To cite the use of this formal theory, please use

  Achim D. Brucker and Michael Herzberg. A Formal Model of the Document Object Model
  with Shadow Roots. In Archive of Formal Proofs, 2020. http://www.isa-afp.org/entries/Shadow_DOM.html,
  Formal proof development


A BibTeX entry for LaTeX users is

@Article{         brucker.ea:afp-shadow-dom:2020,
  author        = {Achim D. Brucker and Michael Herzberg},
  title         = {Shadow DOM: A Formal Model of the Document Object Model with Shadow Roots},
  journal       = {Archive of Formal Proofs},
  month         = sep,
  year          = 2020,
  date          = {2020-09-28},
  note          = {\url{http://www.isa-afp.org/entries/Shadow_DOM.html}, Formal proof development},
  issn          = {2150-914x},
  abstract      = { In this AFP entry, we extend our formalization of the core DOM with \emph{Shadow Roots}. Shadow
                  roots are a recent proposal of the web community to support a component-based development approach for
                  client-side web applications.

                  Shadow roots are a significant extension to the DOM standard and, as web standards are condemned to be
                  backward compatible, such extensions often result in complex specification that may contain unwanted
                  subtleties that can be detected by a formalization.

                  Our Isabelle/HOL formalization is, in the sense of object-orientation, an extension of our
                  formalization of the core DOM and enjoys the same basic properties, i.e., it is extensible, i.e., can
                  be extended without the need of re-proving already proven properties and executable, i.e., we can
                  generate executable code from our specification. We exploit the executability to show that our
                  formalization complies to the official standard of the W3C, respectively, the WHATWG. },
  public        = {yes},
  classification= {formal},
  categories    = {websecurity},
  pdf           = {http://www.brucker.ch/bibliography/download/2020/brucker.ea-afp-shadow-dom-2020.pdf},
  filelabel     = {Outline},
  file          = {http://www.brucker.ch/bibliography/download/2020/brucker.ea-afp-shadow-dom-outline-2020.pdf},
  areas         = {formal methods, security, software engineering},
  url           = {http://www.brucker.ch/bibliography/abstract/brucker.ea-afp-shadow-dom-2020}
}

An overview of the formalization is given in:

  Achim D. Brucker and Michael Herzberg. A Formally Verified Model of
  Web Components. In Formal Aspects of Component Software (FACS).
  Lecture Notes in Computer Science (12018), Springer-Verlag, 2020.
  http://www.brucker.ch/bibliography/abstract/brucker.ea-web-components-2019

A BibTeX entry for LaTeX users is


@InCollection{    brucker.ea:web-components:2019,
  abstract      = {The trend towards ever more complex client-side web applications is unstoppable. Compared to
                  traditional software development, client-side web development lacks a well-established component
                  model, i.e., a method for easily and safely reusing already developed functionality. To address this
                  issue, the web community started to adopt shadow trees as part of the Document Object Model (DOM):
                  shadow trees allow developers to "partition" a DOM instance into parts that should be safely
                  separated, e.g., code modifying one part should not, unintentionally, affect other parts of the DOM.

                  While shadow trees provide the technical basis for defining web components, the DOM standard neither
                  defines the concept of web components nor specifies the safety properties that web components should
                  guarantee. Consequently, the standard also does not discuss how or even if the methods for modifying
                  the DOM respect component boundaries. In this paper, we present a formally verified model of web
                  components and define safety properties which ensure that different web components can only interact
                  with each other using well-defined interfaces. Moreover, our verification of the application
                  programming interface (API) of the DOM revealed numerous invariants that implementations of the DOM
                  API need to preserve to ensure the integrity of components.},
  keywords      = {Web Component, Shadow Tree, DOM, Isabelle/HOL},
  location      = {Amsterdam, The Netherlands},
  author        = {Achim D. Brucker and Michael Herzberg},
  booktitle     = {Formal Aspects of Component Software (FACS)},
  language      = {USenglish},
  publisher     = pub-springer,
  address       = pub-springer:adr,
  series        = s-lncs,
  number        = 12018,
  isbn          = {3-540-25109-X},
  doi           = {10.1007/978-3-030-40914-2_3},
  editor        = {Sung-Shik Jongmans and Farhad Arbab},
  pdf           = {http://www.brucker.ch/bibliography/download/2019/brucker.ea-web-components-2019.pdf},
  title         = {A Formally Verified Model of Web Components},
  classification= {conference},
  areas         = {formal methods, software},
  year          = 2020,
  public        = {yes},
  url           = {http://www.brucker.ch/bibliography/abstract/brucker.ea-web-components-2019}
}