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1. Rotten Cotton » Blog Archive » Bootstrapping From The Pure Lambda Calculus
So languages based on the typed lambda calculus need some builtin form of can’t define a function of that particular type in pure typed lambda calculus.

2. Lambda Calculus | Lambda The Ultimate
All ideas in the paper have been implemented in the the wonderfully elegant Haskell language, which is basically pure typed lambda calculus with lots of
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Lambda Calculus
Natural Deduction for Intuitionistic Non-Commutative Linear Logic
Natural Deduction for Intuitionistic Non-Commutative Linear Logic , Jeff Polakow and Frank Pfenning. TLCA 1999. Intuitionistic logic captures functional programming in a logical way, as can be seen from the Curry-Howard isomorphism between constructive proofs and functional programs. However, there are many structural properties of programs that are not captured within the intuitionistic framework, such as resource usage, computational complexity, and sequentiality. Intuitionistic linear logic can be thought of as a refinement of intuitionistic logic in which the resource consumption properties of functions can be expressed internally. Here, we further refine it to allow the expression of sequencing of computations. We achieve this by controlling the use of the structural rule of exchange to arrive at intuitionistic non-commutative linear logic My earlier post on linguistics reminded me of the Lambek calculus, which is an ordered logic invented in 1958(!) to model how to parse sentences. So I wanted to find a paper on ordered logic (ie, you can't freely swap the order of hypotheses in a context) and link to that.

3. Typed Lambda Calculus - Wikipedia, The Free Encyclopedia
A typed lambda calculus is a typed formalism that uses the lambdasymbol ( ) to of pure typed lambda calculi (including simply typed lambda calculus,
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Typed lambda calculus
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Please improve this article if you can. (December 2007) A typed lambda calculus is a typed formalism that uses the lambda-symbol ( ) to denote anonymous function abstraction. Typed lambda calculi are foundational programming languages and are the base of typed functional programming languages such as ML and Haskell and, more indirectly, typed imperative programming languages . They are closely related to intuitionistic logic via the Curry-Howard isomorphism and they can be considered as the internal language of classes of categories , e.g. the simply typed lambda calculus is the language of Cartesian closed categories (CCCs). Traditionally, typed lambda calculi were seen as refinements of the untyped lambda calculus . A more modern view considers typed lambda calculi the more fundamental theory, and untyped lambda calculus a special case with only one type.

4. MainFrame: The Lambda-calculus, Combinatory Logic, And Type Systems
pure type systems are a family of typed lambda calculi each member of which is The connection between the lambda calculus and pure combinatory logic was
The Lambda-calculus, Combinatory Logic, and Type Systems
Three interrelated topics at the heart of logic and computer science. The -Calculus A pure calculus of functional abstraction and function application, with applications throughout logic and computer science. Types The -calculus is good tool for exploring type systems, invaluable both in the foundations of mathematics and for practical programming languages. Pure Type Systems A further generalisation and systematic presentation of the class of type systems found in the -cube. Combinators Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. Programming Languages The connections between the lambda-calculus and programming languages are diverse and pervasive. Type systems are an important aspect of programming language design. The -cube A graphical presentation of the relationship between combinatory logic, lambda calculi and related logical systems. The -cube A graphical presentation of the relationship between various typed -calculi, illuminating the structure of Coquand's Calculus of Constructions.

5. Typed Lambda Calculus And Applications
Game Semantics for the pure Lazy lambdacalculus. by Pietro Di Gianantonio Explicitly typed lambda µ-calculus for Polymorphism an Call-by-Value
The Digital Librarian's Digital Library search D O CIS  Do cuments in  C omputing and I nformation  S cience Home Journals and Conference Proceedings Typed Lambda Calculus and Applications

6. JSTOR Exact Bounds For Lengths Of Reductions In Typed $\lambda
4 H. SCHWICHTENBERG, Complexity of normalization in the pure typed lambda calculus, The L. E. J. Brouwer centenary symposium (A. S. Troelstra and D. van<1277:EBFLOR>2.0.CO;2-5

7. Lambda Calculus And Lambda Calculators
This article derives a term in the pure untyped lambdacalculus that . Ref 108 is R.Statman The typed lambda calculus is not elementary recursive.
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Lambda Calculus and Lambda Calculators
Negative numbers, subtraction and division in lambda-calculus
This article will demonstrate basic arithmetic operations comparison, addition, subtraction, multiplication, and division on non-negative and negative integer numbers. Both the integers and the operations on them are represented as terms in the pure untyped lambda-calculus. The only building blocks are identifiers, abstractions and applications. No constants or delta-rules are used. Reductions follow only the familiar beta-substitution and eta-rules. We also show two approaches of defining a predecessor of a Church numeral. Curiously, none of the arithmetic operations involve the Y combinator; even the division gets by without Y. Addition, multiplication, squaring, and exponentiation are easily expressed in lambda-calculus. We discuss two approaches to their "opposites" subtraction, division, finding of a square root and of a discrete logarithm. The "opposite" operations present quite a challenge. One approach, based on fixpoints, is more elegant but rather impractical. The "dual" approach, which relies on counting, leads to constructive and useful, albeit messy, terms.

8. Programming: The Pure, Typed Lambda Calculus And Haskell :
The pure, typed lambda calculus and Haskell ( 19 points posted 14 days ago by dons1 comment
register submit help blog ... stats search remember me recover password login sort by other communities The pure, typed lambda calculus and Haskell : ( 19 points posted 1 month ago by dons 1 comment info comments related details you are viewing a single comment's thread jump to the above comments nmessenger (0 children) [+] nmessenger 2 points 1 month ago Man, church-encoded ADTs is some wacky stuff. Neat trick that :skip -ping the abstractions makes it look like simple primitive data. permalink feedback bookmarklets buttons ... User Agreement
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9. A Normaliser For Pure And Typed Lambda-calculus
This program provides a useful environment to write programs in pure or typed lambdacalculus. Given a term, the program will compute and print its normal
A Normaliser for pure and typed lambda-calculus.
Version 2.3
This program provides a useful environment to write programs in pure or typed lambda-calculus. Given a term, the program will compute and print its normal form. This means that, unlike most functional languages, computation is done under function abstractions (or lambdas). This software might be used for teaching lambda-calculus or just to play with it. It has some interesting features :
  • Three modes of evaluation:
  • lazy:
    call-by-name with some sharing
    call-by-name with no sharing
    call-by-name and printing of each beta-reduction step or tracing of particular functions.
  • It is implemented in Objective Caml (a dialect of ML) so easily portable to many machines, even very small ones. It is quite efficient. It uses a High-Order-Abstract-Syntax representation of terms which help to benefit from ML management of closure. This is specially optimised to give both reasonable performance in speed and memory. It's possible to terminate computation of factorial 100 with a binary encoding of natural numbers ! You can define terms (even using recursive definitions) or include files. This gives enough modularity to write fairly large terms.

10. Things That Amuse Me
Here I m going to show some examples of code in pure typed calculus. All the examples are typable in F ; the full lambda cube is not necessary.
@import url(""); @import url("");
Things that amuse me
Friday, November 09, 2007
Some lambda calculus examples
In a previous blog entry I described a simple evaluator and type checker for the lambda cube, i.e., various forms of lambda calculus. ; the full lambda cube is not necessary. ". And as in Haskell I'll allow multiple variables between the " " and " "; it's just a shorthand for multiple lambdas. So what about the dependent function type? The syntax suggests (x::t)->u , so I'll use that. And when the variable doesn't occur we'll write t->u as usual. For type variables Haskell (well, not Haskell 98, but extensions) uses forall (a::*) . t , so I'll allow that too. An example, the identity function: with type forall (a::*) . a->a And using it id Int 5 Writing a pretty printer and parser for this is pretty straight forward so I'll skip that and just point you to the code . BTW, instead of using Parsec for the parser like everyone else I used ReadP. The ReadP library is very nice, partly because the alternative operator is actually commutative (unlike Parsec). But the error messages suck.
Enter let
What makes it awkward is that the name

11. Teach Untyped Lambda Calculus?
In the context of PCF, we can first prove ChurchRosser and SN for pure typed lambda calculus (by logical relations, say). Then, with a fixed-point operator
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teach untyped lambda calculus?

12. Lambda-calculus - SWiK
Saturday, November 10, 2007. The pure, typed lambda calculus and Haskell (An Implementation of a Dependently typed lambda calculus)
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13. Publications
Short Proofs of Normalization for the simplytyped lambda-calculus, . and strong beta-normalization are shown to be equivalent for all pure Type Systems.

14. Foundations Of Computer Science
This work of simplification also yields a particularly short and easy proof of the undecidability of DP for Church pure typed lambdacalculus that will
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 Stanisław Sędziwy Edward Szczypka Paweł Waszkiewicz ... Marek Zaionc secretary: Monika Gillert phd students: Katarzyna Grygiel Jarosław Karpiak Mikołaj 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 (część 2)

15. IngentaConnect Ordinals And Ordinal Functions Representable In The Simply Typed
Ordinals and ordinal functions representable in the simply typed lambda calculus. Author Danner N.1. Source Annals of pure and Applied Logic, Volume 97,

16. Wiki Typed Lambda Calculus
A typed lambda calculus is a typed formalism that uses the lambdasymbol the lambda cube to systematize the relations of pure typed lambda calculi
Wiki: Typed lambda calculus A typed lambda calculus programming languages and are the base of typed functional programming languages such as ML and Haskell and, more indirectly, typed imperative programming languages . They are closely related to intuitionistic logic via the Curry-Howard isomorphism and they can be considered as the internal language of classes of categories , e.g. the simply typed lambda calculus is the language of Cartesian closed categories (CCCs). Traditionally, typed lambda calculi were seen as refinements of the untyped lambda calculus . A more modern view considers typed lambda calculi the more fundamental theory, and untyped lambda calculus a special case with only one type. Home Licensing Wapedia: For Wikipedia on mobile phones

17. Typed Lambda-Calculus
typed lambdacalculus. Monday Concepts and Syntax Tuesday Substitution and Equations Wednesday From pure to Effectful Thursday Denotational Semantics of
Typed Lambda-Calculus
Monday: Concepts and Syntax
Tuesday: Substitution and Equations
Wednesday: From Pure to Effectful
Thursday: Denotational Semantics of Call-By-Value
Answers to Monday's exercises, and futher questions

We introduce pure Type Systems with Pairs generalising earlier work on program extraction in typed lambda calculus. We model the process of program
computer science
Publications in Journals
  • Paula Severi and Fer-Jan de Vries. A Lambda Calculus for infinity eta Böhm trees. To appear in Information and Computation. Mariangiola Dezani-Ciancaglini, Paula Severi and Fer-Jan de Vries. Infinitary Lambda Calculus and Discrimination of Berarducci Trees. Theoretical Computer Science 298(2):275 - 302, 2003. Paula Severi and Nora Szasz. Studies of a Theory of Specifications with built-in Program Extraction. Journal of Automated Reasoning. Vol. 27, no. 1, pages 61-87, 2001. Special Issue on Logical Frameworks and Metalanguages. Femke van Raamsdonk, Paula Severi, Morten Heine S rensen and Hongwei Xi. Perpetual Reductions in Lambda Calculus. Information and Computation, Vol. 149, No 2, pages 173225, 1999. This paper surveys a part of the theory of beta-reductions in lambda calculus which might aptly be called perpetual reductions. The theory is concerned with perpetual reduction strategies, i.e., reduction strategies that compute infinite reduction paths from lambda terms (when possible), and with perpetual redexes, i.e., redexes whose contraction in lambda terms preserves the possibility (when present) of infinite reduction paths. Paula Severi.
  • 19. Completeness Theorem For Typed Lambda-Omega Calculus
    It is motivated by, and leads to a completeness theorem for, the logic of pure, typed lazy lambdacalculus, when not just integers, but terminationeven
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    20. CiteULike: A Typed Lambda Calculus With Categorical Type Constructors
    A typed lambda calculus with Categorical Type Constructors payto-read possibility process pure quantum recursion security semantics symmetric systems
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    21. Typed Lambda Calculi Publications
    Hence a typed calculus, which admits only local rewriting rules, can be introduced in terms of pure lambda calculus can be characterized in this system,
    Type lambda Calculi
    U. Solitro, S. Valentini, Toward Typed lambda-calculi for Linear Logic, proceeding of "The Third Italian Conference on theoretical Computer Science" (ed. Bertoni, Bshm, Miglioli), World Scientific, Mantova 1989, pp. 413-424. Abstract: In this paper it is studied the problem of stating a Curry-Howard isomorphism for Girard's Linear Logic. Two solutions are proposed: one for the intuitionistic variant of the logic and one for a subsytem of the logic which includes the multiplicative and exponential connectives. Different calculi have been developed for the two cases.
    S. Valentini, The judgement calculus for Intuitionistic Linear Logic: proof theory and semantics, Abstract: In this paper I propose a new set of rules for a judgement calculus, i.e. a typed lambda calculus, based on Intuitionistic Linear Logic; these rules ease the problem of defining a suitable mathematical semantics. A proof of the canonical form theorem for this new system is given: it assures, beside the consistency of the calculus, the termination of the evaluation process of every well-typed element. The definition of the mathematical semantics and a completeness theorem, that turns out to be a representation theorem, follow. This semantics is the basis to obtain a semantics for the evaluation process of every well-typed program.
    U. Solitro, S. Valentini

    22. Citebase - Definable Functions In The Simply Typed Lambda-calculus
    and Functional Programming, pages 288297, 1990. G/A, 5. Zaionc, M. -Definability on free algebras. Annals of pure and Applied Logic, 51279-300, 1992.

    23. TYPED LAMBDA CALCULUS Articles A Typed Lambda Calculus Is A Typed
    A typed lambda calculus is a typed formalism that uses the lambdasymbol (? the lambda cube to systematize the relations of pure typed lambda calculi
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    24. Scientific Commons Paula Severi
    Alpha Conversion in Simply typed lambda calculus (2000) In this paper, an extension of pure Type Systems (PTS s) with definitions is presented.
    <6Î.³°HŒ?ú ’0ë7—‘`¡è9O²$–1Y‹þ­ÆÑQíž]ƒätÌÇÈÍ:u’ÓºÊìË?±Á <ªÀÄz¿vÄaa ß¡%@o¥9ØëKFhi¹0…5 [fµÀ[±Róò¤ÝN,·ëÆ <u;±¶6

    25. New England Programming Languages And Systems Symposium Series (NEPLS): Abstract
    The conjecture is concerned with socalled pure type systems which include the well-known typed lambda calculi like the simply-typed lambda calculus,
    S These abstracts are for talks at this event NEPLS is a venue for ongoing research, so the abstract and supplemental material associated with each talk is necessarily temporal. The work presented here may be in a state of flux. In all cases, please consult the authors' Web pages for up-to-date information. Please don't refer to these pages as a definitive source. New Models for Numerical Computing in the Java Programming Language
    Guy L. Steele, Jr. (Sun Microsystems)
    No abstract availble at this time. Conservation and Uniform Normalization in Lambda Calculi with Erasing Reductions
    Peter Møller Neergaard (Boston University)
    Speaker's Supplement
    This talk will only present the main ideas. The person interested in the gory details can consult the following sources: Analyzing Trace and Program Data
    Steve Reiss (Brown University)
    Real-Time FRP
    Paul Hudak (Yale University) Rupiah: Towards an Expressive Static Type System for Java Nate Foster (Williams College) Modular Verification of Layered Software Systems Kathi Fisler (Worcester Polytechnic Institute), Shriram Krishnamurthi (Brown University) and Don Batory (University of Texas at Austin)

    26. Typed Lambda Calculus
    A typed lambda calculus is a typed formalism which uses the the lambda cube to systematize the relations of pure typed lambda calculi (including simply
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    27. Major Scientific Accomplishments 2000. Reflexive Lambda-calculus
    It may be regarded as the pure lambda version of the Logic of Proofs LP (cf. and combinatory logic, typed lambdacalculus and modal lambda-calculus.
    Major scientific accomplishments . Reflexive lambda-calculus. The Curry-Howard isomorphism converting intuitionistic proofs into typed lambda-terms is a simple instance of an internalization property of a our system lambda-infinity which unifies intuitionistic propositions (types) with lambda-calculus and which is capable of internalizing its own derivations as lambda-terms. We establish confluence and strong normalization of lambda-infinity. The system lambda-infinity is confluent and strongly normalizable (a joint result with J.Alt) , considerably extends the expressive power of each of its major components: typed lambda-calculus, intuitionistic and modal logic. It may be regarded as the pure lambda version of the Logic of Proofs LP (cf. below). Reflexive lambda-calculus is likely to change our conception of the appropriate syntax and semantics for ambda-calculus based programming languages, systems of automated deduction and formal verification. . An explicit provability model for verification. The traditional (implicit) provability model leaves a certain loophole in the foundations of formal verification. Namely, by the Goedel Incompleteness Theorem an extension of a verification system by a verified rule generally speaking is not equivalent to the original system. This model leads to a "reflection tower" of metatheories of increasing proof-theoretical strength which itself cannot be verified formally. One has to believe in correctness of a verification system the way we believe in consistency of a set theory.

    28. Théorie De La Démonstration
    The ChurchRosser Theorem for the typed lambda-calculus with Surjective Pairing. Domain-free pure type systems. Journal of functional programming,
    Liste (non exhaustive) d'articles Voir le planning provisoire des soutenances Articles
    • Kanovitch, M. (1992). Horn-programming in linear logic is NP-complete . In Proceedings of the 7th Annual IEEE Symposium on Logic in Computer Science, pp. 200-210. ( P. Baillot and Terui, K., Light types for polynomial time computation in lambda-calculus PS Jean-Marc Andreoli. Focussing and Proof construction Abstract paper.pdf (238KB). (R©serv© par Etienne Miret Andrea Asperti. Light affine logic . In Proc. Symp. Logic in Comp. Sci. (LICS). IEEE, 1998. ( PS A.Asperti, L.Roversi. Intuitionistic Light Affine Logic . ACM Transactions on Computational Logic (TOCL), Volume 3 , Issue 1, January 2002, pp.137 - 175. Y. Lafont, Soft Linear Logic and Polynomial Time , Theoretical Computer Science 318 (special issue on Implicit Computational Complexity) p. 163-180, Elsevier (2004). ( PS Benton, Bierman, de Paiva.

    29. Natural Deduction And Sequent Typed Lambda Calculus
    Two different formulations of the simply typed lambda calculus the More All 0.7 On Zucker s isomorphism for LJ and its extension to pure Type.
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    30. Definition Of Typed Lambda-calculus In Computing
    typed lambdacalculus, polymorphic lambda-calculus, Second-Order lambda-calculus, lambda expression. lambda-calculus, lambda, pure lambda-calculus, TALE lambda-calculus&in=1

    31. Kripke-Style Models For Typed Lambda Calculus. D2R Server
    dcdate, 1991 (xsdgYear). dblpjournal, Ann. pure Appl. Logic. rdfslabel, KripkeStyle Models for typed lambda calculus.

    32. ODOBS - Publication Page: Kripke-Style Models For Typed Lambda Calculus.
    KripkeStyle Models for typed lambda calculus. Year, 1991. Journal, Ann. pure Appl. Logic. Volume, 51. Number, 1-2. Pages, 99-124.;jsessionid=1D1233CFBB41E1

    33. PL Seminar - Jon Riecke, Bell Labs, Security In Lambda Calculus
    15, 1996 10am11am, LH 101 Title Security in the typed lambda calculus Next PL seminar - David S. Wise, pure/Impure LISP and Compiling; Index(es)
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    PL seminar - Jon Riecke, Bell Labs, Security in Lambda Calculus
    Programming Languages Seminar Friday, Nov. 15, 1996 10am-11am, LH 101 Title: Security in the Typed Lambda Calculus Speaker: Jon G. Riecke, Bell Laboratories, Lucent Technologies Abstract: Over twenty years have past since Denning's original work on security of *values* during computation. Denning, and others following her, worked in imperative languages, and used "flow of information" as the primary mechanism for tracking security. We rework and adapt some of these ideas in the context of the programs, written in the typed lambda calculus, that communicate via shared variables. In this language, we can track more accurately the flow of information. This is joint work with Nevin Heintze. A word of caution: the work is very preliminary! For those among us who have been looking for preliminary work that might allow more discussions, this seems to be a good opportunity :-)

    34. Patterns And Compositionality
    Friends have done proofs of imperative programs (heap sorting, and more) in Coq (a logic system based on pure typed lambdacalculus);
    Patterns and Compositionality
    Mon, 31 Jan 2000 13:46:53 -0800 From: Francois-Rene Rideau [mailto: I didn't say it was easy with lambda-like formal calculi. I said it was as easy/difficult with such calculi as with any formal calculi, including sequent calculi that you like. Imperative programming IS a nightmare, stop. Using an imperative calculus as a "primitive" calculus is an abstraction inversion. Not easily. The semantics of computers and turing machines is quite contorted. So are proof sketches in frameworks such as the one used by Coq. The part that's not straightforward is going from the proof sketch to the precise, machine-checkable proof. Having worked with proof checkers for an imperative framework (B, a dialect of Z), I can tell that the latter is certainly not simpler. Not everything. But everything that can be usefully used

    35. Exceptions Are Strictly More Powerful Than Call/CC.
    More precisely, we prove that the simply typed lambda calculus extended with that in the context of statically typed pure functional lambda calculi,

    36. The Weak Normalization Of The Simply Typed Lambda-se Calculus
    The Weak Normalization of the Simply typed lambdase calculus. Ariel Arbiser, F. Kamareddine, Alejandro Ríos. Logic Journal of the Interest Group of pure
    The Weak Normalization of the Simply Typed Lambda-se Calculus
    Ariel Arbiser, F. Kamareddine, Alejandro Ríos Logic Journal of the Interest Group of Pure and Applied Logic - 2006
    BibTex references
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    37. Functional Programming With Haskell
    Recent advances in typedlambda calculus have formed a basis for Haskell, It is also important to note that pure lambda-calculus does not have any
    Functional Programming Using Haskell
    Wade Estabrooks Michael Goit Mark Steeves
    Table of Contents
    1. Introduction to Haskell
    2. Evaluation of the Language 2.1 Readability 2.2 Writability ... 3. Our Program Appendix: Source Code Appendix A - source code for the Dictionary module. Appendix B - source code for the Words module. Appendix C - source code for the Fixwords module.
    1. Introduction to Haskell
    Haskell is a general purpose, purely functional programming language incorporating many recent innovations in programming language design. Haskell provides higher-order functions, non-strict semantics, static polymorphic typing, user-defined algebraic datatypes, pattern-matching, list comprehensions, a module system, a monadic I/O system, and a rich set of primitive datatypes, including lists, arrays, arbitrary and fixed precision integers, and floating-point numbers. Haskell is both the culmination and solidification of many years of research on lazy functional languages. True, this definition is a bit long, but it almost completely shows the power that Haskell has as both a functional language, and as a programming language in general. Because Haskell is a purely functional language is has certain characteristics, and also because Haskell is modern language, many historical mistakes made with language design have been avoided. Recent advances in Typed-Lambda Calculus have formed a basis for Haskell, and the addition of very strong typing to a functional language makes Haskell (unlike LISP) "safe" to use. The typing rules also allow a program Haskell to be validated.

    38. Ulrich Berger, Publications
    Total Sets and Objects in Domain Theory, Annals of pure and Applied Logic 60, An inverse of the evaluation functional for typed lambdacalculus,
    Ulrich Berger - Publications

    39. Full Bibliography
    Normalization by evaluation for typed lambda calculus with coproducts. implies strong normalization in a class of nondependent pure type systems.
    Next Previous Up
    Full Bibliography
    Alessi, F., Barbanera, F., and Dezani-Ciancaglini, M. (2006). Intersection types and lambda models. Theoretical Computer Science Alessi, F., Dezani-Ciancaglini, M., and Lusin, S. (2004). Intersection types and domain operators. Theoretical Computer Science [Alessi and Lusin, 2002] Alessi, F. and Lusin, S. (2002). Simple easy terms. In van Bakel, S., editor, Intersection Types and Related Systems Electronic Notes in Computer Science . Elsevier. Altenkirch, T., Dybjer, P., Hofmann, M., and Scott, P. (2001). Normalization by evaluation for typed lambda calculus with coproducts. In Logic in Computer Science [Altenkirch and Uustalu, 2004] Altenkirch, T. and Uustalu, T. (2004). Normalization by evaluation for . In Functional and Logic Programming , volume 2998 of Lecture Notes in Computer Science [Anderson, 1960] Journal of Symbolic Logic , 25:388. (Abstract). [Anderson and Belnap, 1975] Entailment. The Logic of Relevance and Necessity, Volume . Princeton University Press, U.S.A.

    40. DIKU Graduate/Ph.D. Course: The Curry-Howard Isomorphism
    Written exercise Extend the rules of simply typed lambdacalculus (a la Curry) with types of 13, May 15, The lambda-cube and pure type systems, MHS
    Graduate/Ph.D. course:
    The Curry-Howard isomorphism
    (Spring 1998)
    Course description
    The Curry-Howard isomorphism

    Morten Heine S¸rensen (MHS) (Department of Computer Science, University of Copenhagen) Pawel Urzyczyn (PU) (University of Warsaw)

    Morten Heine S¸rensen

    University of Copenhagen Department of Computer Science (DIKU) Universitetsparken 1 2100 Copenhagen East Denmark Tlf: +45-35 32 14 00 Fax: +45-35 32 14 01 Email:

    Time and place:
    Friday 9-12 in N034. During each of these periods there will be a 1-hour exercise/discussion session followed by a 2-hour lecture.

    Maximum 20 participants.

    4 oral points (corresponding to 33% of full-time study at DIKU averaged over one semester).

    Examination form
    Weekly home exercises. Each home exercise will be graded with a score between and 100 percent. At the end of the course, an average of 50 percent is required. A number of written projects will be offered during and after the course.
    • Exercises due 13/2: 1.66, 1.67, 1.68, 1.69, 1.70, 1.71, 1.76, 1.78, 1.82, 1.84.

    41. Bibliography Of Hugo Herbelin
    The framework of the paper is pure lambdacalculus, not PCF. Abstract We show that a simple simply-typed lambda-calculus with explicit substitution and
    Research articles
    "An approach to call-by-name delimited continuations" ACM for your personal use - not for redistribution) errata bibtex entry
    Abstract: It has been shown by Saurin that de Groote's variant of Parigot's lambda-mu-calculus is strictly more expressive in the untyped case than Parigot's original calculus. We show that this additional expressivity exactly corresponds to adding delimited control so that de Groote's calculus can be seen as the exact call-by-name counterpart of Danvy and Filinski's shift-reset calculus. This "duality" is expressed in the lambda-mu-tp-hat-calculus which is lambda-mu-calculus equipped with a single dynamically-bound continuation variable denoting a resettable toplevel. An equational correspondence having already been proved in A type-theoretic foundation of delimited continuations for call-by-value lambda-mu-tp-hat and Danvy and Filinski's calculus, we simply show here the equivalence between call-by-name lambda-mu-tp-hat and de Groote's calculus. We continue with a comparative study of the operational semantics, continuation-passing-style semantics, and simple typing of both call-by-name and call-by-value versions. Finally, we show the existence of two other canonical calculus of delimited continuations. The first one morally forms an equational correspondance with Sabry's shift/lazy-reset calculus while the second one is a "lazy" version of de Groote's calculus.
    "Control Reduction Theories: the Benefit of Structural Substitution",

    42. Education, Master Class 1988/1999, MRI Nijmegen
    It covers systems with explicit typing (simply typed lambda calculus, secondorder lambda calculus, dependent types and pure type systems), normalisation,
    Education, Master Class, Master Class 1998/1999, Detailed Course Content
    Detailed Content of the Courses
    Course content
    1st semester:

    Model Theory
    W. Veldman
    Lambda Calculus
    H. Barendregt, E. Barendsen
    Recursion Theory and Proof Theory
    H. Schellinx
    Logic Panorama
    2nd semester:
    Type Theory and Applications
    H. Barendregt, E. Barendsen
    Incompleteness Theorems
    J. van Oosten Sheaves and Logics I. Moerdijk Mathematical Logic seminar Courses Name of the course: Model Theory Lecturer: W. Veldman Prerequisites: Some familiarity with mathematical reasoning. Literature: C.C. Chang, H.J. Keisler, Model Theory, North Holland Publ. Co. 1977 W. Hodges, Model Theory, Cambridge UP, 1993 Contents: Model theory studies the variety of mathematical structures that satisfy given formal theory. It may also be described as a study of mathematical structures from the logician's point of view. Model theory at its best is a delightful blend of abstract and concrete reasoning. Among the topics to be treated in this course are Fraisse's characterisation of the notion 'elementary equivalence' (structures A,B are called elementarily equivalent if they satisfy the same first-order-sentences), the compactness theorem and its many consequences, ultraproducts, some non-standard-analysis, Tarski's decision method for the field of real numbers by quantifier elimination and Robinson's notion of model completeness. If time permits, some attention will be given to constructive and recursive model theory.

    43. Extending Reynolds
    Firstly, we consider models P of the polymorphic typed lambda calculus as (I.e. we don t have to limit ourselves to definability in the pure calculus.
    [Prev] [Next] [Index] [Thread]
    Extending Reynolds

    44. Pietro Di Gianantonio Publications
    Game semantics for the pure lazy lambdacalculus. Pietro Di Gianantonio. Proc. of the conference typed lambda calculus and Applications 01; LNCS 2044,
    Papers by Pietro Di Gianantonio
    Real Number Computability
    A certified, corecursive implementation of exact real numbers.
    Alberto Ciaffaglione, Pietro Di Gianantonio.
    Theoretical Computer Science,
    2006, vol. 351, pp. 39-51.
    pdf copy

    A tour with constructive real numbers.
    Alberto Ciaffaglione, Pietro Di Gianantonio.
    Proc. of the workshop Types for Proofs and Programs - Types 2000; LNCS 2277, pp. 41-52.
    pdf copy

    A co-inductive approach to real numbers.
    Alberto Ciaffaglione, Pietro Di Gianantonio.
    Proc. of the workshop ``Types 1999''; LNCS 1956, pp. 114-130.
    pdf copy

    An abstract data type for real numbers.
    Pietro Di Gianantonio.
    Theoretical Computer Science, 1999, vol. 221, n. 1-2, pp. 295-326, extended version of a paper presented at ICALP-97. pdf copy
    A golden notation for real numbers.
    Pietro Di Gianantonio. CWI technical report. pdf copy
    Real number computability and domain theory.
    Pietro Di Gianantonio. Information and Computation, 1996, vol. 127, n. 1, pp. 12-25, extended version of a paper presented at MFCS-93. pdf copy
    A functional approach to computability on real numbers.

    45. TLCA 1995
    Andrea Asperti, Cosimo Laneve Comparing lambdacalculus translations in Sharing Categorical completeness results for the simply-typed lambda-calculus.
    TLCA 1995: Edinburgh, UK
    Mariangiola Dezani-Ciancaglini Gordon D. Plotkin (Eds.): Typed Lambda Calculi and Applications, Second International Conference on Typed Lambda Calculi and Applications, TLCA '95, Edinburgh, UK, April 10-12, 1995, Proceedings. Lecture Notes in Computer Science 902 Springer 1995, ISBN 3-540-59048-X BibTeX DBLP

    46. Equipe De Logique De La Programmation : Bibliographie 1999-2002
    Samson Abramsky, editor, typed lambda Calculi and Applications 01, volume 2044 of Encoding left reduction in the lambdacalculus with interaction nets.
    Page d'accueil Sommaire
    Logique de la programmation
    Bibliographie 1999-2002 Baillot
    Patrick, Pedicini Marco.
    Elementary complexity and geometry of interaction (extended abstract).
    Typed lambda calculi and applications (L'Aquila, 1999), 2539, Lecture Notes in Comput. Sci., 1581, Springer, Berlin Ehrhard Thomas, Regnier Laurent.
    The differential lambda-calculus.
    Ehrhard Thomas
    A completeness theorem for symmetric product phase spaces.
    Bucciarelli Antonio, Ehrhard Thomas
    On phase semantics and denotational semantics: the exponentials.
    Ann. Pure Appl. Logic 109, no. 3, 205241 Ehrhard Thomas On Koethe sequence spaces and linear logic. Bucciarelli Antonio, Ehrhard Thomas On phase semantics and denotational semantics in multiplicative-additive linear logic. Annals of Pure and Applied Logic 102, no. 3, 247282 Ehrhard Thomas Parallel and serial hypercoherences. Theoret. Comput. Sci. 247, no. 1-2, 3981

    47. Gmb://publications
    (with Urban) Proceedings of the Fourth International Conference on typed lambda calculus and Applications. In Volume 1581 of Lecture Notes in Computer
    Quick Links Home Worldwide Search for
    All Microsoft Research Downloads Publications Researcher Pages
    Microsoft Research Home
    About Microsoft Research Research Areas People ... Press Resources
    Being written!
    Contracts for patterns: A comparison. (with Parkinson, Noble and Schulte) UpgradeJ: Incremental typechecking for class upgrades. (with Parkinson and Noble) Submitted. Dec 07. Dynamic Rebinding for Marshalling and Update, via Redex-time and Destruct-time Reduction. (with Hicks, Sewell, Stoyle and Wansborough) Accepted for publication in JFP. 70pp. Separation logic, abstraction and inheritance. (with Parkinson) Accepted to appear in POPL'08. Lost in translation: Formalizing proposed extensions to C# (with Meijer and Torgersen) Proceedings of 22nd OOPSLA. October 2007. [ pdf corrected version (12 Nov 07)] Mutatis Mutandis: Safe and predictable dynamic software updating (Journal Version). (with Stoyle, Hicks, Sewell and Neamtiu) ACM Transactions on Programming Languages and Systems. Volume 29, issue 4, article 22. August 2007. 70pp. pdf (Requires ACM account) Formalizing and extending C# type inference.

    48. A Short Proof Of The Strong Normalization Of Classical Natural
    F. Joachimski and R. Matthes Short proofs of normalization for the simplytyped $\lambda$-calculus, permutative conversions and Gödel s $T$,
    Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options
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      A short proof of the strong normalization of classical natural deduction with disjunction
      Source: J. Symbolic Logic Volume 68, Issue 4 (2003), 1277-1288.
      We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e., in presence of all the usual connectives) classical natural deduction. Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text Links and Identifiers Permanent link to this document: Digital Object Identifier: doi:10.2178/jsl/1067620187

    49. TCLA '95
    On Sunday 9th April, there is a meeting of the lambdacalculus EC Network from 9am5pm. . completeness results for the simply-typed $\lambda$-calculus},
    TCLA '95
    Subject: Rewriting361-TLCA_95 Please find enclosed the TLCA'95 conference programme, and details regarding registration for TLCA'95 and associated events. A World Wide Web page for the conference can be found on

    50. Lambda Calculus - In IMP, We Had A Language With No
    y z * Simplytyped lambda calculus * Let s revisit the abstract syntax of the lambda calculus and add types t in Typ = int t1 - t2 e in Exp = i e1

    51. Samson Abramsky - Publications By Theme
    S. Abramsky and M. Lenisa, Fully Complete Minimal PER Models for the Simply typed lambdacalculus, CSL 2001 Conference Proceedings, Springer LNCS Vol.
    Samson Abramsky: Publications by Theme
    Quantum Information and Computation
    • S. Abramsky, R. Blute and P. Panangaden, Nuclear and trace ideals in tensored *-categories J. Pure and Applied Algebra vol. 143 (1999), 347. PS
    • S. Abramsky and B. Coecke, Physical Traces: Quantum vs. Classical Information Processing , in Electronic Notes in Theoretical Computer Science , vol. 69, 2003, 126. PDF
    • S. Abramsky, High-Level Methods for Quantum Computation and Information , in Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science: LICS 2004 , IEEE Computer Society, 410414, 2004. PS
    • S. Abramsky and B. Coecke, A Categorical Semantics of Quantum Protocols , in Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science: LICS 2004 , IEEE Computer Society, 415425, 2004. PS
    • S. Abramsky and B. Coecke, Abstract Physical Traces , in Theory and Applications of Categories , vol 14, 111124, 2005.

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