Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Functional programming, design and analysis of algorithms / 2 / g

Use the input list as the seed of the tree unfold:

buildUnfold :: [a] -> Tree a
buildUnfold = unfold step
  where
    step []  = error "build: empty input"
    step [x] = Left x
    step xs  = Right (split (length xs `div` 2) xs)

On a singleton seed, unfold produces the same leaf as build; on a longer finite seed, it recursively builds the same two pieces. Induction on input length proves buildUnfold = build on finite nonempty inputs. The empty-input qualification remains essential: a tree unfold cannot supply a missing empty-tree constructor.