Abstract
Divergence/nonterminating behaviors definitely need to be considered in static program analysis [13], in particular for typing [2,11].
Divergence information is part of the classical order-theoretic fixpoint denotational semantics [12] but not explicit in small-step/abstract-machine-based operational semantics [14,15,16] and absent of big-step/natural operational semantics [8]. A standard approach is therefore to generate an execution trace semantics from a (labelled) transition system/small-step operational semantics, using either an order-theoretic [3] or metric [19] fixpoint definition or else a categorical definition as a final coalgebra for a behavior functor (modeling the transition relation) up to a weak bisimulation [7,10,18] or using an equational definition for recursion in an order-enriched category [9].
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Cousot, R. (2008). Abstract Interpretation of Non-monotone Bi-inductive Semantic Definitions. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2008. Lecture Notes in Computer Science, vol 4905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78163-9_1
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