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Results tagged with prop
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user 169
A sort of definitionally proof-irrelevant propositions introduced in "Definitional Proof-Irrelevance without K" and implemented by Agda (as Prop) and Coq (as SProp).
5
votes
Accepted
Pattern matching from `Prop` to `Type` in Lean
If $A : \mathsf{Prop}$ and $B : \mathsf{Type}$, then when defining a map $A \to B$ it is prohibited to match on the argument.
Why would anyone want this? … If we think of $A : \mathsf{Prop}$ as a logical statement then $a : A$ is like a proof, or evidence, that $A$ holds. …
- 11.1k
6
votes
Why does it matter if canonicity holds for irrelevant types?
Consider the following type theory:
\begin{gather}
\frac{ }{\vdash G \; \mathsf{type}} \qquad
\frac{ }{\vdash \Lambda \; \mathsf{type}} \\[2ex]
\frac{\vdash g : G \qquad \vdash e_1 : \Lambda \qquad \v …
- 11.1k