Affiliation:
1. University of Edinburgh, UK
2. National Institute of Informatics, Japan
3. University of Oxford, UK
Abstract
We present a construction which, under suitable assumptions, takes a model of Moggi’s computational λ-calculus with sum types, effect operations and primitives, and yields a model that is adequate and fully abstract. The construction, which uses the theory of fibrations, categorical glueing, ⊤⊤-lifting, and ⊤⊤-closure, takes inspiration from O’Hearn & Riecke’s fully abstract model for PCF. Our construction can be applied in the category of sets and functions, as well as the category of diffeological spaces and smooth maps and the category of quasi-Borel spaces, which have been studied as semantics for differentiable and probabilistic programming.
Funder
Royal Society University Research Fellow Enhancement Award
JST ERATO HASUO Metamathematics for Systems Design Project
Air Force Office of Scientific Research
Publisher
Association for Computing Machinery (ACM)
Subject
Safety, Risk, Reliability and Quality,Software
Reference58 articles.
1. A fully abstract game semantics for general references
2. Games and full completeness for multiplicative linear logic
3. Full Abstraction for PCF
4. J. Adamek H. Herrlich and G.E. Strecker. 2009. Abstract and Concrete Categories: The Joy of Cats. Dover Publications. isbn:9780486469348 lccn:2009010561 https://books.google.co.jp/books?id=rqT4PgAACAAJ J. Adamek H. Herrlich and G.E. Strecker. 2009. Abstract and Concrete Categories: The Joy of Cats. Dover Publications. isbn:9780486469348 lccn:2009010561 https://books.google.co.jp/books?id=rqT4PgAACAAJ
5. A characterization of lambda definability in categorical models of implicit polymorphism