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A Monad for Randomized Algorithms

Tyler Barker
2016 Electronical Notes in Theoretical Computer Science  
Also, there is no distributive law between the probabilistic powerdomain and any of the nondeterministic powerdomains, but there is a distributive law between the monad of random choice and the lower powerdomain  ...  Then, in these categories, there is a distributive law between this monad and the convex powerdomain.  ...  The author also thanks Jean Goubault-Larrecq and Dana Scott for email correspondence regarding the model of continuous random variables and the stochastic lambda calculus, respectively.  ... 
doi:10.1016/j.entcs.2016.09.031 fatcat:5ff642kxm5gu7g67ienctz6khq

Semantics of a sequential language for exact real-number computation

J. Raymundo Marcial-Romero, Martín H. Escardó
2007 Theoretical Computer Science  
We show that the construction cannot be modelled by the Plotkin or Smyth powerdomains, but that the Hoare powerdomain gives a computationally adequate semantics.  ...  We instead introduce a suitable operational notion of strong convergence and show that total correctness can be proved by establishing partial correctness (using denotational methods) and strong convergence  ...  Acknowledgements We thank Achim Jung, Paul Levy, Steve Vickers and Andrew Moshier for comments and suggestions.  ... 
doi:10.1016/j.tcs.2007.01.021 fatcat:aa4hels7dzhblnbookd27p65yq

A characterization of plotkin's order in powerdomains, and some of its properties

D.Frutos Escrig
1984 Theoretical Computer Science  
In 1976, Plotkln introduced powerdomains adapting to them, in some sense, Egli-Milner's order.  ...  L.ately, Sm$h ( 1978) presented the same results starting from generating trees. and adding a new order that he denoted by E (,.  ...  He gives a counterexample: D is (0. l)'U (finite and infinite words of ones and zeros) with lexicographical order, A = {I, 0'7 Ic 1 n E R}, f3 = A u :O'}.  ... 
doi:10.1016/0304-3975(84)90127-0 fatcat:hv74fjnxerg75dxgal4zpauicm

Predicate transformers for extended probability and non-determinism

KLAUS KEIMEL, GORDON D. PLOTKIN
2009 Mathematical Structures in Computer Science  
We therefore first consider predicate transformers for powercones and then specialise to the powerdomains.  ...  with continuous functions where S is the upper powerdomain monad, and (−) ⊥ is the lifting construction.  ...  Then there are y, z with y + z 6 x and r < G(y) + Q(z). If G and Q are continuous, we may find y y and z z such that r 6 G(y ) + Q(z ).  ... 
doi:10.1017/s0960129509007555 fatcat:szyaxvnvrbgjzkstoz32pi3g3q

RETRACTED: Semantic Domains for Combining Probability and Non-Determinism

Regina Tix, Klaus Keimel, Gordon Plotkin
2005 Electronical Notes in Theoretical Computer Science  
For the classical powerdomains we now speak of the lower, upper, and convex powerdomains instead of the Hoare, Smyth, and Plotkin ones.  ...  The results are variants of the upper, lower and convex powerdomains over the probabilistic powerdomain (see Chapter 4).  ...  , we can find open sets U, V, W with U V and U W , but U V ∩ W .  ... 
doi:10.1016/j.entcs.2004.06.063 fatcat:kcsyh7rsgncadlrlnlonoaraau

Semantic Domains for Combining Probability and Non-Determinism

Regina Tix, Klaus Keimel, Gordon Plotkin
2009 Electronical Notes in Theoretical Computer Science  
The results are variants of the upper, lower and convex powerdomains over the probabilistic powerdomain (see Chapter 4).  ...  Our construction combines the well-known domains modelling nondeterminism -the lower, upper and convex powerdomains, with the probabilistic powerdomain of Jones and Plotkin [24] modelling probabilistic  ...  We may find a finite subset F of U such that Q ⊆ F .  ... 
doi:10.1016/j.entcs.2009.01.002 fatcat:d25ftdfq6rbv7ivv6f7olglarq

Tensor Products and Powerspaces in Quantitative Domain Theory

Philipp Sünderhauf
1997 Electronical Notes in Theoretical Computer Science  
V = 0 1] with usual addition and multiplication, reveals a close connection to the powerdomain of extended probability measures.  ...  Powerdomains are then constructed as free modules over this semiring.  ...  Acknowledgement I would like to thank Bob Flagg for many inspiring discussions about Vdomains and value quantales.  ... 
doi:10.1016/s1571-0661(05)80150-1 fatcat:xlbpr2zrzrgu3pm5yhkktf6oby

Static inference of properties of applicative programs

Prateek Mishra, Robert M. Keller
1984 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL '84  
We describe several practical problems and solve them using abstract interpretation.  ...  As a consequence, we can develop inference schemes for a large and useful class of functional programs, including functions defined on streams.  ...  Acknowledgements We thank Prakash Panangaden, Uday Reddy and Esther Shilcrat for helpful discussions and in aiding the preparation of this report.  ... 
doi:10.1145/800017.800535 dblp:conf/popl/MishraK84 fatcat:u2z5oscaajdwtei6plerrzud4e

Page 1262 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
Weak, zero-element and strong data collection types and aggregation op- erators are introduced. We show how adjoints lead to data collec- tions.  ...  Introduction: “Snack-powerdomains and snack-algebras appeared as one of several attempts at modelling databases.  ... 

Fractals and domain theory

KEYE MARTIN
2004 Mathematical Structures in Computer Science  
We show that a measurement µ on a continuous dcpo D extends to a measurementμ on the convex powerdomain CD iff it is a Lebesgue measurement.  ...  Finally, after resolving the existence question for Lebesgue measurements on countably based domains, we uncover the following relationship between classical analysis and domain theory: For an ω-continuous  ...  Then ( i ) i An element with measure zero is maximal, i.e., ker µ ⊆ max(D). Example 3. 3 3 Domains and their canonical measurements.  ... 
doi:10.1017/s0960129504004384 fatcat:urfgjrrs7bfhpfbt74gf5lg7ey

A Domain Theory for Statistical Probabilistic Programming [article]

Matthijs Vákár, Ohad Kammar, Sam Staton
2021 arXiv   pre-print
By contrast, quasi-Borel predomains do support both a commutative probabilistic powerdomain and higher-order functions.  ...  Probability is traditionally treated in cpo models using probabilistic powerdomains, but these are not known to be commutative on any class of cpos with higher order functions.  ...  It has been helpful to discuss this work with the Oxford PL and Foundations groups, at the Domains 2018 and HOPE 2018 workshops, and with Marcelo Fiore, Chris Heunen, Paul Levy, Carol Mak, Gordon Plotkin  ... 
arXiv:1811.04196v2 fatcat:45t52scam5hnbi2pglyrxqbfga

Stably compact spaces

JIMMIE LAWSON
2010 Mathematical Structures in Computer Science  
There are three primary themes that are developed: firstly the property of stable compactness is preserved under a large variety of constructions involving powerdomains, hyperspaces, and function spaces  ...  , secondly the underlying de Groot duality of stably compact spaces, which finds varied expression, is reflected by duality theorems involving the just mentioned constructions, and thirdly the notion of  ...  As was the case for the Smyth powerdomain, one may find a much more extensive treatment of the Hoare powerdomain from various topological perspectives in (Schalk 1993) .  ... 
doi:10.1017/s0960129510000319 fatcat:uwsasrcwgvasfgr6ruvuhj7squ

Mixed powerdomains for probability and nondeterminism [article]

Klaus Keimel, Gordon D. Plotkin
2017 arXiv   pre-print
We consider mixed powerdomains combining ordinary nondeterminism and probabilistic nondeterminism.  ...  As usual with powerdomains, everything comes in three flavours: lower, upper, and order-convex.  ...  Acknowledgements We are very grateful to Jean Goubault-Larrecq for his many helpful comments and suggestions.  ... 
arXiv:1612.01005v6 fatcat:2tuhxgaepvgp5c2ihwbucwktse

A Convenient Category of Domains

Ingo Battenfeld, Matthias Schröder, Alex Simpson
2007 Electronical Notes in Theoretical Computer Science  
We motivate and define a category of topological domains, whose objects are certain topological spaces, generalising the usual ω-continuous dcppos of domain theory.  ...  It also supports the construction of free algebras for (in)equational theories, can be used as the basis for a theory of computability, and provides a model of parametric polymorphism.  ...  Further any one point space 1 is a zero object in TD; that is it is both initial and terminal.  ... 
doi:10.1016/j.entcs.2007.02.004 fatcat:tfvmwjta3bghfip63xew2onqvi

The regular spaces with countably based models

Keye Martin
2003 Theoretical Computer Science  
These results enable us to prove that the probabilistic powerdomain of a countably based model of a metric space always contains a copy of the normalized Borel measures in their weak topology, and to establish  ...  In addition, we give a new and conceptually simple model for complete metric spaces.  ...  : Find a domain theoretic model for analytic spaces and continuous maps.  ... 
doi:10.1016/s0304-3975(02)00700-4 fatcat:txfrqs46rvdbhkfys7cuuvsezu
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