科研之友
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摘要
We investigate the foundations of reasoning over infinite data structures by means of set-theoretical structures arising in the sheaf-theoretic semantics of higher-order intuitionistic logic. Our approach focuses on a natural notion of tiering involving an operation of restriction of elements to levels forming a complete Heyting algebra. We relate these tiered objects to final coalgebras and initial algebras of a wide class of endofunctors of the category of sets, and study their order and convergence properties. As a sample application, we derive a general proof principle for tiered objects.
- 出版日期2016
