Reduction Free Normalisation for a proof irrelevant type of propositions
Thierry Coquand · Logical Methods in Computer Science · 2023
We show normalisation and decidability of convertibility for a type theory with a hierarchy of universes and a proof irrelevant type of propositions, close to the type system used in the proof assistant Lean. Contrary to previous arguments, the proof does not require explicitly to introduce a notion of neutral and normal forms.