Formally deriving an STG machine

Encina, Alberto de la; Peña, Ricardo

doi:10.1145/888251.888262

“…Type consistency for follows from (10) and (Loc2); and for follows directly from the type rule Ind and (Loc1). Compatibility is immediate because the types for and in Γ 0 are exactly M 0 ( ) and M 0 ( ).…”

Section: Soundness Of the Proof Systemmentioning

confidence: 99%

“…As described in Section 4, this type-and-effect system successfully produces resource bounds for examples that could not previously be analysed. Our cost model is based on Launchbury's natural semantics for lazy evaluation [5], as subsequently refined by Sestoft [4], de la Encina and Peña-Marì [10,11]. The proof technique used in Section 5.6 for establishing correspondence between the indirections semantics and the standard one is based on work by Sánchez-Gil, Hidalgo-Herrero and Ortega-Mallén [9].…”

Section: Soundness Of the Proof Systemmentioning

confidence: 99%

Type-Based Allocation Analysis for Co-recursion in Lazy Functional Languages

Vasconcelos

¹

,

Jost

²

,

Florido

³

et al. 2015

Programming Languages and Systems

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Abstract. This paper presents a novel type-and-effect analysis for predicting upper-bounds on memory allocation costs for co-recursive definitions in a simple lazily-evaluated functional language. We show the soundness of this system against an instrumented variant of Launchbury's semantics for lazy evaluation which serves as a formal cost model. Our soundness proof requires an intermediate semantics employing indirections. Our proof of correspondence between these semantics that we provide is thus a crucial part of this work. The analysis has been implemented as an automatic inference system. We demonstrate its effectiveness using several example programs that previously could not be automatically analysed.

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“…Launchbury's semantics forms one of the earliest and most widely-used operational accounts of lazy evaluation for the λ-calculus. De la Encina and Peña-Marí [13,14] subsequently proved that the Spineless Tagless G-Machine [24] is sound and complete w.r.t. one of Sestoft's abstract machines.…”

Section: A Cost Model For Lazy Evaluationmentioning

confidence: 99%

Automatic amortised analysis of dynamic memory allocation for lazy functional programs

Simões

¹

,

Vasconcelos

²

,

Florido

³

et al. 2012

Proceedings of the 17th ACM SIGPLAN International Conference on Functional Programming

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This paper describes the first successful attempt, of which we are aware, to define an automatic, type-based static analysis of resource bounds for lazy functional programs. Our analysis uses the automatic amortisation approach developed by Hofmann and Jost, which was previously restricted to eager evaluation. In this paper, we extend this work to a lazy setting by capturing the costs of unevaluated expressions in type annotations and by amortising the payment of these costs using a notion of lazy potential. We present our analysis as a proof system for predicting heap allocations of a minimal functional language (including higher-order functions and recursive data types) and define a formal cost model based on Launchbury's natural semantics for lazy evaluation. We prove the soundness of our analysis with respect to the cost model. Our approach is illustrated by a number of representative and non-trivial examples that have been analysed using a prototype implementation of our analysis. The detailed soundness proof and a web version of our analysis are available at http://www.dcc.fc.up.pt/~pbv/cgi/aalazy.cgi. † Note that, because we do not consider deallocation, we model total allocation but not residency.

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“…Launchbury's semantics forms one of the earliest and most widely-used operational accounts of lazy evaluation for the λ-calculus. De la Encina and Peña-Marí [13,14] subsequently proved that the Spineless Tagless G-Machine [24] is sound and complete w.r.t. one of Sestoft's ab-stract machines.…”

Section: A Cost Model For Lazy Evaluationmentioning

confidence: 99%

“…As described above, we build heavily on Launchbury's natural semantics for lazy evaluation [30], as subsequently adapted by Sestoft, and exploit ideas that were developed by de la Encina and Peña-Marí [14,15]. There is a significant body of other work on the semantics of call-by-need evaluation.…”

Section: Related Workmentioning

confidence: 99%

Automatic amortised analysis of dynamic memory allocation for lazy functional programs

Simões

¹

,

Vasconcelos

²

,

Florido

³

et al. 2012

View full text Add to dashboard Cite

This paper describes the first successful attempt, of which we are aware, to define an automatic, type-based static analysis of resource bounds for lazy functional programs. Our analysis uses the automatic amortisation approach developed by Hofmann and Jost, which was previously restricted to eager evaluation. In this paper, we extend this work to a lazy setting by capturing the costs of unevaluated expressions in type annotations and by amortising the payment of these costs using a notion of lazy potential. We present our analysis as a proof system for predicting heap allocations of a minimal functional language (including higher-order functions and recursive data types) and define a formal cost model based on Launchbury's natural semantics for lazy evaluation. We prove the soundness of our analysis with respect to the cost model. Our approach is illustrated by a number of representative and non-trivial examples that have been analysed using a prototype implementation of our analysis.

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Formally deriving an STG machine

Cited by 6 publications

References 7 publications

Type-Based Allocation Analysis for Co-recursion in Lazy Functional Languages

Type-Based Allocation Analysis for Co-recursion in Lazy Functional Languages

Automatic amortised analysis of dynamic memory allocation for lazy functional programs

Automatic amortised analysis of dynamic memory allocation for lazy functional programs

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