@inbook {IOPORT.05259548, author = {Cousot, Radhia}, title = {Abstract interpretation of non-monotone bi-inductive semantic definitions.}, year = {2008}, booktitle = {Verification, model checking, and abstract interpretation. 9th international conference, VMCAI 2008, San Francisco, USA, January 7--9, 2008. Proceedings}, isbn = {978-3-540-78162-2}, pages = {1-3}, publisher = {Berlin: Springer}, doi = {10.1007/978-3-540-78163-9_1}, abstract = {Summary: 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].}, identifier = {05259548}, }