Feasible Programs From Proofs

We restrict induction and recursion on notation in all nite types so as to characterize the polynomial time computable functions. The restrictions are obtained by enriching the type structure with the formation of types (and formulas A (B as well as 8 x A with \complete" variables x, and by adding linear concepts to the lambda calculus (for object terms and proof terms). For the arithmetical system we deene modiied realizability and show that the programs extracted from proofs of 0 2-theorems characterize the polynomial time computable functions.

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