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An Invariant Cost Model for the Lambda Calculus

Ugo Dal Lago·Simone Martini
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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 lambda-calculus 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).

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Ugo Dal Lago, Simone Martini. 2005-11-12. An Invariant Cost Model for the Lambda Calculus. https://arxiv.org/abs/cs/0511045

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