@MISC{Dal05aninvariant, author = {Ugo Dal and Lago Simone Martini}, title = {An Invariant Cost Model for the Lambda Calculus}, year = {2005} }

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Abstract

We define a new cost model for the call-by-value lambda-calculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the call-by-value lambdacalculus can simulate each other within a polynomial time overhead. The model only relies on combinatorial properties of usual beta-reduction, without any reference to a specific machine or evaluator. In particular, the cost of a single beta reduction is proportional to the difference between the size of the redex and the size of the reduct. In this way, the total cost of normalizing a lambda term will take into account the size of all intermediate results (as well as the number of steps to normal form). 1