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A characterization of lambda-terms transforming numerals

PAWEŁ PARYS
2016 Journal of functional programming  
As a consequence, we prove that in a λ-term of a fixed type, we can store only a fixed number of natural numbers, in such a way that they can be extracted using λ-terms.  ...  We show that λ-terms of each fixed (but possibly very complicated) type can be described by a finite piece of information (a set of appropriately defined intersection types) and by a vector of natural  ...  A Characterization of Lambda-terms Transforming Numerals ZU064-05-FPR lambda˙value 6 April 2016 16:49 15 A Characterization of Lambda-terms Transforming Numerals 29 obtain a derivation tree  ... 
doi:10.1017/s0956796816000113 fatcat:l4xybtvd7bey3bkihclnumkteu

On Near-cloaking for Linear Elasticity

Richard Craster, André Diatta, Sébastien Guenneau, Harsha Hutridurga
2021 Multiscale Modeling & simulation  
We discuss near-cloaking for elasticity systems via a regularized transform and perform numerical experiments to illustrate our near-cloaking results.  ...  This was remedied in [41] by the introduction of a regularized geometric transform, which blows up a small ball onto the cloaked region.  ...  If \BbbC 1 and \BbbC 2 are isotropic homogeneous tensors, then there is a characterization of the aforementioned ordering property in terms of their Lam\' e parameters.  ... 
doi:10.1137/20m1333201 fatcat:vcmweeg6hfabjor6pk6o2fotqy

Non-determinism, Non-termination and the Strong Normalization of System T [chapter]

Federico Aschieri, Margherita Zorzi
2013 Lecture Notes in Computer Science  
We provide a simple characterization of non-strongly normalizable terms by means of the so called "zoom-in" perpetual reduction strategy.  ...  The first observation is that the zoom-in reduction of ut will contract redexes inside u as long as the term is "blocked", i.e. u does not transform into a function. Proposition 4.  ...  Definition 5 (Generalized Numerals). A generalized numeral is a term of As a second step, we need to define a relation P . P ) . Let t / ∈ SN T and s ∈ E T be a subterm of t.  ... 
doi:10.1007/978-3-642-38946-7_5 fatcat:kosdctak6baaten2wo5dbfq2sq

Page 5089 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
Moreover, storage operators can be typed in the second-order lambda-calculus. For example, if T is a closed term of type Vx(-Int[x] — —Int*[x]), then T is a storage operator for the Church numerals.  ...  In the lambda-calculus, a term T is a storage operator for the set of terms A if for all t € A there exists an a@ such that for all 0 with 6 =, t, Tf@ —; fa’, where a’ is some substitution instance of  ... 

Page 6736 of Mathematical Reviews Vol. , Issue 98K [page]

1998 Mathematical Reviews  
To start with, he presents the genesis of the lambda calculus. The notion of computability was first formalized in terms of definability on numerals represented in the lambda calculus.  ...  The main theorem of the paper states that the combinator XY can be transformed to the form Z/ -.-1K---KW---WU.---U, where Z is a BC combinator.  ... 

The Safe Lambda Calculus [chapter]

William Blum, C. -H. Luke Ong
2007 Lecture Notes in Computer Science  
In the same vein as Schwichtenberg's 1976 characterization of the simply-typed lambda calculus, we show that the numeric functions representable in the safe lambda calculus are exactly the multivariate  ...  Finally we give a game-semantic analysis of safety: We show that safe terms are denoted by P-incrementally justified strategies.  ...  Does the safe lambda calculus characterize a complexity class, in the same way that the simply-typed lambda calculus characterizes the polytime-computable numeric functions [13] ?  ... 
doi:10.1007/978-3-540-73228-0_5 fatcat:wm4gcayyyja6jgxscw5tjf2k7i

Deep Learning Based Opinion Miner and Sentiment Classifier of Social Media Data

2020 International journal of recent technology and engineering  
out the in depth context of a topic, a brand, a celebrity or a theme.  ...  This algorithm calculates a value of probability of positiveness for each sentence.  ...  a) CBOW Model CBOW model predicts an output term (center term), when given a bag of surrounding terms (context words).  ... 
doi:10.35940/ijrte.e6107.018520 fatcat:zpqex2hhxrdcpjv2mxf73y7xd4

Tagging, Encoding, and Jones Optimality [chapter]

Olivier Danvy, Pablo E. Martínez López
2003 Lecture Notes in Computer Science  
string * foexp | FOAPP of foexp * foexp the higher-order abstract syntax of lambda-terms reads as datatype hoexp = HOVAR of string | HOLAM of hoexp -> hoexp | HOAPP of hoexp * hoexp where the constructor  ...  A partial evaluator is said to be Jones-optimal if the result of specializing a self-interpreter with respect to a source program is textually identical to the source program, modulo renaming.  ...  Related Work Specializing Lambda-Interpreters The generating extension of a lambda-interpreter provides an encoding of a lambda-term into the term model of the meta language of this interpreter.  ... 
doi:10.1007/3-540-36575-3_23 fatcat:jvnmc2m3lngndog75mzeowk7vm

Approximate real inversion formulas of the gaussian convolution

S. Saitoh
2004 Applicable Analysis  
In this paper we introduce a unified method of solving inverse problems in some general linear differential equations numerically and as a prototype example we shall show a practical real inversion formula  ...  Twenty years ago, the last author gave a surprise characterization of the image of (15) for $L_{2}(\mathrm{R})=$ L2(R) $dx)$ functions in terms of an analytic function and established a very simple complex  ...  small A and we must calculate the integral (21) hardly in the sense of numerical.  ... 
doi:10.1080/00036810410001657198 fatcat:gotacsjdlnbefp67ewyyhhlsae

Numerical Laplace inversion in rheological characterization

Peter P Valkó, Joseph Abate
2004 Journal of Non-Newtonian Fluid Mechanics  
A new algorithm available for the numerical inversion of Laplace transforms using multi-precision computational environment provides controlled accuracy, that is the inversion can be carried out to yield  ...  One important application is characterizing rheological phenomena, because the modeler is no longer restricted to a narrow class of "analytically treatable" constitutive equations, and the numerical inversion  ...  A deficiency of all numerical inversion algorithms is the inability to handle transforms of non-differentiable functions.  ... 
doi:10.1016/j.jnnfm.2003.11.001 fatcat:4267jrfhprct7f2m4sv3i3mhxm

Local and global moves on locally planar trivalent graphs, lambda calculus and λ-Scale [article]

Marius Buliga
2012 arXiv   pre-print
We give a description of local and global moves on a class of locally planar trivalent graphs and we show that it contains λ-Scale calculus, therefore in particular untyped lambda calculus.  ...  Surprisingly, the beta reduction rule comes from a local "sewing" transformation of trivalent locally planar graphs.  ...  (xy)): Let A → [A] be a transformation of a lambda term A into a graph [A] as described previously (multiple transformations are possible because of the choice of Υ trees).  ... 
arXiv:1207.0332v1 fatcat:a2iqtotphzhinfg4qdbp3d2x4a

A reduced instruction set proof environment [chapter]

Holger Busch
1995 Lecture Notes in Computer Science  
A general-purpose proof interface has been created on top of the higher-order-logic theorem prover LAMBDA in order to improve the efficiency of human interaction and minimize the learning overhead.  ...  All essential [_AMBDA functions for interactive proof development are accessible via a handy set of user commands.  ...  The main groups of Rispe functions are characterized in the following. Interactive Proof Functions These commands are intended for transforming a goal in a stepwise manner.  ... 
doi:10.1007/3-540-59047-1_54 fatcat:uf2jlqgqanaizedlycazatrima

Page 6421 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
Tableau branches are augmented by assigning a nonempty subset of the universe to each simple term.  ...  This assignment is subject to a revision process, comparable to the approximation of functions by a sequence of step functions in numerical mathematics, result- ing in non-Herbrand interpretations for  ... 

Statistical Simulation: Power Method Polynomials and Other Transformations

Hakan Demirtas
2011 Journal of Statistical Software  
Although the focus of the book is on power polynomials, two other general classes (g-h and generalized lambda families) that have been in use for multivariate data simulation are also discussed at relative  ...  Headrick's book is a valuable addition to the simulation world in the sense that it is the first systematic book on power method polynomials that have been gaining popularity during recent years in a broad  ...  All in all, given the utmost importance of multivariate continuous data generation across many fields, Headrick's book is a fairly major contribution to the literature in the sense that it is the first  ... 
doi:10.18637/jss.v043.b02 fatcat:xabtdnssjrhv3cfm4of25sngz4

Preface for special section from FLOPS 2014

MICHAEL CODISH, EIJIRO SUMII
2016 Journal of functional programming  
The aim of the Functional and Logic Programming series of conferences is to bring together researchers interested in declarative programming including functional programming and logic programming.  ...  In the third paper, "A Characterization of Lambda-terms Transforming Numerals", Parys shows that λ-terms of each fixed type can be described by a finite piece of information (a set of intersection types  ...  ) and by a vector of natural numbers.  ... 
doi:10.1017/s0956796816000149 fatcat:kgrhfm4gjzf33luylyuyq7ajs4
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