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Journal Articles Logical Methods in Computer Science Year : 2020

Theory of Higher Order Interpretations and Application to Basic Feasible Functions

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Abstract

Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional language. We develop a theory of higher order functions that is well-suited for the complexity analysis of this programming language. The interpretation domain is a complete lattice and, consequently, we express program interpretation in terms of a least fixpoint. As an application, by bounding interpretations by higher order polynomials, we characterize Basic Feasible Functions at any order.
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Dates and versions

hal-02499206 , version 1 (05-03-2020)
hal-02499206 , version 2 (06-01-2021)

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Emmanuel Hainry, Romain Péchoux. Theory of Higher Order Interpretations and Application to Basic Feasible Functions. Logical Methods in Computer Science, 2020, 16 (4), pp.25. ⟨10.23638/LMCS-16(4:14)2020⟩. ⟨hal-02499206v2⟩
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