The weak lambda calculus as a reasonable machine

Authors:
Ugo Dal Lago;Simone Martini
Affiliations:
Dipartimento di Scienze dellInformazione, Università di Bologna, Mura Anteo Zamboni 7, 40127 Bologna, Italy;Dipartimento di Scienze dellInformazione, Università di Bologna, Mura Anteo Zamboni 7, 40127 Bologna, Italy
Venue:
Theoretical Computer Science
Year:
2008

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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 the 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).