
Denotational semantics for guarded dependent type theory
We present a new model of Guarded Dependent Type Theory (GDTT), a type t...
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Computational Higher Type Theory III: Univalent Universes and Exact Equality
This is the third in a series of papers extending MartinLöf's meaning e...
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A Generalized Modality for Recursion
Nakano's later modality allows types to express that the output of a fun...
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Ticking clocks as dependent right adjoints: Denotational semantics for clocked type theory
Clocked Type Theory (CloTT) is a type theory for guarded recursion usefu...
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Clocked Definitions in HOL
Many potentially nonterminating functions cannot be directly defined in...
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BüchiKamp Theorems for 1clock ATA
This paper investigates Kamplike and Büchilike theorems for 1clock Al...
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Reduction Free Normalisation for a proof irrelevant type of propositions
We show normalisation and decidability of convertibility for a type theo...
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Guarded Computational Type Theory
Nakano's later modality can be used to specify and define recursive functions which are causal or synchronous; in concert with a notion of clock variable, it is possible to also capture the broader class of productive (co)programs. Until now, it has been difficult to combine these constructs with dependent types in a way that preserves the operational meaning of type theory and admits a hierarchy of universes. We present an operational account of guarded dependent type theory with clocks called Guarded Computational Type Theory, featuring a novel clock intersection connective that enjoys the clock irrelevance principle, as well as a predicative hierarchy of universes which does not require any indexing in clock contexts. Guarded Computational Type Theory is simultaneously a programming language with a rich specification logic, as well as a computational metalanguage that can be used to develop semantics of other languages and logics.
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