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The complexity of abstract machinesI previously wrote about a brand of research by Guy Blelloch on the Cost semantics for functional languages, which let us make precise claim about the complexity of functional programs without leaving their usual and comfortable programming models (betareduction). While the complexity behavior of weak reduction strategies, such as callbyvalue and callbyname, is by now relatively wellunderstood, the lambdacalculus has a much richer range of reduction strategies, in particular those that can reduce under lambdaabstractions, whose complexity behavior is sensibly more subtle and was, until recently, not very well understood. (This has become a practical concern since the rise in usage of proof assistants that must implement reduction under binders and are very concerned about the complexity of their reduction strategy, which consumes a lot of time during type/proofchecking.) Beniamino Accatoli, who has been coauthoring a lot of work in that area, recently published on arXiv a new paper that has survey quality, and is a good introduction to this area of work and other pointers from the literature.

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