Unless I'm missing something, all the examples in that PEP are first-order. There's no discussion of what the semantics is in the higher-order case. Pyret's ann

Unless I'm missing something, all the examples in that PEP are first-order. There's no discussion of what the semantics is in the higher-order case. Pyret's annotations are perfectly well-defined and draw on a long history of research of getting these very subtle cases right (starting with Findler and Felleisen's ICFP 2002 paper). There's much more to this than just syntax.