A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Filters
Newton Series, Coinductively
[chapter]
2015
Lecture Notes in Computer Science
Preserved Fulltext
Exploiting the fact that the set of weighted languages is a final coalgebra, we use coinduction to prove that a classical operator from difference calculus in mathematics: the Newton transform, generalises ...
Newton transform of a language, together with concrete calculation rules for computing them. ...
Theorem 53 (Newton series for languages, 1st). ...
doi:10.1007/978-3-319-25150-9_7
fatcat:bdiougf6ijdihdvjeknlm3olhm
Newton series, coinductively: a comparative study of composition
2017
Mathematical Structures in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
Exploiting the fact that the set of weighted languages is a final coalgebra, we use coinduction to prove that an operator of the classical difference calculus, the Newton transform, generalises from infinite ...
Newton transform of a language, together with concrete calculation rules for computing them. ...
The set of weighted languages, together Newton series, coinductively 3 its stream derivative by σ = (σ(1), σ(2), σ(3), . . . ). ...
doi:10.1017/s0960129517000159
fatcat:4l6trke2hvethpppsdhnwps6py
Preface to special issue: ICTAC 2015
2018
Mathematical Structures in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
The paper by Basold, Hansen, Pin and Rutten (Newton Series, Coinductively: A Comparative Study of Composition) uses a coinductive calculus of infinite streams by one of the authors to give an analysis ...
The authors use coinduction to prove that an operator of the classical difference calculus, the Newton transform, generalizes from infinite sequences to weighted languages. ...
doi:10.1017/s0960129518000130
fatcat:7e2hvlpvnjdkladbg6bzzfuzoa
Rationality and Escalation in Infinite Extensive Games
[article]
2012
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
The reasoning is based on the concept of coinduction conceived by computer scientists to model infinite computations and used by economic agents unknowingly. ...
When used consciously, this concept is not as simple as induction and we could paraphrase Newton: "Modeling the madness of people is more difficult than modeling the motion of planets". ...
Like Weierstrass' discovery led to the development of function series, logicians have devised methods for correct deductions on infinite structures. ...
arXiv:1112.1185v3
fatcat:zxkeb6w3argbvgjptf6wfv22ry
Scientific Modelling with Coalgebra-Algebra Homomorphisms
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Kleisli Coinduction e † : X → T Y is a Kleisli-coinductive solution, then so is T h • e † : X → T Z. ...
In a Newton-style modelling approach, this system is specified by a second-order linear differential equationẍ + k m x = 0, which simply states that all acceleration is due to the restoring force. ...
arXiv:1506.07290v1
fatcat:ogbblkrosncxbnvqymysxgic3m
In Praise of Sequence (Co-)Algebra and its implementation in Haskell
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Introduction Consider these titles: Formal Power Series [64] , Power Series, Power Serious [57] , A Coinductive Calculus of Streams [72] , and Concrete Stream Calculus [39] . ...
A proof by coinduction is presented for contrast in item Q of the next section. Let f ∈ S, g ∈ S 0 , then, 2. (af + bg) = a f + b g linear 3. (n + 1)[x n+1 ] = [x n ] power series 4. ...
arXiv:1812.05878v2
fatcat:qu5f7ne6nrcy7hd4zq5xg5tzcq
Stream Differential Equations: Specification Formats and Solution Methods
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been developed in many papers over the past two decades. ...
facts about formal power series. ...
More recently, the Newton transform between the ∆-and tail-structures has been studied in [9] . ...
arXiv:1609.08367v1
fatcat:pwvidt3ubbfxdpsr2qqyyxs44m
Les crashs sont rationnels
[article]
2012
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
Among those new paths, coinduction is the basis of our reasoning in infinite games. ...
L'escalade consisteà prendre, sans se donner de borne, une série de décisions de plus en plus lourdes de conséquences. ...
La base de celui-ci, qui aété conçu pour s'adapter aux objets infinis s'appelle la coinduction. On fait donc de la coinduction rétrograde . En fait, il y a au moins deuxéquilibres : 1. ...
arXiv:1111.7299v5
fatcat:bxpfrmdutzddljhyxrb5kwtsee
On stratification for spaces with Noetherian mod p cohomology
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
The first and second author would furthermore like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Homotopy Harnessing Higher ...
In a series of papers [BIK08, BIK11a] culminating in [BIK11b] , Benson, Iyengar, and Krause classified all modular representations of a finite group G up to a certain equivalence relation: Two representations ...
By Remark 2.15 coinduction along f is also conservative. ...
arXiv:1904.12841v2
fatcat:jxmjfasywnaoznkznar3ti7moa
Formal Verification of Exact Computations Using Newton's Method
[chapter]
2009
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
CoInductive represents (β : Z) : stream digit → R → Prop := | rep : ∀ s r k, −β < k < β → −1 ≤ r ≤ 1 → represents β s r → represents β (Cons k s) k+r β . ...
, Y 0 n + 2 µ n B n ] ⊆ [Y 0 0 − 3B 0 , Y 0 0 + 3B 0 ] ⊂]a, b [ We do not discuss all the details as they are elementary reasoning steps concerning inequalities, second degree equations or geometric series ...
CoFixpoint exact newton (g: stream digit → stream digit) ex0 n:= match (make digit (EXn g ex0 n) with |d1::x' ⇒ d1::exact newton (fun x ⇒ (β ⊙ g (d1::x))) x' n end. ...
doi:10.1007/978-3-642-03359-9_28
fatcat:26eeozkikre3jb66lhyxgnt324
Algebra and coalgebra of stream products
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Below, we consider n × n matrices of power series; power series in z with scalar matrices as coefficients are interpreted element-wise, that is as defining matrices of power series. ...
We also mention [7, 10] , that adopt a coinductive approach to reason on polynomial ODEs. ...
arXiv:2107.04455v1
fatcat:7t7nylwl7ffalayfvddrqpj7p4
Relational Interpretations of Recursive Types in an Operational Setting
1999
Information and Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
, we derive a notion of logical equivalence for expressions of the language that we show coincides with contextual equivalence and which, by virtue of its construction, validates useful induction and coinduction ...
We are grateful to the Newton Institute and the organizers of the program on Semantics of Computation for their support. ...
The work described here was carried out in part at the Isaac Newton Institute for Mathematical Sciences of Cambridge University in the autumn of 1995. ...
doi:10.1006/inco.1999.2828
fatcat:ft3r73aakff2rouohdlguyiwsu
Un acercamiento coinductivo al análisis real
Español
2017
Revista Integración
Español
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Our aim will be to use the framework of stream automata to illustrate the coinductive character of real analysis through classical results as the fundamental theorem of calculus, Taylor series and the ...
Coinduction is a dual concept to induction; it has been discovered and studied recently. ...
Serie de Taylor Considere el conjunto A = {f : R −→ R | f es analítica en 0}. ...
doi:10.18273/revint.v35n1-2017007
fatcat:nxl2l6dvrjhx7hujoxmm67okra
A monadic, functional implementation of real numbers
2007
Mathematical Structures in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Other Versions
It can be seen as a dependently typed functional programming language with inductive and coinductive data types. ...
More Efficient Power Series. A power series converges faster for values closer to 0. ...
((1+n)/2, 1/2) newton (x,err) = (approxBase x' e1, e1*2) where x' = (n+x^2)/(2*x) e1 = err^2/2 sqrtCts :: UniformCts Base (Complete Base) sqrtCts = UniformCts (^2) (approx . rationalSqrt) realSqrt :: ...
doi:10.1017/s0960129506005871
fatcat:4kddlvemijbr3huancudhdpjzi
Continuous Functions on Final Coalgebras
2009
Electronical Notes in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
about representations of continuous functions requires a language whose type system incorporates the dependent function and pair types, inductive definitions at types Set, I → Set and (Σ I : Set) Set I , coinductive ...
It has 0 and +, 1 and ×, ·, Σ f , Π f , Δ f , μ and ν, not to mention some linear logic connectives and connections with the Newton-Leibnitz differential calculus. ...
Working with container technology seems to be much cleaner than the alternative of working with power-series functors. ...
doi:10.1016/j.entcs.2009.07.081
fatcat:rj33jvuzknaszcqwb3a3iyjczy
« Previous
Showing results 1 — 15 out of 39 results