Jan Hoffmann and Martin Hofmann (2010)

# Amortized Resource Analysis with Polymorphic Recursion and Partial Big-Step Operational Semantics

In: APLAS, pp. 172-187.

This paper studies the problem of statically determining upper bounds on the resource consumption of first-order functional programs. A previous work approached the problem with an automatic type-based amortized analysis for polynomial resource bounds. The analysis is parametric in the resource and can be instantiated to heap space, stack space, or clock cycles. Experiments with a prototype implementation have shown that programs are analyzed efficiently and that the computed bounds exactly match the measured worst-case resource behavior for many functions. This paper describes the inference algorithm that is used in the implementation of the system. It can deal with resource-polymorphic recursion which is required in the type derivation of many functions. The computation of the bounds is fully automatic if a maximal degree of the polynomials is given. The soundness of the inference is proved with respect to a novel operational semantics for partial evaluations to show that the inferred bounds hold for terminating as well as non-terminating computations. A corollary is that run-time bounds also establish the termination of programs.

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