Papers › Internal Effectful Forcing in System T
Internal Effectful Forcing in System T
Martin H. Escardo, Bruno da Rocha Paiva, Vincent Rahli, Ayberk Tosun
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The effectful forcing technique allows one to show that the denotation of a closed System T term of type (ι→ι) →ι in the set-theoretical model is a continuous function (ℕ →ℕ) →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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