A Meta-theory for Big-step Semantics

It is well known that big-step semantics not able to distinguish stuck and non-terminating computations. This a strong limitation as it makes very difficult reason about properties involving infinite computations, such type soundness, which cannot even be expressed. We show this issue only apparent: the distinction between diverging computations implicit in any just needs uncovered. To achieve goal, we develop systematic study of semantics: introduce an abstract definition what is, define notion computation by formalizing evaluation algorithm implicitly associated with semantics, how canonically extend characterize Building on these notions, describe general proof technique predicate sound, prevents computation, respect semantics. One check three relating if they hold, sound. The extended essential establish meta-logical result but no concerns user, who prove initial Finally, illustrate several examples, showing applicable also cases where subject reduction does hence standard for small-step used.