Structuring Optimizing Transformations and Proving Them Sound

Kanade, Aditya; Sanyal, Amitabha; Khedker, Uday P.

doi:10.1016/j.entcs.2006.06.018

Cited by 6 publications

(7 citation statements)

References 11 publications

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“…SPOTS is an acronym for 'System for Proving Optimizing Transformations Sound'. It is used for specification and verification of optimizations [1,3]. We have developed novel boolean matrix algebraic formulations of transformation primitives and their soundness conditions [2].…”

Section: Overview Of the Validation Schemementioning

confidence: 99%

“…The TCB consists of only the following components: (1) The functions that convert the RTL representation to PVS theories and (2) the PVS ground evaluator. The conversion routines are syntax-directed translators and in general, it is possible to develop enough confidence in them with repeated use or testing.…”

Section: Development Cost Extensibility and Tcbmentioning

confidence: 99%

“…The notion of transformation primitives and soundness conditions is suitable for both verification and validation of optimizations. Our earlier specifications in [1] are intended for verification and though equally expressive, are not executable. In [2] we proposed constructive definitions of transformation primitives using boolean matrix algebra and used them in simulation and verification of optimization specifications.…”

Section: Related Workmentioning

confidence: 99%

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Validation of GCC optimizers through trace generation

2009

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The translation validation approach involves establishing semantics preservation of individual compilations. In this paper, we present a novel framework for translation validation of optimizers. We identify a comprehensive set of primitive program transformations that are commonly used in many optimizations. For each primitive, we define soundness conditions that guarantee that the transformation is semantics preserving. This framework of transformations and soundness conditions is independent of any particular compiler implementation and is formalized in PVS. An optimizer is instrumented to generate the trace of an optimization run in terms of the predefined transformation primitives. The validation succeeds if (1) the trace conforms to the optimization and (2) the soundness conditions of the individual transformations in the trace are satisfied. The first step eliminates the need to trust the instrumentation. The soundness conditions are defined in a temporal logic and therefore the second step involves model checking. Thus the scheme is completely automatable. We have applied this approach to several intraprocedural optimizations of RTL intermediate code in GNU Compiler Collection (GCC) v4.1.0, namely, loop invariant code motion, partial redundancy elimination, lazy code motion, code hoisting, and copy and constant propagation for sample programs written in a subset of the C language. The validation does not require information about program analyses performed by GCC. Therefore even though the GCC code base is quite large and complex, instrumentation could be achieved easily. The framework requires an estimated 21 lines of instrumentation code and 140 lines of PVS specifications for every 1000 lines of the GCC code considered for validation.However, a mistake in the design or in the implementation of an optimizer can proliferate in the form of bugs in the softwares compiled through it.The issue of soundness of optimizers is usually addressed at two levels: (1) One time guarantees are obtained at the design level by verifying optimization specifications and (2) run-time guarantees are obtained at the implementation level by validating optimization runs.Both these approaches involve proofs of semantic equivalence between the input and the optimized programs. However, they are usually tedious. Even in the case of validation where semantic equivalence is to be shown for a particular execution, it cannot be accomplished with ease. This complexity can be conquered by taking advantage of the fact that optimizations with similar objectives employ similar program transformations. For example, 'replacement of some occurrences of an expression by a variable' is a transformation that is common to optimizations such as common subexpression elimination, lazy code motion, loop invariant code motion, and several others whose aim is to avoid unnecessary recomputations of a value.This observation led to identification of transformation primitives and soundness conditions, and their use in verification of optimization specificat...

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Section: Overview Of the Validation Schemementioning

confidence: 99%

Section: Development Cost Extensibility and Tcbmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Validation of GCC optimizers through trace generation

2009

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“…The complexity of proofs can be conquered by taking advantage of the fact that optimizations with similar objectives employ similar program transformations. This observation lead to identification of transformation primitives and their soundness conditions [KSK07].…”

Section: Introductionmentioning

confidence: 95%

A Logic for Correlating Temporal Properties across Program Transformations

Kanade¹,

Sanyal²,

Khedker³

2012

Preprint

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Program transformations are widely used in synthesis, optimization, and maintenance of software. Correctness of program transformations depends on preservation of some important properties of the input program. By regarding programs as Kripke structures, many interesting properties of programs can be expressed in temporal logics. In temporal logic, a formula is interpreted on a single program. However, to prove correctness of transformations, we encounter formulae which contain some subformulae interpreted on the input program and some on the transformed program. An example where such a situation arises is verification of optimizing program transformations applied by compilers.In this paper, we present a logic called Temporal Transformation Logic (TTL) to reason about such formulae. We consider different types of primitive transformations and present TTL inference rules for them. Our definitions of program transformations and temporal logic operators are novel in their use of the boolean matrix algebra. This results in specifications that are succinct and constructive. Further, we use the boolean matrix algebra in a uniform manner to prove soundness of the TTL inference rules.

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“…A distinguishing feature of our proof technique is that we use an abstraction function, α, to enable us to convert between a configuration in the language domain to a corresponding configuration in the typing domain. Using an abstraction function in proving soundness is a technique used frequently in the domain of processor construction, as introduced in [36], or compiler optimization [37,38]. Lemma 1.…”

Section: Type Preservationmentioning

confidence: 99%

A Rewriting Logic Approach to Type Inference

Ellison

Şerbănuţă

Roşu

2009

Recent Trends in Algebraic Development Techniques

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Abstract. Meseguer and Ros , u proposed rewriting logic semantics (RLS) as a programing language definitional framework that unifies operational and algebraic denotational semantics. RLS has already been used to define a series of didactic and real languages, but its benefits in connection with defining and reasoning about type systems have not been fully investigated. This paper shows how the same RLS style employed for giving formal definitions of languages can be used to define type systems. The same termrewriting mechanism used to execute RLS language definitions can now be used to execute type systems, giving type checkers or type inferencers. The proposed approach is exemplified by defining the Hindley-Milner polymorphic type inferencer W as a rewrite logic theory and using this definition to obtain a type inferencer by executing it in a rewriting logic engine. The inferencer obtained this way compares favorably with other definitions or implementations of W . The performance of the executable definition is within an order of magnitude of that of highly optimized implementations of type inferencers, such as that of OCaml.

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Structuring Optimizing Transformations and Proving Them Sound

Cited by 6 publications

References 11 publications

Validation of GCC optimizers through trace generation

Validation of GCC optimizers through trace generation

A Logic for Correlating Temporal Properties across Program Transformations

A Rewriting Logic Approach to Type Inference

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