We define a small-step semantics for the untyped λ-calculus, that traces the β-reductions that occur during evaluation. By abstracting the computation traces, we reconstruct -CFA using abstract interpretation, and justify constraint-based -CFA in a semantic way. The abstract interpretation of the trace semantics also paves the way for introducing widening operators in CFA that go beyond existing analyses, that are all based on exploring a finite state space. We define ∇CFA, a widening-based

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... ysis that limits the cycles in call stacks, and can achieve better precision than -CFA at a similar cost.