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The Impact of the Lambda Calculus in Logic and Computer Science

Henk Barendregt
1997 Bulletin of Symbolic Logic  
Church to logic is his invention of the lambda calculus.  ...  [103] succeeded to give lambda calculus also an extensional interpretation by interpreting lambda terms as (continuous) functions on some topological space D having its space of continuous functions  ...  One solution is not to explicitly mention the I/O channels, as in the lambda calculus with continuations.  ... 
doi:10.2307/421013 fatcat:v7nedk3s3vfk3mob6ao5sl4b74

150 Years of vortex dynamics [chapter]

Hassan Aref
2009 IUTAM Bookseries  
They are $\frac{dl_{\alpha\beta}^{2}}{dt}=\frac{2}{\pi}\sum_{\lambda=1}^{N}//\Gamma_{\lambda}\epsilon_{\alpha\beta\lambda}A_{\alpha\beta\lambda}(\frac{1}{l_{\beta\lambda}^{2}}-\frac{1}{l_{\lambda\alpha  ...  Figure 4 reproduces the original drawing from [72] where we find this description: $\Pi e$ diagram represents precisely the convex outline referred to, and the lines of motion of the interior fluid  ... 
doi:10.1007/978-90-481-8584-9_1 fatcat:rkaee7ywinhe5lq2wni6y4fhyq

Some Lambda Calculus and Type Theory Formalized

James McKinna, Robert Pollack
1997 BRICS Report Series  
We have continued to pursue this hobby on and off ever since, and have developed a substantial body of formal knowledge, including Church-Rosser and standardization<br />theorems for beta reduction, and  ...  That is the first sentence of [MP93], the first report on our formal development of lambda calculus and type theory, written in autumn 1992.  ...  Remark 2.1 (Notation) Often when doing case analysis by term structure, we want to say that the binders, lambda and pi, behave the same way.  ... 
doi:10.7146/brics.v4i51.19272 fatcat:l3sb5cg2obeq7foyc6b6ifbdzi

Domain theoretic models of polymorphism

Thierry Coquand, Carl Gunter, Glynn Winskel
1989 Information and Computation  
In fact, understanding universal types of the polymorphic I-calculus as categories of continuous sections appears to be useful generally.  ...  are interpreted as the category of continuous sections of the fibration.  ...  We may also write (Ff)R or even I;(f)" when the meaning is clear from context.  ... 
doi:10.1016/0890-5401(89)90068-0 fatcat:5t6bwgsyzjdwtjpyepfqziuehu

The Wright ω Function [chapter]

Robert M. Corless, D. J. Jeffrey
2002 Lecture Notes in Computer Science  
In particular, although Wright ω is a cognate of the Lambert W function, it presents a different model for handling the branches and multiple values that make the properties of W difficult to work with  ...  A final point of interest is that some of the techniques used to establish the mathematical properties can themselves potentially be automated, as was discussed in a paper presented at AISC Madrid [3]  ...  The colour graph of the Riemann Surface for ω (not shown here, but used in the upcoming Lambert W poster, was produced with a Maple program written by George Labahn (getting the colours to come out continuous  ... 
doi:10.1007/3-540-45470-5_10 fatcat:bs2fzcvolfg47le6a6ou67264m

Using Programming Language Theory to Make Automatic Differentiation Sound and Efficient [chapter]

Barak A. Pearlmutter, Jeffrey Mark Siskind
2008 Lecture Notes in Computational Science and Engineering  
Using novel analysis techniques, it accepts source code involving free use of a first-class forward AD operator and generates object code which attains numerical performance comparable to, or better than  ...  Because the λ -calculus is the basis for modern programming-language implementation techniques, integration of AD into the λ -calculus allows AD to be integrated into an aggressive compiler.  ...  This work was supported, in part, by NSF grant CCF-0438806, Science Foundation Ireland grant 00/PI.1/C067, and a grant from the Higher Education Authority of Ireland.  ... 
doi:10.1007/978-3-540-68942-3_8 fatcat:q6mfgwtuhjbehngz45umahgy2e

Polymorphic type inference and containment

John C. Mitchell
1988 Information and Computation  
Type expressions may be used to describe the functional behavior of untyped lambda terms.  ...  We present a general semantics of polymorphic type expressions over models of untyped lambda calculus and give complete rules for inferring types for terms.  ...  If the containment is an axiom, then we use Lemma 12 or 11. If the containment follows by (trans), then it is trivial, and if it follows by (tong) then we use (AI) and (VIZ).  ... 
doi:10.1016/0890-5401(88)90009-0 fatcat:hnxkw7bne5amznoo5hyszv4c4a

Covert Movement in Logical Grammar [chapter]

Carl Pollard
2011 Lecture Notes in Computer Science  
So there is no reason why it has to be derived from SS (or anything else).  ...  Moroever the idea of extending the Curry-Howard conception to substructural logics was continually being rediscovered 2 ; so, in hindsight at least, it is easy perceive these labelled bracketings as Curry-Howard  ... 
doi:10.1007/978-3-642-21490-5_2 fatcat:4wuroemcobgphp53jr5fs7dh6m

SEMANTIC NETS ARE IN THE EYE OF THE BEHOLDER [chapter]

Lenhart K. Schubert
1991 Principles of Semantic Networks  
This terminological problem is not due to lack of substance or coherence of work done under the semantic net banner, Rather, it is due to convergence of the major KR schemes: the representational and computational  ...  are described as logic-based, frame-based, rule-based, or something else.  ...  It is often faster to rediscover something within the framework of one's colony than to glean it from the writings of another.  ... 
doi:10.1016/b978-1-4832-0771-1.50008-4 fatcat:dcb4ratdhbabpnm5z5agbmvfmm

Dynamic trust negotiation for flexible e-health collaborations

Oluwafemi Ajayi, Richard Sinnott, Anthony Stell
2008 Proceedings of the 15th ACM Mardi Gras conference on From lightweight mash-ups to lambda grids: Understanding the spectrum of distributed computing requirements, applications, tools, infrastructures, interoperability, and the incremental adoption of key capabilities - MG '08  
In an organisation we provide security by granting privileges to either identities or roles.  ...  Numerous access control approaches exist today to address the cross-boundary control issues.  ...  Acknowledgments This work is supported by a grant from the Medical Research Council (MRC) UK and is undertaken as part of the Virtual Organisation for Trials of Epidemiological Studies (VOTES) 3-year project  ... 
doi:10.1145/1341811.1341821 dblp:conf/mg/AjayiSS08 fatcat:dzy2hkmhl5eetav4ghnv75i7he

Quasi-prime algebraic domains

Guo-Qiang Zhang
1996 Theoretical Computer Science  
It is then possible to give, for example, a model for the un-typed lambda calculus with a reflexive quasi-prime algebraic domain. PART I. QUASI-PRIME ALGEBRAIC DOMAINS I.  ...  We show further that with the usual Scott continuous functions as morphisms, quasi-prime algebraic domains are cartesian closed.  ...  Thanks go to Michael Huth for pointing out to me that I had, as a by-product of considering quasiprime algebraic domains, rediscovered the notion of completely irreducible elements.  ... 
doi:10.1016/0304-3975(95)00133-6 fatcat:pieragw4yvgr3anckacwtvg6aq

A scheme for multisource interior tomography

Ge Wang, Hengyong Yu, Yangbo Ye
2009 Medical Physics (Lancaster)  
To demonstrate the merits of this approach, the authors report interior reconstruction from in vivo lung CT data at a much reduced radiation dose, which is roughly proportional to the ROI size.  ...  Currently, x-ray computed tomography ͑CT͒ requires source scanning so that projections can be collected from various orientations for image reconstruction.  ...  flow of oil and water that is pumped from oil reservoirs. 35 A promising way to suppress image artifacts and/or increase the FOV is to use detectors in a time-sharing fashion which can also be referred  ... 
doi:10.1118/1.3157103 pmid:19746792 pmcid:PMC2724174 fatcat:iffm2ktqtjhf3jgx3zo5nbgr5q

History of the formulas and algorithms for pi [article]

Jesus Guillera
2009 arXiv   pre-print
Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals. Some expressions which are (amazingly) related to pi have been evaluated.  ...  Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi.  ...  the continued fraction.  ... 
arXiv:0807.0872v3 fatcat:cjo2epcy2nff7gqkwdqrgq5ufq

Categorical Models for a Semantically Linear Lambda-calculus

Marco Gaboardi, Mauro Piccolo
2010 Electronic Proceedings in Theoretical Computer Science  
This paper is about a categorical approach to model a very simple Semantically Linear lambda calculus, named Sll-calculus. This is a core calculus underlying the programming language SlPCF.  ...  This category is general enough to catch interesting models in Scott Domains and Coherence Spaces.  ...  Girard [12] discovered linear logic starting from a semantical investigation of the second-order lambda calculus.  ... 
doi:10.4204/eptcs.22.1 fatcat:kbeaid46cnasnj7wceoouoaauu

Continuity and discontinuity during hominization

Anne Dambricourt Malassé
1993 Quaternary International  
The hypothesis is that hominizatîon represents a continous phenomenon from fossil apes to Sapiens, i.e. an increase in thé embryonic contraction, but with discontinous effects, i.e. ontogenic organization  ...  Récent observations on an ontogenetic craniofacial phenomenon hâve led to new concepts of facial morphogenesis and to récognition of a process called craniofacial contraction.  ...  ACKNOWLEDGEMENTS I would like to thank Dr. Jean Chaline for inviting me to thé workshop on 'Modes and Tempos of Evolution in thé Quaternary' and to Dr.  ... 
doi:10.1016/1040-6182(93)90027-d fatcat:qjiqp6auyralzh3qezc7rzhhsi
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