Machine-Checked Verification of the Correctness and Amortized Complexity of an Efficient Union-Find Implementation

Charguéraud, Arthur; Pottier, François

doi:10.1007/978-3-319-22102-1_9

Cited by 32 publications

(30 citation statements)

References 27 publications

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“…The technique has been generalized to derive polynomial bounds [50,52,53,57,58], lower bounds [76], and to handle (strictly evaluated) programs with arrays and references [70], higher-order functions [51,61], lazy functional programs [86,90], object-oriented programs [56,59], and user defined data types [51,62]. It also has been integrated into separation logic [6] and proof assistants [25,81]. A distinctive common theme of sharing is compositionality and automatic bound inference via LP solving.…”

Section: Related Workmentioning

confidence: 99%

Bounded expectations: resource analysis for probabilistic programs

Ngo

Carbonneaux

Hoffmann

2018

Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation

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This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials in the inputs. The new technique combines manual state-of-theart reasoning techniques for probabilistic programs with an effective method for automatic resource-bound analysis of deterministic programs. It can be seen as both, an extension of automatic amortized resource analysis (AARA) to probabilistic programs and an automation of manual reasoning for probabilistic programs that is based on weakest preconditions. An advantage of the technique is that it combines the clarity and compositionality of a weakest-precondition calculus with the efficient automation of AARA. As a result, bound inference can be reduced to off-the-shelf LP solving in many cases and automatically-derived bounds can be interactively extended with standard program logics if the automation fails. Building on existing work, the soundness of the analysis is proved with respect to an operational semantics that is based on Markov decision processes. The effectiveness of the technique is demonstrated with a prototype implementation that is used to automatically analyze 39 challenging probabilistic programs and randomized algorithms. Experiments indicate that the derived constant factors in the bounds are very precise and even optimal for some programs.CCS Concepts · Software and its engineering → General programming languages; · Social and professional topics → History of programming languages;

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Section: Related Workmentioning

confidence: 99%

Bounded expectations: resource analysis for probabilistic programs

Ngo

Carbonneaux

Hoffmann

2018

Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation

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“…However, none of these systems consider relational analysis of costs. Charguéraud and Pottier [2015] present an amortized resource analysis based on an extension of separation logic with time credits. Our use of triples and separation-based management of arrays references is similar to theirs.…”

Section: Related Workmentioning

confidence: 99%

Relational cost analysis for functional-imperative programs

Gaboardi

Garg

2019

Proc. ACM Program. Lang.

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Relational cost analysis aims at formally establishing bounds on the difference in the evaluation costs of two programs. As a particular case, one can also use relational cost analysis to establish bounds on the difference in the evaluation cost of the same program on two different inputs. One way to perform relational cost analysis is to use a relational type-and-effect system that supports reasoning about relations between two executions of two programs.Building on this basic idea, we present a type-and-effect system, called ARel, for reasoning about the relative cost of array-manipulating, higher-order functional-imperative programs. The key ingredient of our approach is a new lightweight type refinement discipline that we use to track relations (differences) between two mutable arrays. This discipline combined with Hoare-style triples built into the types allows us to express and establish precise relative costs of several interesting programs which imperatively update their data. We have implemented ARel using ideas from bidirectional type checking.how ARel is implemented and used ARel to reason about the relational cost of several nontrivial examples.

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“…A more precise approach is taken by Charguéraud and Pottier [7], who argue about the number of β-reduction steps taken by the program.…”

Section: Related Workmentioning

confidence: 99%

Formalizing Network Flow Algorithms: A Refinement Approach in Isabelle/HOL

Lammich

Sefidgar

2017

J Autom Reasoning

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We present a formalization of classical algorithms for computing the maximum flow in a network: The Edmonds-Karp algorithm and the push-relabel algorithm. We prove correctness and time complexity of these algorithms. Our formal proof closely follows a standard textbook proof, and is accessible even without being an expert in Isabelle/HOL -the interactive theorem prover used for the formalization.Using stepwise refinement techniques, we instantiate the generic Ford-Fulkerson algorithm to Edmonds-Karp algorithm, and the generic push-relabel algorithm of Goldberg and Tarjan to both the relabel-to-front and the FIFO push-relabel algorithm. Further refinement then yields verified efficient implementations of the algorithms, which compare well to unverified reference implementations.

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Machine-Checked Verification of the Correctness and Amortized Complexity of an Efficient Union-Find Implementation

Cited by 32 publications

References 27 publications

Bounded expectations: resource analysis for probabilistic programs

Bounded expectations: resource analysis for probabilistic programs

Relational cost analysis for functional-imperative programs

Formalizing Network Flow Algorithms: A Refinement Approach in Isabelle/HOL

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