Polymorphic variants in Haskell

Kagawa, Keiichiro

doi:10.1145/1159842.1159848

Cited by 7 publications

(2 citation statements)

References 21 publications

(21 reference statements)

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“…Choice types are similar to variant types [10], which are used to uniformly manipulate heterogeneous collection of types. A significant difference between the two is that choices (at the expression level) contain all of the information needed for inferring their corresponding choice type.…”

Section: Related Workmentioning

confidence: 99%

An error-tolerant type system for variational lambda calculus

2012

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Conditional compilation and software product line technologies make it possible to generate a huge number of different programs from a single software project. Typing each of these programs individually is usually impossible due to the sheer number of possible variants. Our previous work has addressed this problem with a type system for variational lambda calculus (VLC), an extension of lambda calculus with basic constructs for introducing and organizing variation. Although our type inference algorithm is more efficient than the brute-force strategy of inferring the types of each variant individually, it is less robust since type inference will fail for the entire variational expression if any one variant contains a type error. In this work, we extend our type system to operate on VLC expressions containing type errors. This extension directly supports locating ill-typed variants and the incremental development of variational programs. It also has many subtle implications for the unification of variational types. We show that our extended type system possesses a principal typing property and that the underlying unification problem is unitary. Our unification algorithm computes partial unifiers that lead to result types that (1) contain errors in as few variants as possible and (2) are most general. Finally, we perform an empirical evaluation to determine the overhead of this extension compared to our previous work, to demonstrate the improvements over the brute-force approach, and to explore the effects of various error distributions on the inference process.

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Section: Related Workmentioning

confidence: 99%

An error-tolerant type system for variational lambda calculus

2012

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“…Choice types are in some ways similar to variant types [Kagawa 2006]. Variant types support the uniform manipulation of a heterogeneous collection of types.…”

Section: Programming Languages and Type Systemsmentioning

confidence: 99%

Extending Type Inference to Variational Programs

Sheng

Erwig

Walkingshaw

2014

ACM Trans. Program. Lang. Syst.

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Through the use of conditional compilation and related tools, many software projects can be used to generate a huge number of related programs. The problem of typing such variational software is difficult. The brute-force strategy of generating all variants and typing each one individually is: (1) usually infeasible for efficiency reasons and (2) produces results that do not map well to the underlying variational program. Recent research has focused mainly on efficiency and addressed only the problem of type checking. In this work we tackle the more general problem of variational type inference and introduce variational types to represent the result of typing a variational program. We introduce the variational lambda calculus (VLC) as a formal foundation for research on typing variational programs. We define a type system for VLC in which VLC expressions are mapped to correspondingly variational types. We show that the type system is correct by proving that the typing of expressions is preserved over the process of variation elimination, which eventually results in a plain lambda calculus expression and its corresponding type. We identify a set of equivalence rules for variational types and prove that the type unification problem modulo these equivalence rules is unitary and decidable; we also present a sound and complete unification algorithm. Based on the unification algorithm, the variational type inference algorithm is an extension of algorithm W . We show that it is sound and complete and computes principal types. We also consider the extension of VLC with sum types, a necessary feature for supporting variational data types, and demonstrate that the previous theoretical results also hold under this extension. Finally, we characterize the complexity of variational type inference and demonstrate the efficiency gains over the brute-force strategy.

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Combinators and type-driven transformers in Objective Caml

Boulytchev

2015

Science of Computer Programming

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Polymorphic variants in Haskell

Cited by 7 publications

References 21 publications

An error-tolerant type system for variational lambda calculus

An error-tolerant type system for variational lambda calculus

Extending Type Inference to Variational Programs

Combinators and type-driven transformers in Objective Caml

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