Yes, we do codify that, but I guess I was approaching the conversation from the perspective of an ideal world. And, to be frank, our laws about who is imprisoned for life are far from ideal and I'm not sure I'd agree that the bar is always high. I wouldn't be comfortable at all with equating "life in prison" with "irredeemable" in the current frame. There is such a wide degree in variance from state to state, judge to judge, and jury to jury about how to sentence people that I'm not really comfortable with that. I think your point just moves the goalposts. If we say, "Ok, irredeemable is anyone we sentence to life in prison" then I'd counter that we need to take a serious look at that declaration. Yes, we can codify it, but in it's current state I'd say we do a pretty crappy job of that. There are people being imprisoned for life for drug possession and a host of other things I certainly don't consider "irredeemable".