Embedding by Unembedding #244
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Embedding by Unembedding
Embedding is a language development technique that implements the object language as a library in a host language. There are many advantages of the approach, including being lightweight and the ability to inherit features of the host language. A notable example is the technique of HOAS, which makes crucial use of higherorder functions to represent abstract syntax trees with binders. Despite its popularity, HOAS has its limitations. We observe that HOAS struggles with semantic domains that cannot be naturally expressed as functions, particularly when open expressions are involved. Prominent examples of this include incremental computation and reversiblebidirectional languages. In this paper, we pinpoint the challenge faced by HOAS as a mismatch between the semantic domain of host and object language functions, and propose a solution. The solution is based on the technique of unembedding , which converts from the finallytagless representation to de Bruijnindexed terms with strong correctness guarantees. We show that this approach is able to extend the applicability of HOAS while preserving its elegance. We provide a generic strategy for Embedding by Unembedding, and then demonstrate
Matsuda, Kazutaka, et al. “Embedding by Unembedding. Proceedings of the ACM on Programming Languages, vol. 7, no. ICFP, Aug. 2023, pp. 147. Crossref, https://doi.org/10.1145/3607830.
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