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What you usually would want to supress is not a specific type of warning, but specific occurences of the warning... What I would like is an attribute to specify something like "don't warn me about this specific signal being stuck at GND", but keep warning me about other signals.
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The message suppression feature on the message right-click menu does support what I think you are saying. You can select "Suppress Exact Selected Messages" to suppress a specific occurrence. So you can suppress the message about the specific stuck-at-GND signal while still seeing the similar messages for other signals.
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Quartus can also hide warning at the module level, but it is not good enough. What I would like is an attribute...
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I'm guessing you are talking about the "altera message_off" synthesis directive. The documentation in the Quartus handbook sounds like that can be done only for modules, entities, and architectures. I was thinking you could suppress an individual message with a synthesis directive, but I guess module-level control is all you get when doing the suppression in the RTL.