Logical Approaches to Computational Barriers

An Invariant Cost Model for the Lambda Calculus

Speaker:
| Ugo Dal Lago |

Author(s): |
Ugo Dal Lago and Simone Martini |

Slot: |
Array, 11:30-11:50, col. 2 |

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).

websites: Arnold Beckmann | 2006-06-09 |