Embedding the Calendar and Time Type System in Temporal Type Theory

Temporal Type Theory, a member of the family of Martin-Löf style type theories, has been recently introduced as a topos-theoretic approach to understanding the behaviour of systems over time. We describe how the main notions of the Calendar and Time Type System were embedded in Temporal Type Theory, attempting to address a common requirement in the practical use of temporal formalisms: the ability to speak about certain time moments and appropriate time windows in (past and future) time, in the form of hours, dates, holidays, etc. With a view to concrete applications, we then provide examples on how calendar types can be combined with elements of Temporal Type Theory to augment its expressive power, placing special emphasis on capturing crucial temporal aspects of business processes that stem from (smart) contracts. In that respect, the addition of calendar types genuinely adds to the range of Temporal Type Theory as a powerful specification language.
Georgios V. Pitsiladis
Last modified: Mon Dec 9 2024