Internal Effectful Forcing in System T
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913842040143872 |
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| author | Escardo, Martin H. Paiva, Bruno da Rocha Rahli, Vincent Tosun, Ayberk |
| author_facet | Escardo, Martin H. Paiva, Bruno da Rocha Rahli, Vincent Tosun, Ayberk |
| contents | The effectful forcing technique allows one to show that the denotation of a closed System T term of type $(ι\to ι) \to ι$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_11055 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Internal Effectful Forcing in System T Escardo, Martin H. Paiva, Bruno da Rocha Rahli, Vincent Tosun, Ayberk Logic in Computer Science Logic 03B38, 03B40, 03F50 F.4.1; F.3.1; F.3.2 The effectful forcing technique allows one to show that the denotation of a closed System T term of type $(ι\to ι) \to ι$ 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. |
| title | Internal Effectful Forcing in System T |
| topic | Logic in Computer Science Logic 03B38, 03B40, 03F50 F.4.1; F.3.1; F.3.2 |
| url | https://arxiv.org/abs/2505.11055 |