An Invariant Cost Model for the Lambda Calculus
<|reference_start|>An Invariant Cost Model for the Lambda Calculus: 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).<|reference_end|>
@article{lago2005an,
    title={An Invariant Cost Model for the Lambda Calculus},
    author={Ugo Dal Lago and Simone Martini},
    journal={arXiv preprint arXiv:cs/0511045},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0511045},
    primaryClass={cs.LO cs.CC}
}