Polymorphic type schemes and recursive definitions

Mycroft, Alan

doi:10.1007/3-540-12925-1_41

Cited by 128 publications

(77 citation statements)

References 7 publications

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“…This not only simplifies the following steps, but also leads to practically better algorithms. We then show how the principal typing property for our type system can be established by a generalization of Mycroft's method [12] we call Kleene-Mycroft Iteration (KMI). The availability of disjunctive binding-time annotations is used to eliminate neutral binding-time variables; that is, binding-time variables occurring in C in a judgement C, A ⊢ κ, but not in A or κ.…”

Section: Polymorphic Binding-time Analysis With Polymorphic Recursionmentioning

confidence: 99%

“…Consider an ML-polymorphic type system [11,5,4], extended with a rule for polymorphic recursion [12]:…”

Section: Polymorphic Recursion Revisited: Kleene-mycroft Iterationmentioning

confidence: 99%

“…It is syntax-directed and operates on open expressions, with arbitrary nesting depth of fix-expressions. Algorithm W was originally introduced by Milner [11] for ML type inference and later extended by Mycroft [12] to polymorphic recursion. We use the following auxiliary partial functions in it:…”

Section: Principality: Kleene-mycroft Iteration For Qualified Type Scmentioning

confidence: 99%

“…The algorithm is an adaption of Mycroft's algorithm for computing principal types for ML extended with polymorphic recursion [12]. We show that, in contrast to polymorphic recursion over standard types (as considered by Mycroft), polymorphic recursion over binding times can be done in polynomial time in the size of the underlying statically typed program.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

“…Polymorphic recursion was introduced in [12] as an extension of ML style polymorphism that allows recursive definitions to be used at different types inside the definition. Mycroft was the first to give a (semi)-algorithm for computing principal types for his system.…”

Section: Introductionmentioning

confidence: 99%

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Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time

Dussart

Henglein²,

Mossin³

1995

Static Analysis

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Abstract. The combination of parameter polymorphism, subtyping extended to qualified and polymorphic types, and polymorphic recursion is useful in standard type inference and gives expressive type-based program analyses, but raises difficult algorithmic problems. In a program analysis context we show how Mycroft's iterative method of computing principal types for a type system with polymorphic recursion can be generalized and adapted to work in a setting with subtyping. This does not only yield a proof of existence of principal types (most general properties), but also an algorithm for computing them. The punch-line of the development is that a very simple modification of the basic algorithm reduces its computational complexity from exponential time to polynomial time relative to the size of the given, explicitly typed program.This solves the open problem of finding an inference algorithm for polymorphic binding-time analysis [7].

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Section: Polymorphic Binding-time Analysis With Polymorphic Recursionmentioning

confidence: 99%

“…Consider an ML-polymorphic type system [11,5,4], extended with a rule for polymorphic recursion [12]:…”

Section: Polymorphic Recursion Revisited: Kleene-mycroft Iterationmentioning

confidence: 99%

Section: Principality: Kleene-mycroft Iteration For Qualified Type Scmentioning

confidence: 99%

Section: Conclusion and Further Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time

Dussart

Henglein²,

Mossin³

1995

Static Analysis

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Principal Types and Unification for Simple Intersection Type Systems

Coppo

Giannini

1995

Information and Computation

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Region-Based Memory Management

Tofte

Talpin

1997

Information and Computation

469

207

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This paper describes a memory management discipline for programs that perform dynamic memory allocation and de-allocation. At runtime, all values are put into regions. The store consists of a stack of regions. All points of region allocation and de-allocation are inferred automatically, using a type and effect based program analysis. The scheme does not assume the presence of a garbage collector. The scheme was first presented in 1994 (M. Tofte and J.-P. Talpin, in``Proceedings of the 21st ACM SIGPLAN SIGACT Symposium on Principles of Programming Languages,'' pp. 188 201); subsequently, it has been tested in The ML Kit with Regions, a region-based, garbage-collection free implementation of the Standard ML Core language, which includes recursive datatypes, higher-order functions and updatable references L. Birkedal, M. Tofte, and M. Vejlstrup, (1996), in``Proceedings of the 23 rd ACM SIGPLAN SIGACT Symposium on Principles of Programming Languages,'' pp. 171 183. This paper defines a region-based dynamic semantics for a skeletal programming language extracted from Standard ML. We present the inference system which specifies where regions can be allocated and de-allocated and a detailed proof that the system is sound with respect to a standard semantics. We conclude by giving some advice on how to write programs that run well on a stack of regions, based on practical experience with the ML Kit. ] 1997 Academic Press

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Polymorphic type schemes and recursive definitions

Cited by 128 publications

References 7 publications

Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time

Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time

Principal Types and Unification for Simple Intersection Type Systems

Region-Based Memory Management

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