So that would be the traditional analysis of quicksort, mucked up with linear logic terminology so you can't see what's going on. The sweet spot of lambda calc

So that would be the traditional analysis of quicksort, mucked up with linear logic terminology so you can't see what's going on. The sweet spot of lambda calculus is structurally recursive algorithms on trees. You can use it for other kinds of algorithms, but there it just makes things harder, and I've never seen it solve a problem that wasn't solved first by other means.