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Some Domain Theory and Denotational Semantics in Coq [chapter]

Nick Benton, Andrew Kennedy, Carsten Varming
2009 Lecture Notes in Computer Science  
We present a Coq formalization of constructive ω-cpos (extending earlier work by Paulin-Mohring) up to and including the inverselimit construction of solutions to mixed-variance recursive domain equations, and the existence of invariant relations on those solutions. We then define operational and denotational semantics for both a simplytyped CBV language with recursion and an untyped CBV language, and establish soundness and adequacy results in each case. Research supported in part by National
more » ... cience Foundation Grants CCF-0541021, CCF-0429505. Our formalization is based on a Coq library for constructive pointed ω-cpos and continuous functions written by Paulin-Mohring [20] as a basis for a semantics of Kahn networks, and of probabilistic programs [6] . Section 2 describes our slight generalization of Paulin-Mohring's library to treat predomains and a general lift monad. In Section 3, we then define a simply-typed call-by-value functional language, give it a denotational semantics using our predomains and prove the standard soundness and adequacy theorems, establishing the correspondence between the operational and denotational semantics. These results seem not to have been previously mechanized for a higher-order language. Section 4 is about solving recursive domain equations. We formalize Scott's inverse limit construction along the lines of work by Freyd [11, 12] and Pitts [22, 23] . This approach characterizes the solutions as minimal invariants, yielding reasoning principles that allow one to construct and work with recursively-defined predicates and relations over the recursively-defined domains. In Section 5, we define the semantics of an untyped call-by-value language using a particular recursive domain, and use the associated reasoning principles to again establish soundness and adequacy theorems. Basic Domain Theory This first part of the development is essentially unchanged from the earlier work of Paulin-Mohring [20] . The main difference is that Paulin-Mohring formalized pointed cpos and continuous maps, with a special-case construction of flat cpos (those that arise from adding a bottom element under all elements of an otherwise discretely ordered set), whereas we use potentially bottomless cpos ('predomains') and formalize a general constructive lift monad. Complete Partial Orders We start by defining the type of preorders, comprising a carrier type tord (to which :> means we can implicitly coerce), a binary relation Ole (written infix as ), and proofs that Ole is reflexive and transitive: Record ord := mk ord {tord :> Type; Ole : tord → tord → Prop; Ole refl : ∀ x : tord, Ole x x ; Ole trans : ∀ x y z : tord, Ole x y → Ole y z → Ole x z }. Infix " " := Ole. The equivalence relation == is then defined to be the symmetrisation of : Definition Oeq (O : ord ) (x y : O) := x y ∧ y x. Infix "==" := Oeq (at level 70). Both == and are declared as parametric Setoid relations, with being a partial order modulo ==. Most of the constructions that follow are proved and declared to be morphisms with respect to these relations, which then allows convenient (in)equational rewriting in proofs.
doi:10.1007/978-3-642-03359-9_10 fatcat:ettw3j3mw5hmnni2jex66aom3q

Higher-Order Separation Logic in Isabelle/HOLCF

Carsten Varming, Lars Birkedal
2008 Electronical Notes in Theoretical Computer Science  
Varming & Birkedal = {h | true} emp = {λx.  ...  Varming & Birkedal To support modularity and data abstraction (the first purpose of higher-order separation logic mentioned in the Introduction), we have a derived rule for let declarations that lets the  ...  Varming & Birkedal h.  ... 
doi:10.1016/j.entcs.2008.10.022 fatcat:dxrjw4q46nfmvk2k6rkgq7z7pi

Semantic-based Automated Reasoning for AWS Access Policies using SMT

John Backes, Pauline Bolignano, Byron Cook, Catherine Dodge, Andrew Gacek, Kasper Luckow, Neha Rungta, Oksana Tkachuk, Carsten Varming
2018 2018 Formal Methods in Computer Aided Design (FMCAD)  
Cloud computing provides on-demand access to IT resources via the Internet. Permissions for these resources are defined by expressive access control policies. This paper presents a formalization of the Amazon Web Services (AWS) policy language and a corresponding analysis tool, called ZELKOVA, for verifying policy properties. ZELKOVA encodes the semantics of policies into SMT, compares behaviors, and verifies properties. It provides users a sound mechanism to detect misconfigurations of their
more » ... licies. ZELKOVA solves a PSPACE-complete problem and is invoked many millions of times daily.
doi:10.23919/fmcad.2018.8602994 dblp:conf/fmcad/BackesBCDGLRTV18 fatcat:jnyqutkzbrdz3lhlhkud6gig4i

Stratified Abstraction of Access Control Policies [chapter]

John Backes, Ulises Berrueco, Tyler Bray, Daniel Brim, Byron Cook, Andrew Gacek, Ranjit Jhala, Kasper Luckow, Sean McLaughlin, Madhav Menon, Daniel Peebles, Ujjwal Pugalia (+6 others)
2020 Lecture Notes in Computer Science  
The shift to cloud-based APIs has made application security critically depend on understanding and reasoning about policies that regulate access to cloud resources. We present stratified predicate abstraction, a new approach that summarizes complex security policies into a compact set of positive and declarative statements that precisely state who has access to a resource. We have implemented stratified abstraction and deployed it as the engine powering AWS's IAM Access Analyzer service, and
more » ... ce, demonstrate how formal methods and SMT can be used for security policy explanation.
doi:10.1007/978-3-030-53288-8_9 fatcat:qkbunkwznjewvawjkh2zn4dr7u

Reachability Analysis for AWS-Based Networks [chapter]

John Backes, Sam Bayless, Byron Cook, Catherine Dodge, Andrew Gacek, Alan J. Hu, Temesghen Kahsai, Bill Kocik, Evgenii Kotelnikov, Jure Kukovec, Sean McLaughlin, Jason Reed (+7 others)
2019 Lecture Notes in Computer Science  
Cloud services provide the ability to provision virtual networked infrastructure on demand over the Internet. The rapid growth of these virtually provisioned cloud networks has increased the demand for automated reasoning tools capable of identifying misconfigurations or security vulnerabilities. This type of automation gives customers the assurance they need to deploy sensitive workloads. It can also reduce the cost and time-to-market for regulated customers looking to establish compliance
more » ... ification for cloud-based applications. In this industrial case-study, we describe a new network reachability reasoning tool, called Tiros, that uses off-the-shelf automated theorem proving tools to fill this need. Tiros is the foundation of a recently introduced network security analysis feature in the Amazon Inspector service now available to millions of customers building applications in the cloud. Tiros is also used within Amazon Web Services (AWS) to automate the checking of compliance certification and adherence to security invariants for many AWS services that build on existing AWS networking features.
doi:10.1007/978-3-030-25543-5_14 fatcat:cs4tezb2trb7nff6ragcqxzea4

Page 182 of Bogens Verden Vol. 74, Issue 3 [page]

1992 Bogens Verden  
Vi har ikke râd til at lade veere i »B'89« (Bibliotekscentralens Forlag 1989) Berthelsen, Carsten: Kunstens graenser.  ...  Hun var en varm fortaler for en kunstnerisk udsmykning af de danske biblioteker. CB BOGENS VERDEN Nr.3/1992  ... 

Page 591 of Bogens Verden Vol. 46, Issue 8 [page]

1964 Bogens Verden  
Esther Östergaard Carstens, Erik. Freud, Jung og Freeman. Et problemdrama om psykoanalyse og kultur.  ...  Dens per- sonskildring stikker mâske ikke dybt, men den er egte og skgnt uidealiseret ikke uden varme. Sin stgrste verdi har bogen som tids- og samfundsskildring.  ... 

Page 444 of Bogens Verden Vol. 54, Issue 7 [page]

1972 Bogens Verden  
Carsten siger til en kammerat, at »nâr du kun gâr i fgrste klasse, tror jeg sgutte, du kan lese den der«, mens tre halvstore  ...  Bgrnene er ledsaget af en lille, meget vâd hund af ubestemmelig race og farve, der âbenlyst nyder at komme ind i varme og tgrvejr.  ... 

Page 473 of Bogens Verden Vol. 48, Issue 6 [page]

1966 Bogens Verden  
Romose blev efter afstemning overleerer Carsten Rorbeck, Osted. Neest- formanden rettede en varm tak til 4.  ... 

Page 93 of Bogens Verden Vol. 30, Issue 2 [page]

1948 Bogens Verden  
Overs. og bearb. af Louis Carstens og Ib Thykier. Berlingske. 116 s. ill. 4.so. (62.397 Ha42.7r).  ...  Hans interesse for sygdommen og hans varme folelser for dem, der rammes eller trues, har fort til et grundigt studium af tuberkulosens mangeartede problemer, saaledes som de vender ud mod offentligheden  ... 

Page 459 of Bogens Verden Vol. 42, Issue 8 [page]

1960 Bogens Verden  
Introduktion til Erik Carstens’ forfatterskab. Redigeret af et udvalg. Jesp. og Pio. 1960. 85 s. 6.50. (99.4).  ...  Hvis denne forstem- mende omgang panegyrik skulle anspore nogen til at kaste sig over Erik Carstens’ egne bgger, er det et mirakel.  ... 

Page 262 of Bogens Verden Vol. 39, Issue 4 [page]

1957 Bogens Verden  
Bogen har noget af den samme charme som Agnes Henningsens memoirer, og man mâ som mandfolk nesten uden forbehold overgive sig til denne varme kvindelighed.  ...  Carsten Hauch: Befrielsens Aand og andre Digte. Ved Per Lange. 75 s. Frank Jeeger: Til en folsom Veninde. Ved Tage Skou-Hansen. 104 s. Igen to bind i serien, et klassisk og et moderne.  ... 

Sønderjyllands Betydning for dansk Kultur

Georg Brandes
1901 Sønderjydske Årbøger  
Bryst: Thi den, hvem Føbus tidlig laerte sin underlige Harmoni, hans varme, store fulde Hjerte udbreder Himlene sig i.  ...  Jeg naevner forst med Varme H. A. Brorson, Salmedigteren, Pietismens Repraesentant i dansk Poesi. Jeg ser rent kunstnerisk paa ham.  ... 
doi:10.7146/soenderjydskeaarboeger.v13i1.80582 fatcat:brglnca57vgzdlcg7cprfzc7va

Velbekomme: familien i madkassen – om madpakker, kultur, historie og forbundethed

Beth Elverdam
2011 Tidsskrift for forskning i sygdom og samfund  
Carsten gør opmaerksom på, at det netop er spisningen at og tilberedningen af maden, der viser, hvem der hører sammen, og etablerer og understreger denne forbundethed (Carsten 2004: 37 og 41).  ...  Borgerskabet opgav også den varme mad, men de spiste smørrebrød, ikke madpakker.  ... 
doi:10.7146/tfss.v8i14.5421 fatcat:vvvtppuxgzf7pgfdjepmw2ro6y

Gratulerer med dagen, Trygve!

Margrethe Buskerud Christoffersen, Amund Bjøranger Tørum, Eirik Wold Sund og John Asland
2021 Tidsskrift for forretningsjus  
Der har han etterfulgt andre størrelser fra Institutt for privatrett, som Carsten Smith og Viggo Hagstrøm.  ...  I en friere rolle som emeritus blir det nok også tid til å dyrke andre interesser, som besøk hos barnebarn i Berlevåg, varme soldager på den franske Rivieraen eller fredelige dager hjemme i Vestfossen.  ... 
doi:10.18261/issn.0809-9510-2021-01-01 fatcat:ulwy57mu6fgzjnfymv626hvrnu
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