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arXiv · 2505.11055

Internal Effectful Forcing in System T

Martin H. Escardo·Bruno da Rocha Paiva·Vincent Rahli·Ayberk Tosun
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Abstract

The effectful forcing technique allows one to show that the denotation of a closed System T term of type $(\iota \to \iota) \to \iota$ in the set-theoretical model is a continuous function $(\mathbb{N} \to \mathbb{N}) \to \mathbb{N}$. For this purpose, an alternative dialogue-tree semantics is defined and related to the set-theoretical semantics by a logical relation. In this paper, we apply effectful forcing to show that the dialogue tree of a System T term is itself System T-definable, using the Church encoding of trees.

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Martin H. Escardo, Bruno da Rocha Paiva, Vincent Rahli, Ayberk Tosun. 2025-05-16. Internal Effectful Forcing in System T. https://arxiv.org/abs/2505.11055

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