Hezekiah's Signet Ring
No opponent may search any draw pile or discard pile. Play As: Restrict opponents from searching decks or discard piles.
Sing and Praise
Remove from the game all cards (except Heroes) in a discard pile.
Ashtaroth Worship
Discard a good enhancement or remove from the game all cards in a discard pile.
If player A has HSR active, we all agree that player B cannot use a card like Confusion to target and discard a card from their deck (this targets player A's deck, then searches for a card within that deck).
But if player A has HSR active, what happens when player B uses Sing and Praise? I presume that in order to remove all except heroes there is an implied search for the heroes that are to remain in the discard pile.
What about Ashtaroth Worship? There is no implied search, as the card has the ability to remove the entire discard pile without specific targets or exceptions.