An official website of the United States government
This article gives an overview of automatic amortized resource analysis (AARA), a technique for inferring symbolic resource bounds for programs at compile time. AARA has been introduced by Hofmann and Jost in 2003 as a type system for deriving linear worst-case bounds on the heap-space consumption of first-order functional programs with eager evaluation strategy. Since then AARA has been the subject of dozens of research articles, which extended the analysis to different resource metrics, other evaluation strategies, non-linear bounds, and additional language features. All these works preserved the defining characteristics of the original paper: local inference rules, which reduce bound inference to numeric (usually linear) optimization; a soundness proof with respect to an operational cost semantics; and the support of amortized analysis with the potential method.
more »
« less
Automatic amortized resource analysis with the Quantum physicist’s method
We present a novel method for working with the physicist's method of amortized resource analysis, which we call the quantum physicist's method. These principles allow for more precise analyses of resources that are not monotonically consumed, like stack. This method takes its name from its two major features, worldviews and resource tunneling, which behave analogously to quantum superposition and quantum tunneling. We use the quantum physicist's method to extend the Automatic Amortized Resource Analysis (AARA) type system, enabling the derivation of resource bounds based on tree depth. In doing so, we also introduce remainder contexts, which aid bookkeeping in linear type systems. We then evaluate this new type system's performance by bounding stack use of functions in the Set module of OCaml's standard library. Compared to state-of-the-art implementations of AARA, our new system derives tighter bounds with only moderate overhead.
more »
« less
- PAR ID:
- 10603248
- Publisher / Repository:
- Association for Computing Machinery (ACM)
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 5
- Issue:
- ICFP
- ISSN:
- 2475-1421
- Format(s):
- Medium: X Size: p. 1-29
- Size(s):
- p. 1-29
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Automatic amortized resource analysis (AARA) is a type-based technique for inferring concrete (non-asymptotic) bounds on a program's resource usage. Existing work on AARA has focused on bounds that are polynomial in the sizes of the inputs. This paper presents and extension of AARA to exponential bounds that preserves the benefits of the technique, such as compositionality and efficient type inference based on linear constraint solving. A key idea is the use of the Stirling numbers of the second kind as the basis of potential functions, which play the same role as the binomial coefficients in polynomial AARA. To formalize the similarities with the existing analyses, the paper presents a general methodology for AARA that is instantiated to the polynomial version, the exponential version, and a combined system with potential functions that are formed by products of Stirling numbers and binomial coefficients. The soundness of exponential AARA is proved with respect to an operational cost semantics and the analysis of representative example programs demonstrates the effectiveness of the new analysis.more » « less
-
There are two approaches to automatically deriving symbolic worst-case resource bounds for programs: static analysis of the source code and data-driven analysis of cost measurements obtained by running the program. Static resource analysis is usually sound but incomplete. Data-driven analysis can always return a result, but its lack of robustness often leads to unsound results. This paper presents the design, implementation, and empirical evaluation of hybrid resource bound analyses that tightly integrate static analysis and data-driven analysis. The static analysis part builds on automatic amortized resource analysis (AARA), a state-of-the-art type-based resource analysis method that performs cost bound inference using linear optimization. The data-driven part is rooted in novel Bayesian modeling and inference techniques that improve upon previous data-driven analysis methods by reporting an entire probability distribution over likely resource cost bounds. A key innovation is a new type inference system calledHybrid AARAthat coherently integrates Bayesian inference into conventional AARA, combining the strengths of both approaches. Hybrid AARA is proven to be statistically sound under standard assumptions on the runtime cost data. An experimental evaluation on a challenging set of benchmarks shows that Hybrid AARA (i) effectively mitigates the incompleteness of purely static resource analysis; and (ii) is more accurate and robust than purely data-driven resource analysis.more » « less
-
This article presents a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs. The analysis is naturally compositional, parametric in the cost model, and supports higher-order functions and inductive data types. The derived bounds are multivariate polynomials that are functions of data structures. Bound inference is enabled by local type rules that reduce type inference to linear constraint solving. The type system is based on the potential method of amortized analysis and extends automatic amortized resource analysis (AARA) for deterministic programs. A main innovation is that bounds can contain symbolic probabilities, which may appear in data structures and function arguments. Another contribution is a novel soundness proof that establishes the correctness of the derived bounds with respect to a distribution-based operational cost semantics that also includes nontrivial diverging behavior. For cost models like time, derived bounds imply termination with probability one. To highlight the novel ideas, the presentation focuses on linear potential and a core language. However, the analysis is implemented as an extension of Resource Aware ML and supports polynomial bounds and user defined data structures. The effectiveness of the technique is evaluated by analyzing the sample complexity of discrete distributions and with a novel average-case estimation for deterministic programs that combines expected cost analysis with statistical methods.more » « less
-
Baier, Christel; Goubault-Larrecq, Jean (Ed.)Being a fully automated technique for resource analysis, automatic amortized resource analysis (AARA) can fail in returning worst-case cost bounds of programs, fundamentally due to the undecidability of resource analysis. For programmers who are unfamiliar with the technical details of AARA, it is difficult to predict whether a program can be successfully analyzed in AARA. Motivated by this problem, this article identifies classes of programs that can be analyzed in type-based polynomial AARA. Firstly, it is shown that the set of functions that are typable in univariate polynomial AARA coincides with the complexity class PTime. Secondly, the article presents a sufficient condition for typability that axiomatically requires every sub-expression of a given program to be polynomial-time. It is proved that this condition implies typability in multivariate polynomial AARA under some syntactic restrictions.more » « less
