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We revisit the famous notion of sheaves through the lens of type theory and side-effects. Using the language of \(\textsf{MLTT}\) , we show that they inductively approximate idealized functional objects as decision trees, realizing a generalized form of continuity. We materialize this intuition in \(\textsf{MLTT}^{\textsf{F}}\) , a case-study sheaf extension of \(\textsf{MLTT}\) with a Cohen real and leverage it to show uniform continuity of all \(\textsf{MLTT}\) functionals of type \(({\mathbb {N}}\rightarrow {\mathbb {B}}) \rightarrow {\mathbb {N}}\) . The latter results were mechanized in Rocq.

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In Cantor Space No One Can Hear You Stream

  • 会议论文

  • 出版模式：

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  • 发表日期：

    2026年

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

摘要

We revisit the famous notion of sheaves through the lens of type theory and side-effects. Using the language of \(\textsf{MLTT}\) , we show that they inductively approximate idealized functional objects as decision trees, realizing a generalized form of continuity. We materialize this intuition in \(\textsf{MLTT}^{\textsf{F}}\) , a case-study sheaf extension of \(\textsf{MLTT}\) with a Cohen real and leverage it to show uniform continuity of all \(\textsf{MLTT}\) functionals of type \(({\mathbb {N}}\rightarrow {\mathbb {B}}) \rightarrow {\mathbb {N}}\) . The latter results were mechanized in Rocq.