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Infinitary lambda calculus and discrimination of Berarducci trees

2003
*
Theoretical Computer Science
*

a normal form ⇔ C[N ] has a normal form:

doi:10.1016/s0304-3975(02)00809-5
fatcat:znym7awldzbtrcfoyt3g4xskgu
*The*results*of*[26, 13] can be rephrased as follows:*The**lambda**calculus*internally*discriminates*as B ohm tree modulo inÿnite (respectively, ÿnite) Á-expansions ... We propose an extension*of**lambda**calculus*for which*the*Berarducci trees equality coincides with observational equivalence, when we observe rootstable or rootactive behavior*of*terms. ... This paper was made possible, thanks to*the*hospitality ETL o ered*in*March 1999 to both Mariangiola Dezani and Paula Severi. Acknowledgements We thank Vincent van Oostrom for discussions. ...##
###
A type theory for memory allocation and data layout

2003
*
Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '03
*

*in*such a way as to account for optimizations such as

*the*coalescing

*of*

*multiple*calls to

*the*allocator. ...

*The*fuse constructor from ordered logic describes adjacency

*of*values

*in*memory, and

*the*mobility modal describes pointers into

*the*heap. ...

*in*a

*lambda*

*calculus*setting. ...

##
###
A type theory for memory allocation and data layout

2003
*
SIGPLAN notices
*

*in*such a way as to account for optimizations such as

*the*coalescing

*of*

*multiple*calls to

*the*allocator. ...

*The*fuse constructor from ordered logic describes adjacency

*of*values

*in*memory, and

*the*mobility modal describes pointers into

*the*heap. ...

*in*a

*lambda*

*calculus*setting. ...

##
###
On the discriminating power of tests in resource lambda-calculus
[article]

2012
*
arXiv
*
pre-print

Proof nets can be used naturally to extend

arXiv:1205.4691v2
fatcat:55cemwrkdfdv3ls6vzlarhcg4u
*the*into*the**lambda**calculus*with resources, a*calculus*that contains notions*of*linearity and differentiations. ...*In*denotational semantics, categorical models*of*DLL are now commune, and*the*simplest one is Rel,*the*category*of*sets and relations. ... which is very*powerful**in*this*calculus*. ...##
###
Page 3791 of Mathematical Reviews Vol. , Issue 95g
[page]

1995
*
Mathematical Reviews
*

This (kind

*of*) nondeterminism is actually necessary,*in**the*precise sense that*the*same*discriminating**power*cannot be recovered by adding only Church-Rosser operators, such as parallel convergence testing ... {For*the*entire collection see MR 95e:68012.} 95¢:03015 03B40 03B70 68Q10 68Q55 Sangiorgi, Davide (4-EDIN-FC; Edinburgh)*The*lazy*lambda**calculus**in*a concurrency scenario. ...##
###
A Typedriven Vector Semantics for Ellipsis with Anaphora using Lambek Calculus with Limited Contraction
[article]

2019
*
arXiv
*
pre-print

vector interpretable

arXiv:1905.01647v1
fatcat:ko42wdgqsffghmoaked2dy6gfu
*lambda*terms to derivations*of*LCC*in**the*style*of*Muskens & Sadrzadeh (2016). ... Formal semantics on*the*other hand, has*powerful*mechanisms for dealing with relative pronouns, coordinators, and*the*like. ... However, we want to employ*the*copying*power**of*non-linear*lambda**calculus*, and so we will move from*the*direct interpretation below I I What we end up with is*in*fact a more intricate target than*in*...##
###
Order-incompleteness and finite lambda reduction models

2003
*
Theoretical Computer Science
*

Many familiar models

doi:10.1016/s0304-3975(02)00038-5
fatcat:iklf5xdrtvbtvpklntvijhjycu
*of**the*untyped*lambda**calculus*are constructed by order-theoretic methods. This paper provides some basic new facts about ordered models*of**the**lambda**calculus*. ... Equivalently,*the*open and closed term algebras*of**the*untyped*lambda**calculus*cannot be non-trivially partially ordered. ... Acknowledgements I would like to thank Gordon Plotkin for introducing me to*the*problem*of*partial orders on term models, and for many stimulating discussions. ...##
###
Ordinals and ordinal functions representable in the simply typed lambda calculus

1999
*
Annals of Pure and Applied Logic
*

*The*results

*of*this paper have

*the*same flavor as those

*of*Schwichtenberg and Statman on numeric functions representable

*in*

*the*simply typed

*lambda*

*calculus*. ... We define ordinal representations

*in*

*the*simply typed

*lambda*

*calculus*, and consider

*the*ordinal functions representable with respect to these notations. ... Acknowledgements I would like to thank Daniel Leivant for suggesting this line

*of*research, and for many discussions regarding it. ...

##
###
Book reports

2005
*
Computers and Mathematics with Applications
*

*Lambda*

*Calculus*. 2.1. Compositionality. 2.2. Two Experiments. 2.3.

*The*

*Lambda*

*Calculus*. 2.4. Implementing

*Lambda*

*Calculus*. 2.5. Grammar Engineering. 3. Underspeeified Representations. 3.1. ... Analysis

*of*a greedy active learning strategy.

*The*

*Power*

*of*Selective Memory: Self-Bounded Learning

*of*Prediction Suffix Trees. Bayesian inference

*in*spiking neurons. ...

##
###
Interactive foundations of computing

1998
*
Theoretical Computer Science
*

*The*extension

*of*Turing to interaction machines parallels that

*of*

*the*

*lambda*to

*the*pi

*calculus*. ...

*In*

*the*final section

*the*robustness

*of*interactive models

*in*expressing open systems, programming

*in*

*the*large, graphical user interfaces, and agent-oriented artificial intelligence is compared to

*the*... Though

*the*simplicity and

*power*

*of*

*the*pi

*calculus*is aesthetically appealing, its primitives are too low-level to specify real interactive applications, just as

*lambda*

*calculus*primitives are too low-level ...

##
###
Discrimination by Parallel Observers: The Algorithm

1999
*
Information and Computation
*

Another consequence is that

doi:10.1006/inco.1998.2773
fatcat:jmsyiepgc5dltgslws3emmxkfi
*the**discriminating**power**of*concurrent*lambda*contexts is*the*same as that*of*Boudol-Laneve's contexts with*multiplicities*. ...*The*main result*of**the*paper is a constructive proof*of**the*following equivalence: two pure -terms are observationally equivalent*in**the*lazy concurrent -*calculus*i they have*the*same L evy-Longo trees ... Acknowledgments*The*nal form*of*this paper di ers deeply from*the*initial one. This is essentially due to*the*constructive criticism*of**the*Referees*of**the*LICS paper 20] and*of**the*journal version. ...##
###
iRho: the Software

2006
*
Electronical Notes in Theoretical Computer Science
*

This paper describes

doi:10.1016/j.entcs.2005.09.023
fatcat:m5xbmnvmtvbs5ncacwkfv4pz5a
*the*first implementation*of*an interpreter for iRho, an imperative version*of**the*Rewriting-*calculus*, based on pattern-matching, pattern-abstractions, and side-effects. ...*The*final objective is to make iRho a, so called, agile programming language,*in**the*vein*of*some useful scripts languages, like, e.g. ... Note that*the*Rewriting-*calculus*is a generalization*of**the**Lambda*-*calculus*if*the*pattern P is a variable. ...##
###
Proposal for a natural formalization of functional programming concepts

1988
*
RAIRO - Theoretical Informatics and Applications
*

NUMERALS: Numerals are defined following Church's numerals

doi:10.1051/ita/1988220303411
fatcat:4oytquplojdrph4pc4ewalb5hi
*of**Lambda*-*Calculus*[2]. ... -*calculus*allowing*the**lambda*-notation with a séquence*of*variables as first parameter*of**the**lambda*operator,*the*problem is not resolved unless we fall into*the*Lisp conception which is equivalent to ...##
###
Quantum computation, quantum theory and AI

2010
*
Artificial Intelligence
*

parts

doi:10.1016/j.artint.2009.11.009
fatcat:gthhfdrthnervcs2xg2jvzsqg4
*of**the*map are very rough and other parts are empty, and waiting for*the*readers to fill*in*. ... Also, a (quite personal) survey*of*quantum computation is presented*in*order to give*the*readers a (unbalanced) panorama*of**the*field. ...*The*author would like to express his sincere thanks to Professor Chengqi Zhang, Director*of**the*Center*of*Quantum Computation and Intelligent Systems, University*of*Technology, Sydney, for providing*the*...##
###
Names, Equations, Relations: Practical Ways to Reason about new

1997
*
BRICS Report Series
*

<p>

doi:10.7146/brics.v4i39.18965
fatcat:7pwfi6oxwffnxcq6hrwu6jhpjm
*The*nu-*calculus**of*Pitts and Stark is a typed*lambda*-*calculus*, extended with state<br />*in**the*form*of*dynamically-generated names. ...*in**the*spi-*calculus*. ... It was subsequently completed at BRICS (Basic Research*in*Computer Science, a centre*of**the*Danish National Research Foundation),*in**the*University*of*Aarhus, Denmark. ...
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