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Partial type constructors: Or, making ad hoc datatypes less ad hoc
Jones, Mark P. Morris, J. Garrett Eisenberg, Richard A.
Jones, Mark P.
Morris, J. Garrett
Eisenberg, Richard A.
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Abstract
Functional programming languages assume that type constructors are total. Yet functional programmers know better: counterexamples range from container types that make limiting assumptions about their contents (e.g., requiring computable equality or ordering functions) to type families with defining equations only over certain choices of arguments. We present a language design and formal theory of partial type constructors, capturing the domains of type constructors using qualified types. Our design is both simple and expressive: we support partial datatypes as first-class citizens (including as instances of parametric abstractions, such as the Haskell Functor and Monad classes), and show a simple type elaboration algorithm that avoids placing undue annotation burden on programmers. We show that our type system rejects ill-defined types and can be compiled to a semantic model based on System F. Finally, we have conducted an experimental analysis of a body of Haskell code, using a proof-of-concept implementation of our system; while there are cases where our system requires additional annotations, these cases are rarely encountered in practical Haskell code.
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This work is licensed under a Creative Commons Attribution 4.0 International License.
Date
2020-01
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Association for Computing Machinery (ACM)
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Keywords
Theory of computation, Software and its engineering, Data types and structures, Type constructors, Parametric polymorphism
Citation
Mark P. Jones, J. Garrett Morris, and Richard A. Eisenberg. 2019. Partial type constructors: or, making ad hoc datatypes less ad hoc. Proc. ACM Program. Lang. 4, POPL, Article 40 (January 2020), 28 pages. DOI:https://doi.org/10.1145/3371108