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## Final Report for EPSRC Grant GR/S46710/01 Topological Models for Computational Metalanguages Background and context

### Citations

15 |
Compactly generated domain theory
- Battenfeld, Schröder, et al.
(Show Context)
Citation Context ...d through him having read [30]. A paper containing the mathematical development of topological domain theory and its relationship to classical domain theory was written for Klaus Keimel’s Festschrift =-=[5]-=-. The relationship with known topological models of higher types (cartesian closed categories of topological spaces) was established by Simpson in collaboration with Escardó and Lawson [1]. Due to the... |

8 | Coalgebraic semantics for timed processes
- Kick, Power, et al.
(Show Context)
Citation Context ... Brattka and Schröder’s observations on the influence of set-theoretic axioms on computability theory for certain spaces [10]; and Kick, Power and Simpson’s coalgebraic formulation of timed processes =-=[4]-=-. (CM) Computational Metalanguages The proposed second (and secondary) thread of the project was to exploit the unparalleled richness of structure of topological domains to define powerful metalanguag... |

8 | Representing probability measures using probabilistic processes
- Schröder, Simpson
(Show Context)
Citation Context ...ly by different methods as the main result of [22]. 3spaper, Schröder and Simpson showed that this approach does indeed define a candidate probabilistic powerdomain with good computability properties =-=[11, 6]-=-. In a second, Schröder proved that this coincides with the observationally-induced powerdomain (see (TM2) above) for a wide class of spaces [14]. Other loosely related investigations of computability... |

7 | Two constructive embedding-extension theorems with applications to continuity principles and to Banach-Mazur computability
- Bauer, Simpson
(Show Context)
Citation Context ... spaces [14]. Other loosely related investigations of computability included: Bauer and Simpson’s proof that BanachMazur computability differs from Markov computability on a wide collection of spaces =-=[2]-=- (possibly the only time that a new result in the theory of computability has been proved using the internal logic of a topos); Schröder’s study of topological properties of spaces related to them bei... |

7 |
Spaces allowing type-2 complexity theory revisited
- SCHRÖDER
(Show Context)
Citation Context ...computability has been proved using the internal logic of a topos); Schröder’s study of topological properties of spaces related to them being able to support a decent computational complexity theory =-=[3, 9]-=-; Brattka and Schröder’s observations on the influence of set-theoretic axioms on computability theory for certain spaces [10]; and Kick, Power and Simpson’s coalgebraic formulation of timed processes... |

7 | Two Preservation Results for Countable Products of Sequential Spaces. Probabilistic observations and valuations (extended abstract
- Schröder, Simpson
- 2007
(Show Context)
Citation Context ... constructions, it proved necessary to establish some technical properties of countable products in topological domain theory, which were published in a purely technical paper by Schröder and Simpson =-=[7]-=-. (TM2) Probabilistic powerdomain Probabilistic choice is one particular form of computational effect, and thus falls under (TM2) above. However, it is of particular interest in its own right for a nu... |

7 | Computational Effects in Topological Domain Theory
- Battenfeld
- 2006
(Show Context)
Citation Context ...g prominence to the program commands that cause effects. Battenfeld undertook the task of studying the construction in topological domain of a wide class of free algebras useful for modelling effects =-=[13]-=-. An important aspect of his work was obtaining explicit descriptions of such free algebras, which allowed it to be shown that their construction in topological domain theory agrees, when restricted t... |

3 | Computing with sequences, weak topologies and the axiom of choice
- Brattka, Schröder
- 2005
(Show Context)
Citation Context ... to them being able to support a decent computational complexity theory [3, 9]; Brattka and Schröder’s observations on the influence of set-theoretic axioms on computability theory for certain spaces =-=[10]-=-; and Kick, Power and Simpson’s coalgebraic formulation of timed processes [4]. (CM) Computational Metalanguages The proposed second (and secondary) thread of the project was to exploit the unparallel... |

2 |
A.: Comparing Cartesian-closed Categories of Core Compactly Generated Spaces. Topology and its Applications 143
- Escardó, Lawson, et al.
- 2004
(Show Context)
Citation Context ...Festschrift [5]. The relationship with known topological models of higher types (cartesian closed categories of topological spaces) was established by Simpson in collaboration with Escardó and Lawson =-=[1]-=-. Due to the technical nature of the above papers, the need was felt to provide an accessible summary of the work. The resulting paper [8] has been accepted to appear in Gordon Plotkin’s Festschrift, ... |

2 | Some Examples of NonMetrizable Spaces Allowing a Simple - Kunkl, Schröder - 2005 |

1 |
A Convenient Category of Domains. To appear in Computation, Meaning and Logic, Articles Dedicated to Gordon
- Battenfeld, Schröder, et al.
(Show Context)
Citation Context ...tablished by Simpson in collaboration with Escardó and Lawson [1]. Due to the technical nature of the above papers, the need was felt to provide an accessible summary of the work. The resulting paper =-=[8]-=- has been accepted to appear in Gordon Plotkin’s Festschrift, which seems an excellent permanent home for a readable overview of our approach to domain theory. (TM3) Free algebras In a recent body of ... |