Lazily consuming a self-referential linked list

VegOwOtenks:

run :: [q] -> s -> (q -> s -> [q] -> ([q], s)) -> s

This looks to me as if the [q] is really part of the state being modified:

data PipelineState = PS {globalState :: s, jobs :: [q]}
run :: PipelineState -> (q ->  PipelineState -> PipelineState) -> s

and supposedly the final s is really a PS s [], no more jobs to do. Now I wonder: Why does the action argument of run have an extra q argument at all, when it could pop one off the [q]? Perhaps that is the missing occasion for pattern-matching on the empty list? So suppose you could merge run and go into a single recursive function that does not need the extra q for non-emptyness. Suppose further that we agree the final state is just a special PipelineState. Now a function with the signature

run :: x -> (x -> x) -> x

looks like something that seeks the least fixed point of an endo-function above a given starting value, as per Kleene’s fixed point theorem.