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Conference Papers Year : 2024

On Basic Feasible Functionals and the Interpretation Method


The class of basic feasible functionals BFF is the analog of FP (polynomial time functions) for type-two functionals, that is, functionals that can take (first-order) functions as arguments. BFF can be defined by means of oracle Turing machines of time bounded by a second-order polynomial. On the other hand, higher-order term rewriting provides an elegant formalism for expressing higher-order computation. We address the problem of characterizing the class BFF by higher-order term rewriting. Various kinds of interpretations for first-order term rewriting have been introduced in the literature for proving termination and characterizing (first-order) complexity classes. Here we consider a recently introduced notion of cost-size interpretations for higher-order term rewriting and see definitions as ways of computing functionals. We then prove that the class of functionals represented by higher-order terms admitting a certain kind of cost-size interpretation is exactly BFF.
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Dates and versions

hal-04376613 , version 1 (06-01-2024)


  • HAL Id : hal-04376613 , version 1


Patrick Baillot, Ugo Dal Lago, Cynthia Kop, Deivid Vale. On Basic Feasible Functionals and the Interpretation Method. FoSSaCS 2024 - International Conference on Foundations of Software Science and Computation Structures, Apr 2024, Luxembourg City, Luxembourg. ⟨hal-04376613⟩
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