We present four calculi for gradual typing: λB, based on the blame calculus of Wadler and Findler (2009); λC, based on the coercion calculus of Henglein (1994); and λT and λW, based on the three- some calculi with and without blame of Siek and Wadler (2010). We define translations from λB to λC, from λC to λT, and from λT to λW. We show each of the translations is fully abstract—far stronger correctness results than have previously appeared.
Philip Wadler is Professor of Theoretical Computer Science at the University of Edinburgh. He is an ACM Fellow and a Fellow of the Royal Society of Edinburgh, past chair of ACM SIGPLAN, past holder of a Royal Society-Wolfson Research Merit Fellowship, and a winner of the POPL Most Influential Paper Award. Previously, he worked or studied at Stanford, Xerox Parc, CMU, Oxford, Chalmers, Glasgow, Bell Labs, and Avaya Labs, and visited as a guest professor in Copenhagen, Sydney, and Paris. He has an h-index of 60, with more than 18,000 citations to his work according to Google Scholar. He contributed to the designs of Haskell, Java, and XQuery, and is a co-author of Introduction to Functional Programming (Prentice Hall, 1988), XQuery from the Experts (Addison Wesley, 2004) and Generics and Collections in Java (O’Reilly, 2006). He has delivered invited talks in locations ranging from Aizu to Zurich.