Higher-Order Linear Ramified Recurrence
نویسندگان
چکیده
Higher-Order Linear Ramified Recurrence (HOLRR) is a PTIME sound and complete typed lambda caluclus. Its terms are those of a linear (affine) λ-calculus – every variable occurs at most once – extended with a limited recursive scheme on a word algebra. Completeness for PTIME holds by embedding Leivant’s ramified recurrence on words into HOLRR. Soundness is established at all types – and not only for first order terms. Type connectives are limited to tensor and linear implicaation. Moreover, typing rules are given as a simple deductive system. On one side, HOLRR allows to “program” higher-order functions, whose PTIME soundness is assured by their types. On the other, HOLRR looks like a usual recursive language.
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