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- W4385328034 abstract "$text{TT}^{Box}_{{mathcal C}}$ is a generic family of effectful, extensional type theories with a forcing interpretation parameterized by modalities. This paper identifies a subclass of $text{TT}^{Box}_{{mathcal C}}$ theories that internally realizes continuity principles through stateful computations, such as reference cells. The principle of continuity is a seminal property that holds for a number of intuitionistic theories such as System T. Roughly speaking, it states that functions on real numbers only need approximations of these numbers to compute. Generally, continuity principles have been justified using semantical arguments, but it is known that the modulus of continuity of functions can be computed using effectful computations such as exceptions or reference cells. In this paper, the modulus of continuity of the functionals on the Baire space is directly computed using the stateful computations enabled internally in the theory." @default.
- W4385328034 created "2023-07-28" @default.
- W4385328034 creator A5029629039 @default.
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- W4385328034 date "2023-07-26" @default.
- W4385328034 modified "2023-10-14" @default.
- W4385328034 title "$text{TT}^{Box}_{{mathcal C}}$: a Family of Extensional Type Theories with Effectful Realizers of Continuity" @default.
- W4385328034 doi "https://doi.org/10.48550/arxiv.2307.14168" @default.
- W4385328034 hasPublicationYear "2023" @default.
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