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Results tagged with type-theory
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user 2004
9
votes
Reference request for type theory
The kind of type theory you're asking about, Russell's simple theory of types, is from about the early 1900's. Here's a reference:
Russell, Bertrand: Mathematical Logic as Based on the Theory of Typ …
- 1,467
8
votes
Accepted
Reduction rules for inductive types
Your second reduction is called a commutative conversion. You can read about it in Girard, Taylor and Lafont, Proofs and Types, p. 80, for example. The congruence relation with commutative conversions …
- 1,467
2
votes
Why no morphisms from the contradictory proposition to the inconsistent context?
I'm not sure what you mean by the individual propositional objects having models or not.
In any case, as you said, as morphism in $\mathbb P$ simply is a context morphism compatible with the preorder …
- 1,467
7
votes
Accepted
categorifying induction in homotopy type theory
The first reason you give is sufficient to answer your question: any interpretation of nat (and any other type with decidable equality) must have contractible components. Let me try to unpack the proo …
- 1,467