Proving optimizations correct using parameterized program equivalence

Two programs are mutually equivalent if they both diverge or they end up in similar states. Mutual equivalence is an adequate notion of equivalence for programs written in deterministic languages. It is useful in many contexts, such as capturing the correctness of program transformations within the same language, or capturing the correctness of compilers between two different languages. In this paper we introduce a language-independent proof system for mutual equivalence, which is parametric in the operational semantics of two languages and in a statesimilarity relation. The proof system is sound: if it terminates then it establishes the mutual equivalence of the programs given to it as input. We illustrate it on two programs in two different languages (an imperative one and a functional one), that both compute the Collatz sequence.

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“…full) equivalence only. In [9], an implementation of a parametrized equivalence prover is presented.…”

Section: Discussion Related Work and Conclusionmentioning

confidence: 99%

A Language-Independent Proof System for Mutual Program Equivalence

Ciobâcă

Lucanu

Rusu

et al. 2014

Formal Methods and Software Engineering

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“…Another approach is to provide a domain-specific language for writing verified compiler optimizations [43], [37], [38], [34], [14]; this doesn't verify the whole compiler, but verifies that a single optimization (or other) pass is correct.…”

Section: Related Workmentioning

confidence: 99%

Доверя́й, но проверя́й: SFI safety for native-compiled Wasm

Johnson

Thien²,

Alhessi

et al. 2021

Proceedings 2021 Network and Distributed System Security Symposium

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WebAssembly (Wasm) is a platform-independent bytecode that offers both good performance and runtime isolation. To implement isolation, the compiler inserts safety checks when it compiles Wasm to native machine code. While this approach is cheap, it also requires trust in the compiler's correctness-trust that the compiler has inserted each necessary check, correctly formed, in each proper place. Unfortunately, subtle bugs in the Wasm compiler can break-and have broken-isolation guarantees. To address this problem, we propose verifying memory isolation of Wasm binaries post-compilation. We implement this approach in VeriWasm, a static offline verifier for native x86-64 binaries compiled from Wasm; we prove the verifier's soundness, and find that it can detect bugs with no false positives. Finally, we describe our deployment of VeriWasm at Fastly.

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“…There has been a long line of work on making optimizers extensible or easier to develop, including Sharlit [23], Whitfield and Soffa's Gospel system [24], the Broadway extensible compiler [11], and the Rhodium system for expressing optimizations [14,15]. In all these systems, however, the programmer has to learn a new language or compiler interface to express optimizations.…”

Section: Related Workmentioning

confidence: 99%

Generating compiler optimizations from proofs

Tate

Stepp

Lerner

2010

Proceedings of the 37th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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We present an automated technique for generating compiler optimizations from examples of concrete programs before and after improvements have been made to them. The key technical insight of our technique is that a proof of equivalence between the original and transformed concrete programs informs us which aspects of the programs are important and which can be discarded. Our technique therefore uses these proofs, which can be produced by translation validation or a proof-carrying compiler, as a guide to generalize the original and transformed programs into broadly applicable optimization rules. We present a category-theoretic formalization of our proof generalization technique. This abstraction makes our technique applicable to logics besides our own. In particular, we demonstrate how our technique can also be used to learn query optimizations for re-lational databases or to aid programmers in debugging type errors. Finally, we show experimentally that our technique enables programmers to train a compiler with application-specific optimizations by providing concrete examples of original programs and the desired transformed programs. We also show how it enables a compiler to learn efficient-to-run optimizations from expensive-to-run super-optimizers.

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Proving optimizations correct using parameterized program equivalence

Cited by 33 publications

References 34 publications

A Language-Independent Proof System for Mutual Program Equivalence

A Language-Independent Proof System for Mutual Program Equivalence

Доверя́й, но проверя́й: SFI safety for native-compiled Wasm

Generating compiler optimizations from proofs

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