Tries, a form of string-indexed look-up structure, are generalized, in a manner first discovered by Wadsworth, to permit indexing by terms built according to an arbitrary signature. The construction is parametric with respect to the type of data to be stored as values; this is essential, because the recursion that defines tries appeals from one value type to others. ‘Trie’ (for any fixed signature) is then a functor, and the corresponding look-up function is a natural isomorphism. The trie functor is in principle definable by the ‘initial fixed point’ semantics of Smyth and Plotkin. We simplify the construction, however, by introducing the ‘category-cpo’, a class of category within which calculations can retain some domain-theoretic flavor. Our construction of tries extends easily to many-sorted signatures.

Article Free Access Share on A Metalanguage for interactive proof in LCF Authors: M. Gordon University of Edinburgh University of EdinburghView Profile , R. Milner University of Edinburgh University of EdinburghView Profile , L. Morris Syracuse University Syracuse UniversityView Profile , M. Newey Australian National University Australian National UniversityView Profile , C. Wadsworth University of Edinburgh University of EdinburghView Profile Authors Info & Claims POPL '78: Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languagesJanuary 1978Pages 119–130https://doi.org/10.1145/512760.512773Published:01 January 1978Publication History 55citation684DownloadsMetricsTotal Citations55Total Downloads684Last 12 Months96Last 6 weeks5 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

The purpose of this paper is to advise an approach (and to support that advice by discussion of an example) towards achieving a goal first announced by John McCarthy: that compilers for higher-level programming languages should be made completely trustworthy by proving their correctness. The author believes that the compiler-correctness problem can be made much less general and better-structured than the unrestricted program-correctness problem; to do so will of course entail restricting what a compiler may be.