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Results tagged with type-theory
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user 38527
2
votes
Why in Martin-Löf type theory any natural number is assumed to be either $0$ or $S(a)$ for s...
First, we should pin down that we're talking about closed terms with natural number type, that is, terms without free variables. A free variable with type $\mathsf{N}$ is clearly not of the form $0$ o …
- 213
8
votes
Accepted
Is $\prod_{X : \mathcal{U}} (X \to X) \cong 1$ consistent with type theory?
$\prod_{X : \mathcal{U}} (X \to X) \cong 1$ is consistent. It follows from parametricity and function extensionality. Usual parametric models also support function extensionality. The simplest one whi …
- 213