: Why could I open Document normaly when using Konqueror as Root ? You had 'Use index.html' checked in the View menu, but Root didn't? Pam R: Don't put off until tomorrow what you can leave to the day after. Linux StepbyStep: . Archives:

19. Inge De Bruijn - Timeline Index
In the process of winning three golds in Sydney, Inge de bruijn did so by setting three new world records. She broke her own 100 meter butterfly world
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In the process of winning three golds in Sydney, Inge de Bruijn did so by setting three new world records. She broke her own 100 meter butterfly world record for the third time in three months. When she returned to the Athletes' Village, she received a letter of congratulations from Queen Beatrix of the Netherlands. "The Queen congratulated the team and especially Inge for the gold medal and the world record," a Dutch team official said. Her second gold came in the 100 meter freestyle, where she finished 0.06 seconds behind the world record time she set in the semi-finals. Her third and final gold came in the 50 meter freestyle. "I'm floating on a big cloud. I hope I don't land for a long time," de Bruijn said after her 50 meter freestyle race.
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20. De Bruijn, Inge - Hutchinson Encyclopedia Article About De Bruijn, Inge
Inge. de bruijn, Inge. Information about de bruijn, Inge in the Hutchinson encyclopedia. De bruijn index De bruijn indices De bruijn notation Bruijn, Inge
Domain='' word='de Bruijn, Inge' Printer Friendly 727,646,681 visitors served. TheFreeDictionary Google Word / Article Starts with Ends with Text subscription: Dictionary/
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Email Feedback Sign in Email: Password: Register Charity('US') Mentioned in No references found Hutchinson browser Full browser De Beer, Gavin Rylands de bene esse de Blois, Natalie de Bono, Edward (Francis Charles Publius) ... de Broglie de Bruijn, Inge de Burgos, Julia De Carava, Roy De Carlo, Giancarlo de Chauliac, Guy ... De Bruijn torus de Bruijn, Inge De Bruijn-Newman constant de Bruin spatula De Brullier De Bruyn, Cornelis ... De Carne Christi TheFreeDictionary Google Word / Article Starts with Ends with Text Free Tools: For surfers: Browser extension Word of the Day Help For webmasters: Free content NEW!

21. Search Engine, Meta Search Engine, Best Search Engine
De bruijn digraph, View Interesting Sites. De bruijn graph, View Interesting Sites. De bruijn index, View Interesting Sites
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  • 22. De Bruijn Cycle
    Java demonstration of debruijn Cycle, Java demonstration of de bruijn Cycle. visit Sun s website at http//,
    var MyPageLoc = document.location; var MyPageTitle = document.title; G o o g ... e Web CTK Sites for teachers
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    The de Bruijn Cycle
    This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.
    Buy this applet A few more words A related problem of universal coloring gives an insight into the workings of de Bruijn's cycle. Alexander Bogomolny addthis_url = location.href; addthis_title = document.title; addthis_pub = '';
    Search: All Products Apparel Baby Beauty Books DVD Electronics Gourmet Food Personal Care Housewares Magazines Musical Instruments Music Computers Software VHS Computer Games Cell Phones Keywords:
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    8 messages
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    Monty Hall Problem
    Posted by linkdon 69 messages 07:38 AM, Dec-14-07 Four numbers equal 24?

    23. Tijdschrift Voor Psychiatrie - Author Index: Bruijn, J.A.
    Author index bruijn, J.A.. New research. Dutch Journal of Psychiatry 33 (1991) 9. A.M. den Hollander, J.A. bruijn, R.W. Trijsburg

    24. Info On Necklaces, Lyndon Words, De Bruijn Sequences
    Information Index Generation Index COS homepage At first glance De bruijn sequences appear to have little to do with necklaces or Lyndon words
    Information on necklaces, unlabelled necklaces, Lyndon words, De Bruijn sequences
    A k -ary necklace is an equivalence class of k -ary strings under rotation. We take the lexicographically smallest such string as the representative of each equivalence class and use this in the output of the program. A Lyndon word is an aperiodic necklace representative. The illustration on the right shows the 6 binary necklaces with 4 beads and the corresponding equivalence classes of strings. The representatives are colored and green indicates a Lyndon word.
    The number of binary necklaces for n =1,2,...,15 is 2, 3, 4, 6, 8, 14, 20, 36, 60, 108, 188, 352, 632, 1182, 2192. This is sequence in Neil J. Sloane's database of integer sequences. The number of binary Lyndon words for n =1,2,...,15 is 2, 1, 2, 3, 6, 9, 18, 30, 56, 99, 186, 335, 630, 1161, 2182. This is sequence in Neil J. Sloane's database of integer sequences. There are explicit formulae for both of these sequences, given below over a k -ary alphabet: L k n n d n n d k d N k n n d n n d k d Lyndon words Necklaces The function m m is the product of non-distinct primes, +1 if it is the product of an even number of distinct primes, and

    25. Henk M. De Bruijn - Re: Error Message: .infig.status: Error Cannot Find Input Fi
    On Sun, 28 May 2006 012518 0700GMT (28-5-2006, 1025 +0200, where I live), Brian Dessent wrote Henk M. de bruijn wrote checking whether
    This is the mail archive of the cygwin mailing list for the Cygwin project Index Nav: Date Index Subject Index Author Index Thread Index Message Nav: Date Prev Date Next Thread Prev ] [Thread Next] Other format: Raw text
    Re: error message: .infig.status: error cannot find input file
    • From : "Henk M. de Bruijn" <henkdebruijn at wanadoo dot nl> To : cygwin at cygwin dot com Date : Sun, 28 May 2006 11:19:23 +0200 Subject : Re: error message: .infig.status: error cannot find input file References Reply-to : "Henk M. de Bruijn" <henkdebruijn at wanadoo dot nl> Gossamer Spider Web of Trust A progressive and innovative Web of Trust Unsubscribe info: Problem reports: Documentation: FAQ:

    26. Publications
    Its implementation of lambdaterms does not use named variables or de bruijn indices (the two common approaches) but instead uses a graph representation.
  • Indag. Math.
  • F. Wiedijk, Conforme supergravitatie zonder constraints. M.Sc. thesis (in Dutch), University of Amsterdam, 1986.
  • Int. J. of Foundations of Computer Science
  • Algebraic Methods II: Theory, Tools and Applications, Springer LNCS
  • F. Wiedijk, Persistence in Algebraic Specifications. Ph.D. thesis, University of Amsterdam, 204 pp., 1991: ps.gz pdf
  • Theorem Proving in Higher Order Logics, 13th International Conference, TPHOLs 2000, Portland, Oregon, Springer LNCS ps.gz pdf dvi tex Abstract.
  • Theorem Proving in Higher Order Logics, 14th International Conference, TPHOLs 2001, Edinburgh, Springer LNCS ps.gz pdf dvi tex Abstract. There are two different approaches to formalizing proofs in a computer: the procedural approach (which is the one of the HOL system) and the declarative approach (which is the one of the Mizar system). Most provers are procedural. However declarative proofs are much closer in style to informal mathematical reasoning than procedural ones.
    There have been attempts to put declarative interfaces on top of procedural proof assistants, like John Harrison's Mizar mode for HOL and Markus Wenzel's Isar mode for Isabelle. However in those cases the declarative assistant is a layer on top of the procedural basis, having a separate syntax and a different "feel" from the underlying system.
  • 27. Practical Foundations Of Mathematics
    The de bruijn index of a bound variable is the number of ls which separate its use from its declaration in the tree structure of the term. For example lx.
    Practical Foundations of Mathematics
    Paul Taylor
    Exercises II
  • Give a construction of the integers ( Z ) from the natural numbers such that z m n m n z
  • Show how to add and multiply complex numbers as pairs of reals, verifying the commutative, associative and distributive laws and the restriction of the operations to the reals.
  • The volume-flow (in m s ) down a pipe of radius r of a liquid under pressure p is c h n r m p k for some dimensionless c , where h is the dynamic viscosity , in units of kg m s . Find n m and k
  • Show how to add Dedekind cuts and multiply them by rationals , justifying the case analysis of the latter into positive, zero and negative. What do your definitions say when the cuts represent rationals? Verify the associative, commutative and distributive laws.
  • Express 3 and 6 as Dedekind cuts, and hence show that
  • Let x L U ) and y M V ) be Dedekind cuts of Q define a Dedekind cut of R . Calling it x y , verify the usual laws for multiplication, without using case analysis [
  • n m ) which satisfies n m n m m n
  • Show how to add Cauchy sequences and to multiply them by rational numbers.
  • 28. RPM Shipped By Bert De Bruijn
    Index index by Group index by Distribution index by Vendor index by creation date RPM shipped by Bert de bruijn
    Index index by Group index by Distribution index by Vendor ...
    JPEG pixel interpolator DAG packages for Fedora Core 1 i386 jpegpixi-1.1.0-1.1.fc1.rf.i386 JPEG pixel interpolator DAG packages for Fedora Core 1 i386 muttprint-0.72-1.1.fc1.rf.noarch Pretty printing of mails with Mutt DAG packages for Fedora Core 1 i386 jpegpixi-1.1.1-1.1.fc2.rf.i386 JPEG pixel interpolator DAG packages for Fedora Core 2 i386 jpegpixi-1.1.1-1.1.fc2.rf.x86_64 JPEG pixel interpolator DAG packages for Fedora Core 2 x86_64 jpegpixi-1.1.0-1.1.fc2.rf.i386 JPEG pixel interpolator DAG packages for Fedora Core 2 i386 jpegpixi-1.1.0-1.1.fc2.rf.x86_64 JPEG pixel interpolator DAG packages for Fedora Core 2 x86_64 muttprint-0.72-1.1.fc2.rf.noarch Pretty printing of mails with Mutt DAG packages for Fedora Core 2 i386 muttprint-0.72-1.1.fc2.rf.noarch Pretty printing of mails with Mutt DAG packages for Fedora Core 2 x86_64 jpegpixi-1.1.1-1.1.fc3.rf.i386 JPEG pixel interpolator DAG packages for Fedora Core 3 i386 jpegpixi-1.1.1-1.1.fc3.rf.x86_64 JPEG pixel interpolator DAG packages for Fedora Core 3 x86_64 jpegpixi-1.1.0-1.1.fc3.rf.i386

    29. British Journal Of Cancer - Author Index
    J H W de Wilt, T L M ten Hagen, G de Boeck, S T van Tiel, E A de bruijn R H J Mathijssen, J Verweij, W J Loos, P de bruijn, K Nooter and A Sparreboom
    @import "/bjc/style_article.css"; @import "/bjc/style_article.css"; SEARCH advanced search help site index 22 December 2007 Journal Home Current issue Previous issue Advance Online Publication ... Web focus For authors Submitting to BJC Author Licence Services Receive Table of Contents by email Online sample copy FREE Order sample copy ... About nature publishing group
    Author Index Browse by letter: A B C E ... Z Or Search for author's name: Search results for: "D"
    Results of shown below
    de Boer-Dennert, M
    J H M Schellens, ASTh Planting, N van Zandwijk, J Ma, M Maliepaard, M E L van der Burg, M de Boer-Dennert, E Brouwer, A van der Gaast, M J van den Bent and J Verweij
    Adaptive intrapatient dose escalation of cisplatin in combination with low-dose vp16 in patients with nonsmall cell lung cancer
    Full article PDF
    de Bono, J
    C Benson, S Kaye, P Workman, M Garrett, M Walton and J de Bono
    Clinical anticancer drug development: targeting the cyclin-dependent kinases advance online publication, 2004-11-23 00:00:00.000; doi:10.1038/sj.bjc.6602229

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