A Concrete Framework for Environment Machines

Biernacka, Małgorzata; Danvy, Olivier

doi:10.7146/brics.v12i15.21881

Cited by 9 publications

(13 citation statements)

References 13 publications

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“…BD07a] follow the traditional (rather than the contextual) approach to ES; 2) none of these works deals with complexity analysis nor with linear logic. On the other hand,[BD07a] provides a deeper analysis of Leroy's ZINC machine, as ours does not account for the avoidance of needless closure creations that is a distinct feature of the ZINC. Last, what here we call commutative transitions essentially corresponds to what Danvy and Nielsen call decompose phase in [DN04].…”

mentioning

confidence: 96%

Distilling abstract machines

AccattoliBeniamino¹,

BarenbaumPablo²,

MazzaDamiano³

2014

SIGPLAN Not.

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It is well-known that many environment-based abstract machines can be seen as strategies in lambda calculi with explicit substitutions (ES). Recently, graphical syntaxes and linear logic led to the linear substitution calculus (LSC), a new approach to ES that is halfway between big-step calculi and traditional calculi with ES. This paper studies the relationship between the LSC and environment-based abstract machines. While traditional calculi with ES simulate abstract machines, the LSC rather distills them: some transitions are simulated while others vanish, as they map to a notion of structural congruence. The distillation process unveils that abstract machines in fact implement weak linear head reduction, a notion of evaluation having a central role in the theory of linear logic. We show that such a pattern applies uniformly in call-by-name, call-by-value, and call-by-need, catching many machines in the literature. We start by distilling the KAM, the CEK, and the ZINC, and then provide simplified versions of the SECD, the lazy KAM, and Sestoft's machine. Along the way we also introduce some new machines with global environments. Moreover, we show that distillation preserves the time complexity of the executions, i.e. the LSC is a complexity-preserving abstraction of abstract machines.

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confidence: 96%

Distilling abstract machines

AccattoliBeniamino¹,

BarenbaumPablo²,

MazzaDamiano³

2014

SIGPLAN Not.

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“…Danvy and Nielsen [9] introduce the refocusing technique, a general procedure transforming small-step reduction systems defined with evaluation contexts into abstract machines operating on the same syntax. Biernacka and Danvy [4] extend refocusing and obtain environment-based abstract machines. This yields a framework where the derived machines are provably correct with respect to small-step bisimulation.…”

Section: Related Workmentioning

confidence: 99%

“…Swierstra [21] formally verifies the correctness of a Krivine machine for simply typed λ-calculus in the dependently typed programming language Agda. Also following Biernacka and Danvy [4], Swierstra does this by showing the correctness of a Krivine-style evaluator for an iterative and environment-based head reduction evaluator. This way substitution does not appear.…”

Section: Related Workmentioning

confidence: 99%

Formal Small-Step Verification of a Call-by-Value Lambda Calculus Machine

Kunze

Smolka

Forster

2018

Programming Languages and Systems

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We formally verify an abstract machine for a call-by-value λ-calculus with de Bruijn terms, simple substitution, and small-step semantics. We follow a stepwise refinement approach starting with a naive stack machine with substitution. We then refine to a machine with closures, and finally to a machine with a heap providing structure sharing for closures. We prove the correctness of the three refinement steps with compositional small-step bottom-up simulations. There is an accompanying Coq development verifying all results.

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“…For background on concepts, terminology, and notation employed in this paper, we refer the reader to Semantics Engineering with PLT Redex [15]. Our construction of machines from reduction semantics follows Danvy, et al's refocusing-based approach [13,4,12]. Finally, for background on systematic abstract interpretation of abstract machines, see our recent work on the approach [39].…”

Section: Background and Notationmentioning

confidence: 99%

Pushdown Abstractions of JavaScript

Van Horn,

Might

2011

Preprint

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We design a family of program analyses for JavaScript that make no approximation in matching calls with returns, exceptions with handlers, and breaks with labels. We do so by starting from an established reduction semantics for JavaScript and systematically deriving its intensional abstract interpretation. Our first step is to transform the semantics into an equivalent low-level abstract machine: the JavaScript Abstract Machine (JAM). We then give an infinite-state yet decidable pushdown machine whose stack precisely models the structure of the concrete program stack. The precise model of stack structure in turn confers precise control-flow analysis even in the presence of control effects, such as exceptions and finally blocks. We give pushdown generalizations of traditional forms of analysis such as k-CFA, and prove the pushdown framework for abstract interpretation is sound and computable. escape continuations from crossing interprocedural boundaries, but unrestrictedor optimized λJS-may violate these constraints. For completeness, we handle full, unrestricted λJS, which means we must model these general escape continuations.

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A Concrete Framework for Environment Machines

Cited by 9 publications

References 13 publications

Distilling abstract machines

Distilling abstract machines

Formal Small-Step Verification of a Call-by-Value Lambda Calculus Machine

Pushdown Abstractions of JavaScript

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