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It is well-known that big-step semantics is not able to distinguish stuck and non-terminating computations. This is a strong limitation as it makes very difficult to reason about properties involving infinite computations, such as type soundness, which cannot even be expressed. We show that this issue is only apparent: the distinction between stuck and diverging computations is implicit in any big-step semantics and it just needs to be uncovered. To achieve this goal, we develop a systematic study of big-step semantics: we introduce an abstract definition of what a big-step semantics is, we define a notion of computation by formalising the evaluation algorithm implicitly associated with any big-step semantics, and we show how to canonically extend a big-step semantics to characterise stuck and diverging computations. Building on these notions, we describe a general proof technique to show that a predicate is sound, that is, it prevents stuck computation, with respect to a big-step semantics. One needs to check three properties relating the predicate and the semantics and, if they hold, the predicate is sound. The extended semantics are essential to establish this meta-logical result, but are of no concerns to the user, who only needs to prove the three properties of the initial big-step semantics. Finally, we illustrate the technique by several examples, showing that it is applicable also in cases where subject reduction does not hold, hence the standard technique for small-step semantics cannot be used.
We investigate representations of imperative programs as constrained Horn clauses. Starting from operational semantics transition rules, we proceed by writing interpreters as constrained Horn clause programs directly encoding the rules. We then speci
We propose a general proof technique to show that a predicate is sound, that is, prevents stuck computation, with respect to a big-step semantics. This result may look surprising, since in big-step semantics there is no difference between non-termina
Structural operational semantic specifications come in different styles: small-step and big-step. A problem with the big-step style is that specifying divergence and abrupt termination gives rise to annoying duplication. We present a novel approach t
A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious undertaking. In
PROMELA (Process Meta Language) is a high-level specification language designed for modeling interactions in distributed systems. PROMELA is used as the input language for the model checker SPIN (Simple Promela INterpreter). The main characteristics