Who else thought of an H. P. Lovecraft story when watching this?
In the early 1930s, Lovecraft wrote a story thematically anticipating Prince of Darkness. That story was The Dreams in the Witch-House, about a doomed college student in a story where physics recapitulates the supernatural.
Lovecraft also adapted alternate dimensions, ambiguous dream sequences, and malevolent entities seeking to come into our world--all aspects of Prince of Darkness' story--into his narrative.
Whether Carpenter knew about the Lovecraft story or not when scripting Prince of Darkness I have no clue, but the movie betrays a clear Lovecraftian influence in its storyline and bears a number of resemblances to what Lovecraft wrote. Personally I think the similarities are enough to at least justify speculation that Carpenter had Lovecraft in mind when writing his script.
Requiescat in pace, Krystle Papile. I'll always miss you.