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Types and Semantics for Extensible Data Types

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Programming Languages and Systems (APLAS 2023)

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Abstract

Developing and maintaining software commonly requires (1) adding new data type constructors to existing applications, but also (2) adding new functions that work on existing data. Most programming languages have native support for defining data types and functions in a way that supports either (1) or (2), but not both. This lack of native support makes it difficult to use and extend libraries. A theoretically well-studied solution is to define data types and functions using initial algebra semantics. While it is possible to encode this solution in existing programming languages, such encodings add syntactic and interpretive overhead, and commonly fail to take advantage of the map and fold fusion laws of initial algebras which compilers could exploit to generate more efficient code. A solution to these is to provide native support for initial algebra semantics. In this paper, we develop such a solution and present a type discipline and core calculus for a language with native support for initial algebra semantics.

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Notes

  1. 1.

    This intuition is made formal in the extended version [33, Theorem 1].

  2. 2.

    For presentational purposes, we omit some necessary restrictions on sizes here. The extended version [33, §4] defines these restrictions and the precise semantics.

  3. 3.

    Similar models of type expressions with mixed variance appear, for example, when considering Mendler-style inductive types [37], or in the object calculus semantics by Glimming and Ghani [17].

  4. 4.

    Here, we mean “\(\beta \)-reduction” in the more general sense of simplifying an application of an elimination form to an introduction form.

  5. 5.

    This property implies what Devesas Campos and Levy [15] call soundness of the denotational model with respect to the operational model. Their soundness property is about a big-step relation; ours is small-step.

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Acknowledgements

This research was partially funded by the NWO VENI Composable and Safe-by-Construction Programming Language Definitions project (VI.Veni.192.259).

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  1. Delft University of Technology, Delft, The Netherlands

    Cas van der Rest & Casper Bach Poulsen

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  1. Seoul National University, Seoul, Korea (Republic of)

    Chung-Kil Hur

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van der Rest, C., Poulsen, C.B. (2023). Types and Semantics for Extensible Data Types. In: Hur, CK. (eds) Programming Languages and Systems. APLAS 2023. Lecture Notes in Computer Science, vol 14405. Springer, Singapore. https://doi.org/10.1007/978-981-99-8311-7_3

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