We formalize two proofs of weak head normalization for the simply typed lambdacalculus in first-order minimal logic: one for normal-order reduction, and one for applicative-order ...
Malgorzata Biernacka, Olivier Danvy, Kristian St&o...
Church's Higher Order Logic is a basis for proof assistants -- HOL and PVS. Church's logic has a simple set-theoretic semantics, making it trustworthy and extensible. We ...
Set theories are traditionally based on first-order logic. We show that in a constructive setting, basing a set theory on a dependent logic yields many benefits. To this end, we...