{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/really-natural-linear-indexed-type-checking","title":"Really Natural Linear Indexed Type Checking","arxiv_id":"1503.04522","date":"2015-03-16","proceeding":null,"authors":["Arthur Azevedo de Amorim","Emilio Jesús Gallego Arias","Marco Gaboardi","Justin Hsu"],"abstract":"Recent works have shown the power of linear indexed type systems for enforcing complex program properties. These systems combine linear types with a language of type-level indices, allowing more fine-grained analyses. Such systems have been fruitfully applied in diverse domains, including implicit complexity and differential privacy. A natural way to enhance the expressiveness of this approach is by allowing the indices to depend on runtime information, in the spirit of dependent types. This approach is used in DFuzz, a language for differential privacy. The DFuzz type system relies on an index language supporting real and natural number arithmetic over constants and variables. Moreover, DFuzz uses a subtyping mechanism to make types more flexible. By themselves, linearity, dependency, and subtyping each require delicate handling when performing type checking or type inference; their combination increases this challenge substantially, as the features can interact in non-trivial ways. In this paper, we study the type-checking problem for DFuzz. We show how we can reduce type checking for (a simple extension of) DFuzz to constraint solving over a first-order theory of naturals and real numbers which, although undecidable, can often be handled in practice by standard numeric solvers.","url_abs":"https://arxiv.org/abs/1503.04522v1","url_pdf":"https://arxiv.org/pdf/1503.04522v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"really-natural-linear-indexed-type-checking","repo_url":"https://github.com/ejgallego/dfuzz","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"really-natural-linear-indexed-type-checking","repo_url":"https://github.com/junewunder/bunched-fuzz","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}