Gardening with the Pythia A Model of Continuity in a Dependent Setting

Baillon, Martin; Mahboubi, Assia; Pédrot, Pierre-Marie

doi:10.4230/lipics.csl.2022.5

Cited by 1 publication

(1 citation statement)

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“…In [BMP22] the authors prove that all BTT [PT17] functions are continuous by generalizing the method used in [Esc13b]. Their model is built in three steps as follows: an axiom model/translation adds an oracle to the theory at hand; a branching model/translation interprets types as intensional D-algebras, i.e., as types equipped with pythias; and an algebraic parametricity model/translation that relates the two previous translations by relating the calls to the pythia to the oracle.…”

Section: Vol 20:2 Tt □mentioning

confidence: 99%

$\text{TT}^{\Box}_{\mathcal C}$: a Family of Extensional Type Theories with Effectful Realizers of Continuity

Cohen,

Rahli

2024

Logical Methods in Computer Science

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$\text{TT}^{\Box}_{{\mathcal C}}$ 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.

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Section: Vol 20:2 Tt □mentioning

confidence: 99%