An Invariant Cost Model for the Lambda Calculus
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).
- Publication:
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arXiv e-prints
- Pub Date:
- November 2005
- DOI:
- 10.48550/arXiv.cs/0511045
- arXiv:
- arXiv:cs/0511045
- Bibcode:
- 2005cs.......11045D
- Keywords:
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- Computer Science - Logic in Computer Science;
- Computer Science - Computational Complexity;
- F.4.1
- E-Print:
- 19 pages