Being reminded of QPLs by Valiron's talk, I reread Altenkirch and Grattage's mid-decade paper on QML during my lunch break. It makes a lot more sense to me now. I thought the emphasis on controlling weakening and being careless about contraction was crazy the first time I read the paper back in March. It's easy (for me) to forget that the no-cloning theorem doesn't forbid (basis-specific) copying of a quantum state, (that is, a transformation that takes |0> to |00> and |1> to |11>) and so QML just tacitly performs such a copy every time you use a variable more than once. What's dangerous is pretending that you can go ahead and naively do weakening. If I have a state like |aa> - |ab> and I try to "ignore" the second qubit, it's crazy to think I get the state |a> - |a> = 0. First of all, such a move is blatantly nonunitary, and anyhow I can't cause two kets to become identical by just failing to pay attention to part of each of them. Their distinguishability is a real physical property.
"California Über Alles" is stuck in my head for some reason. I blame
techstep and I think also "The Social Network"? Either it was playing in one scene or it compelled me to imagine it being played somehow. 