Another project idea: formalize the semantics of HOL in Mizar.
This is actually quite straightforward, since Andrew Pitts formalized most of the work back in his 1991 presentation of HOL's semantics.
But I don't think it's been formalized! Perhaps it has, I don't know, I wrote this up as the city I live is engulfed in flames: I didn't have the luxury of time to find out.
But that shouldn't stop you from having fun! There are a million variations to consider, as well: typeclasses, inductive types, etc. etc. etc.
#Mizar #HOL #ProofAssistant #Semantics
https://thmprover.wordpress.com/2025/01/14/hol-in-mizar/