Towards automatic resource bound analysis for OCaml

Abstract

This article presents a resource analysis system for OCaml programs. The system automatically derives worst-case resource bounds for higher-order polymorphic programs with user-defined inductive types. The technique is parametric in the resource and can derive bounds for time, memory allocations and energy usage. The derived bounds are multivariate resource polynomials which are functions of different size parameters that depend on the standard OCaml types. Bound inference is fully automatic and reduced to a linear optimization problem that is passed to an off-the-shelf LP solver. Technically, the analysis system is based on a novel multivariate automatic amortized resource analysis (AARA). It builds on existing work on linear AARA for higher-order programs with user-defined inductive types and on multivariate AARA for first-order programs with built-in lists and binary trees. This is the first amortized analysis, that automatically derives polynomial bounds for higherorder functions and polynomial bounds that depend on user-defined inductive types. Moreover, the analysis handles a limited form of side effects and even outperforms the linear bound inference of previous systems. At the same time, it preserves the expressivity and efficiency of existing AARA techniques. The practicality of the analysis system is demonstrated with an implementation and integration with Inria's OCaml compiler. The implementation is used to automatically derive resource bounds for 411 functions and 6018 lines of code derived from OCaml libraries, the CompCert compiler, and implementations of textbook algorithms. In a case study, the system infers bounds on the number of queries that are sent by OCaml programs to DynamoDB, a commercial NoSQL cloud database service.

ATLAS: Automated Amortised Complexity Analysis of Self-adjusting Data Structures

“…However, there is a vast amount of literature on (automated) resource analysis. Without hope for a completeness, we briefly mention [1][2][3][4][5][6][7][9][10][11]14,15,17,18,20,[22][23][24][25]39,[44][45][46]52] for an overview of the field. Logarithmic and sublinear bounds are typically not in the focus of the cited approaches, but can be inferred by some tools.…”

“…Based on earlier work [6,20,[22][23][24][25]27,28] employs a type-and-effect system that uses template potential functions, i.e. functions of a fixed shape with indeterminate coefficients.…”

“…We implement and extend a recently proposed type-and-effect system for amortised resource analysis [26,27]. This system belongs to a line of work (see [20,[22][23][24][25]28] and the references therein), where types are template potential functions with unknown coefficients and the type-and-effect system extracts constraints over these coefficients in a syntax directed way from the program under analysis. Our work improves over [26,27] in three regards: 1) The approach of [26,27] only supports type checking, i.e.…”

Teaching the art of functional programming using automated grading (experience report)

“…Aside from correctness, test quality, and code style, another metric of student code that would be useful to assess automatically is time complexity. Hoffmann et al's work on automatically analyzing resource bounds of OCaml programs has led to the development of Resource Aware ML (RAML) [Hoffmann et al 2012[Hoffmann et al , 2017, a resourceaware version of the OCaml language. Currently only a subset of OCaml is supported and the language is not ready for deployment in a learning setting.…”

A Functional Reactive Programming Language for Small-Scale Embedded Systems with Recursive Data Types

“…To decompose a tree of size 21, (m, n), the third and fourth size parameters of the constructor T, have the constraint 21 = 1+m+n. Therefore, (m, n) = (1, 19), (2,18), (3,17), . .…”