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Outline of a Mathematical Theory of Computation
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However, Scott does realize that the approach argued for above is simply an argument for an approach that accomodates human understanding of computation and that the operational approach must not be ignored because the machines that the programs of study run on are not capable of dealing with such an abstract level of understanding.Abstract:
However, Scott does realize that the approach argued for above is simply an argument for an approach that accomodates human understanding of computation and that the operational approach must not be ignored because, as he points out, the machines that the programs of study run on are not capable of dealing with such an abstract level of understanding. That is, the computaional approach should not be abandoned because the machines that we build operate on that lower level.read more
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Journal ArticleDOI
Classifying topoi in synthetic guarded domain theory
Dan Palombi,Jonathan Sterling +1 more
TL;DR: It is shown that several important topos models of SGDT classify very simple geometric theories, and that the passage to various forms of multi-clock guarded recursion can be rephrased more compositionally in terms of the lower bagtopos construction of Vickers and variations thereon due to Johnstone.
Book ChapterDOI
An abstract strong normalization theorem
TL;DR: A strong normalization theorem for abstract term rewriting systems based on domain-theoretic models is proved and extensions of Godel's system T by various forms of recursion related to bar recursion are extended.
Journal ArticleDOI
Towards a Higher-Order Mathematical Operational Semantics
TL;DR: A theory of abstract GSOS specifications for higher-order languages is developed, in effect transferring the core principles of Turi and Plotkin’s framework to a higher- order setting, and a general compositionality result is given that applies to all systems speci fied.
Journal ArticleDOI
An Order Model for Infinite Classical States
TL;DR: In this paper, the authors extended the Coecke and Martin model to a model for the infinite classical states, which are the states which result when an observable is applied to a quantum system.
Dissertation
On the lambda calculus with constructors
TL;DR: A polymorphic type system for this calculus is proposed, and a realisability model is developed, based on Girard's reducibility candidates, which leads to a strong normalisation result for the typed calculus, and guaranties that the type system prevents match failure.