A Functional Correspondence between Monadic Evaluators and Abstract Machines for Languages with Computational Effects

Ager, Mads Sig; Danvy, Olivier; Midtgaard, Jan

doi:10.7146/brics.v11i28.21853

Cited by 6 publications

(6 citation statements)

References 15 publications

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“…The programmatic transformation of formal semantics dates to work by Reynolds [15]. More recent work by Danvy et al has shown that formal semantics are highly amenable to program transformations and that it is possible to automatically convert denotational semantics into operational semantics and vice versa [2,3,1,[6][7][8]. These techniques, combined with ours, should permit the mechanizable construction of static analyzers for a wider variety of formal semantics paradigms.…”

Section: Related Workmentioning

confidence: 99%

Abstract Interpreters for Free

Might

2010

Static Analysis

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Abstract. In small-step abstract interpretations, the concrete and abstract semantics bear an uncanny resemblance. In this work, we present an analysis-design methodology that both explains and exploits that resemblance. Specifically, we present a two-step method to convert a smallstep concrete semantics into a family of sound, computable abstract interpretations. The first step re-factors the concrete state-space to eliminate recursive structure; this refactoring of the state-space simultaneously determines a store-passing-style transformation on the underlying concrete semantics. The second step uses inference rules to generate an abstract state-space and a Galois connection simultaneously. The Galois connection allows the calculation of the "optimal" abstract interpretation. The two-step process is unambiguous, but nondeterministic: at each step, analysis designers face choices. Some of these choices ultimately influence properties such as flow-, field-and context-sensitivity. Thus, under the method, we can give the emergence of these properties a graphtheoretic characterization. To illustrate the method, we systematically abstract the continuation-passing style lambda calculus to arrive at two distinct families of analyses. The first is the well-known k-CFA family of analyses. The second consists of novel "environment-centric" abstract interpretations, none of which appear in the literature on static analysis of higher-order programs.

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Section: Related Workmentioning

confidence: 99%

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Might

2010

Static Analysis

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“…As in recent work on abstracting abstract machines [23], our semantic transformation implicitly utilizes the techniques of Danvy et al [1,2,7] in order to calculate an abstract 1 machine equivalent to the concrete semantics. It diverges with this line of work by applying a monadic-normalform transformation [6] (instead of a store-passing-style transformation) to the rules for the machine.…”

Section: Overviewmentioning

confidence: 99%

“…We have chosen Haskell in lieu of formal mathematics for the presentation for two reasons: (1) Haskell is directly executable, and (2) Haskell has concise, convenient and readable syntax for expressing monads-the central actor in our work. Our fundamental results are no more restricted to Haskell than monads are restricted to Haskell.…”

Section: Introductionmentioning

confidence: 99%

Monadic abstract interpreters

Sergey

Devriese

Might

et al. 2013

Proceedings of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation

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Recent developments in the systematic construction of abstract interpreters hinted at the possibility of a broad unification of concepts in static analysis. We deliver that unification by showing context-sensitivity, polyvariance, flow-sensitivity, reachabilitypruning, heap-cloning and cardinality-bounding to be independent of any particular semantics. Monads become the unifying agent between these concepts and between semantics. For instance, by plugging the same "context-insensitivity monad" into a monadicallyparameterized semantics for Java or for the lambda calculus, it yields the expected context-insensitive analysis.To achieve this unification, we develop a systematic method for transforming a concrete semantics into a monadically-parameterized abstract machine. Changing the monad changes the behavior of the machine. By changing the monad, we recover a spectrum of machines-from the original concrete semantics to a monovariant, flow-and context-insensitive static analysis with a singly-threaded heap and weak updates.The monadic parameterization also suggests an abstraction over the ubiquitous monotone fixed-point computation found in static analysis. This abstraction makes it straightforward to instrument an analysis with high-level strategies for improving precision and performance, such as abstract garbage collection and widening.While the paper itself runs the development for continuationpassing style, our generic implementation replays it for direct-style lambda-calculus and Featherweight Java to support generality.

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“…Ager et al [2] investigate a correspondence between semantics described in terms of monadic evaluators and languages with computational effects. They show that a calculus for tail-recursive stack inspection corresponds to a lifted state monad.…”

Section: Related Workmentioning

confidence: 99%

From type checking by recursive descent to type checking with an abstract machine

Sergey

Clarke

2011

Proceedings of the Eleventh Workshop on Language Descriptions, Tools and Applications

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Modern type systems for programming languages usually incorporate additional information useful for program analysis, e.g., effects, control flow, non-interference, strictness etc. When designing a typing predicate for such systems, a form of logical derivation rules is normally taken. Despite the expressivity of this approach, the straightforward implementation of an appropriate type checker is usually inefficient in terms of stack consumption and further optimisations. This leads to a significant gap between an analysis and program implementing the analysis.In this paper we demonstrate an application of techniques investigated by Danvy et al. to derive an abstract machine for typing from the traditional recursive descent approach. All used techniques are off-the-shelf and no appropriate correspondence theorems between an initial type system and the derived abstract machine needs to be proven: they are instead corollaries of the correctness of inter-derivation and of the initial specification. Whereas a recursive descent is something straightforward to implement based on declarative typing rules, the derived abstract machine exposes behaviour similar to Landin's SECD machine and gives a solid basis for further optimizations using abstract interpretation.

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A Functional Correspondence between Monadic Evaluators and Abstract Machines for Languages with Computational Effects

Cited by 6 publications

References 15 publications

Abstract Interpreters for Free

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Monadic abstract interpreters

From type checking by recursive descent to type checking with an abstract machine

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