Polyvariant Analysis of the Untyped Lambda Calculus

Palsberg, Jens; Schwartzbach, Michael I.

doi:10.7146/dpb.v21i386.6619

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…In addition to p, which controls how precisely parametric polymorphism is analyzed, their algorithm has a second integer parameter, k, that affects analysis of data polymorphism. The p-level expansion algorithm is also discussed in [17] where it is applied to the untyped lambda calculus. We consider the p-level expansion unrealistic.…”

Section: The P-level Expansion Algorithmmentioning

confidence: 99%

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Constraint-based type inference and parametric polymorphism

Agesen

1994

Static Analysis

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Abstract. Constraint-based analysis is a technique for inferring implementation types. Traditionally it has been described using mathematical formalisms. We explain it in a different and more intuitive way as a flow problem. The intuition is facilitated by a direct correspondence between run-time and analysis-time concepts.Precise analysis of polymorphism is hard; several algorithms have been developed to cope with it. Focusing on parametric polymorphism and using the flow perspective, we analyze and compare these algorithms, for the first time directly characterizing when they succeed and fail.Our study of the algorithms lead us to two conclusions. First, designing an algorithm that is either efficient or precise is easy, but designing an algorithm that is efficient and precise is hard. Second, to achieve efficiency and precision simultaneously, the analysis effort must be actively guided towards the areas of the program with the highest pay-off. We define a general class of algorithms that do this: the adaptive algorithms. The two most powerful of the five algorithms we study fall in this class.

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Section: The P-level Expansion Algorithmmentioning

confidence: 99%

“…In [17] a constraint-based closure analysis of the untyped lambda calculus is given. On top of the closure analysis a binding time analysis and a safety analysis is defined.…”

Section: Related Workmentioning

confidence: 99%

Constraint-based type inference and parametric polymorphism

Agesen

1994

Static Analysis

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“…✷ Given a pure term, the -least annotated version for which BA is solvable can be computed in cubic time. The idea is to compute the least solution of the C constraint system and then apply annotate, see [10]. Bondorf's original algorithm [1] was given in a compositional style; its time complexity appears to be worse than cubic time.…”

Section: Consider First Subterms Of Ementioning

confidence: 99%

Binding Time Analysis: Abstract Interpretation vs. Type Inference

Palsberg¹,

Schwartzbach²

1992

DPB

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Binding time analysis is important in partial evaluators. Its task is to determine which parts of a program can be specialized if some of the expected input is known. Two approaches to do this are abstract interpretation and type inference. We compare two specific such analyses to see which one determines most program parts to be eliminable. The first is the abstract interpretation approach of Bondorf, and the second is the type inference approach of Gomard. Both apply to the untyped lambda calculus. We prove that Bondorf's analysis is better than Gomard's.

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Safety Analysis versus Type Inference

Palsberg

Schwartzbach

1995

Information and Computation

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Safety analysis is an algorithm for determining if a term in an untyped lambda calculus with constants is safe, i.e., if it does not cause an error during evaluation. This ambition is also shared by algorithms for type inference. Safety analysis and type inference are based on rather di erent perspectives, however. Safety analysis is global in that it can only analyze a complete program. In contrast, type inference is local in that it can analyze pieces of a program in isolation. In this paper we prove that safety analysis is sound, relative to both a strict and a lazy operational semantics. We also prove that safety analysis accepts strictly more safe lambda terms than does type inference for simple types. The latter result demonstrates that global program analyses can be more precise than local ones.

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Polyvariant Analysis of the Untyped Lambda Calculus

Cited by 3 publications

References 24 publications

Constraint-based type inference and parametric polymorphism

Constraint-based type inference and parametric polymorphism

Binding Time Analysis: Abstract Interpretation vs. Type Inference

Safety Analysis versus Type Inference

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