Proving correctness of compiler optimizations by temporal logic

Lacey, David; Jones, Neil D.; Wyk, Eric Van; Frederiksen, Carl Christian

doi:10.1145/503272.503299

Cited by 63 publications

(13 citation statements)

References 20 publications

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“…Human-assisted correctness checking of optimizations. A significant amount of work has been done on manually proving optimizations correct, including abstract interpretation [3,4], the work on the VLISP compiler [7], Kleene algebra with tests [10], manual proofs of correctness for optimizations expressed in temporal logic [25,13], and manual proofs of correctness based on partial equivalence relations [1]. Analyses and transformations have also been proven correct mechanically, but not automatically: the soundness proof is performed with an interactive theorem prover that requires guidance from the user.…”

Section: Related Workmentioning

confidence: 99%

“…The idea of analyzing optimizations written in a specialized language was introduced by Whitfield and Soffa with the Gospel language [29]. Many other frameworks and languages have been proposed for specifying dataflow analyses and transformations, including Sharlit [26], System-Z [30], languages based on regular path queries [24], and temporal logic [25,13]. None of these approaches addresses automated correctness checking of the specified optimizations.…”

Section: Related Workmentioning

confidence: 99%

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Proving optimizations correct using parameterized program equivalence

2009

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Translation validation is a technique for checking that, after an optimization has run, the input and output of the optimization are equivalent. Traditionally, translation validation has been used to prove concrete, fully specified programs equivalent. In this paper we present Parameterized Equivalence Checking (PEC), a generalization of translation validation that can prove the equivalence of parameterized programs. A parameterized program is a partially specified program that can represent multiple concrete programs. For example, a parameterized program may contain a section of code whose only known property is that it does not modify certain variables. By proving parameterized programs equivalent, PEC can prove the correctness of transformation rules that represent complex optimizations once and for all, before they are ever run. We implemented our PEC technique in a tool that can establish the equivalence of two parameterized programs. To highlight the power of PEC, we designed a language for implementing complex optimizations using many-to-many rewrite rules, and used this language to implement a variety of optimizations including software pipelining, loop unrolling, loop unswitching, loop interchange, and loop fusion. Finally, to demonstrate the effectiveness of PEC, we used our PEC implementation to verify that all the optimizations we implemented in our language preserve program behavior.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Proving optimizations correct using parameterized program equivalence

2009

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“…The idea to achieve that flexibility via a form of logic programming augmented with path expressions originated in our own work [6,20]. A separate branch of research, instigated by Lacey, is the formal verification of compiler optimisations that are specified in this style [19]. Indeed, Lerner et al have demonstrated how to automate such proofs [21,22].…”

Section: Related Workmentioning

confidence: 99%

JunGL

Verbaere

Ettinger

Moor

2006

Proceedings of the 28th International Conference on Software Engineering

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Refactorings are behaviour-preserving program transformations, typically for improving the structure of existing code. A few of these transformations have been mechanised in interactive development environments. Many more refactorings have been proposed, and it would be desirable for programmers to script their own refactorings. Implementing such source-to-source transformations, however, is quite complex: even the most sophisticated development environments contain significant bugs in their refactoring tools.We present a domain-specific language for refactoring, named JunGL. It manipulates a graph representation of the program: all information about the program, including ASTs for its compilation units, variable binding, control flow and so on is represented in a uniform graph format. The language is a hybrid of a functional language (in the style of ML) and a logic query language (akin to Datalog). JunGL furthermore has a notion of demand-driven evaluation for constructing computed information in the graph, such as control flow edges. Borrowing from earlier work on the specification of compiler optimisations, JunGL uses socalled 'path queries' to express dataflow properties.We motivate the design of JunGL via a number of nontrivial refactorings, and describe its implementation on the .NET platform.

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“…Lacey, et.al. [21] formalized program optimization as rewriting systems with temporal logic side conditions (described in CTL-FV) and shows that CTL-FV plays a crucial role in the proofs of correctness of classical optimizations. Instead of temporal logic, de Moor, et.al.…”

Section: Related Workmentioning

confidence: 99%

“…The definition, given in Figure 12, is similar to that in [21], except for the additional "while" construct. For simplicity, this language has no exceptions or procedures.…”

Section: Live Variables Detection For Spmentioning

confidence: 99%

Iterative-free program analysis

2003

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Program analysis is the heart of modern compilers. Most control flow analyses are reduced to the problem of finding a fixed point in a certain transition system, and such fixed point is commonly computed through an iterative procedure that repeats tracing until convergence. This paper proposes a new method to analyze programs through recursive graph traversals instead of iterative procedures, based on the fact that most programs (without spaghetti GOTO) have wellstructured control flow graphs, graphs with bounded tree width. Our main techniques are; an algebraic construction of a control flow graph, called SP Term, which enables control flow analysis to be defined in a natural recursive form, and the Optimization Theorem, which enables us to compute optimal solution by dynamic programming. We illustrate our method with two examples; dead code detection and register allocation. Different from the traditional standard iterative solution, our dead code detection is described as a simple combination of bottom-up and top-down traversals on SP Term. Register allocation is more interesting, as it further requires optimality of the result. We show how the Optimization Theorem on SP Terms works to find an optimal register allocation as a certain dynamic programming.

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Proving correctness of compiler optimizations by temporal logic

Cited by 63 publications

References 20 publications

Proving optimizations correct using parameterized program equivalence

Proving optimizations correct using parameterized program equivalence

JunGL

Iterative-free program analysis

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