The typechecking of programs with implicit type structure

McCracken, Nancy

doi:10.1007/3-540-13346-1_15

Cited by 34 publications

(16 citation statements)

References 3 publications

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“…We now extend the design of System HMV to include higher-rank polymorphism [17]. This extension allows function parameters to be used at multiple types.…”

Section: Higher-rank Type Systemsmentioning

confidence: 99%

Visible Type Application

Eisenberg

Weirich

Ahmed

2016

Lecture Notes in Computer Science

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Abstract. The Hindley-Milner (HM) type system automatically infers the types at which polymorphic functions are used. In HM, the inferred types are unambiguous, and every expression has a principal type. Type annotations make HM compatible with extensions where complete type inference is impossible, such as higher-rank polymorphism and type-level functions. However, programmers cannot use annotations to explicitly provide type arguments to polymorphic functions, as HM requires type instantiations to be inferred. We describe an extension to HM that allows visible type application. Our extension requires a novel type inference algorithm, yet its declarative presentation is a simple extension to HM. We prove that our extended system is a conservative extension of HM and admits principal types. We then extend our approach to a higher-rank type system with bidirectional type-checking. We have implemented this system in the Glasgow Haskell Compiler and show how our approach scales in the presence of complex type system features.

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“…We now extend the design of System HMV to include higher-rank polymorphism [17]. This extension allows function parameters to be used at multiple types.…”

Section: Higher-rank Type Systemsmentioning

confidence: 99%

Visible Type Application

Eisenberg

Weirich

Ahmed

2016

Lecture Notes in Computer Science

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“…We have seen that nested datatypes and polymorphic recursion are necessary for the implementation of generalized tries. Implementing tries for polymorphic datatypes, especially nested datatypes, places even greater demands on the type system: it requires rank-2 type signatures (McCracken, 1984), higher-order polymorphic datatypes (Jones, 1995), and higher-order polymorphic nests. Fortunately, all major Haskell system provide the necessary extensions.…”

Section: Lookupbinmentioning

confidence: 99%

Generalizing generalized tries

Hinze¹

2000

J. Funct. Prog.

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A trie is a search tree scheme that employs the structure of search keys to organize information. Tries were originally devised as a means to represent a collection of records indexed by strings over a fixed alphabet. Based on work by C. P. Wadsworth and others, R. H. Connelly and F. L. Morris generalized the concept to permit indexing by elements built according to an arbitrary signature. Here we go one step further, and define tries and operations on tries generically for arbitrary datatypes of first-order kind, including parameterized and nested datatypes. The derivation employs techniques recently developed in the context of polytypic programming and can be regarded as a comprehensive case study in this new programming paradigm. It is well known that for the implementation of generalized tries, nested datatypes and polymorphic recursion are needed. Implementing tries for first-order kinded datatypes places even greater demands on the type system: it requires rank-2 type signatures and second-order nested datatypes. Despite these requirements, the definition of tries is surprisingly simple, which is mostly due to the framework of polytypic programming.

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“…The algorithm given in [McCracken84], and our slg@ rithm, will fail on the above example. The reason is that the natural typing of (close (lambda (z) 2)) is WA, which cannot be applied to two types (8 and P), but only to a single type.…”

Section: 6mentioning

confidence: 99%

“…McCracken's system did not provide the generic let construct of ML, although it did attempt to support the automatic instantiation of explicitly typed polymorphic functions in application position. Both [McCracken84] and [Leivant83] attempted to provide automatic type abstraction in more general type systems, but these results are flawed (see sections 4.5 and 4.6).…”

Section: Previousmentioning

confidence: 99%

Type reconstruction with first-class polymorphic values

O’Toole

Gifford

1989

Proceedings of the ACM SIGPLAN 1989 Conference on Programming Language Design and Implementation

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We present the first type reconstruction system which combines the implicit typing of ML with the full power of the explicitly typed second-order polymorphic lambda calculus. The system will accept ML-style pre grams, explicitly typed programs, and programs that use explicit types for all first-class polymorphic values. We accomplish this flexibility by providing both generic and explicitly-quantified polymorphic types, as well as operators which convert between these two forms of polymorphism. This type reconstruction system is an integral part of the FX-89 programming language. We present a type reconstruction algorithm for the system. The type reconstruction algorithm is proven sound and complete with respect to the formal typing rules. 207

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The typechecking of programs with implicit type structure

Cited by 34 publications

References 3 publications

Visible Type Application

Visible Type Application

Generalizing generalized tries

Type reconstruction with first-class polymorphic values

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