Abstract
In a recent article [L. Birkedal, R. E. Møgelberg, and R. L. Petersen. Parametric domain-theoretic models of linear Abadi & Plotkin logic. Technical Report TR-2005-57, IT University of Copenhagen, February 2005] the first two authors and R.L. Petersen have defined a notion of parametric LAPL-structure. Such structures are parametric models of the equational theory PILLY, a polymorphic intuitionistic / linear type theory with fixed points, in which one can reason using parametricity and, for example, solve a large class of domain equations [L. Birkedal, R. E. Møgelberg, and R. L. Petersen. Parametric domain-theoretic models of linear Abadi & Plotkin logic. Technical Report TR-2005-57, IT University of Copenhagen, February 2005, L Birkedal, R. E. Møgelberg, and R. L. Petersen. Parametric domain-theoretic models of polymorphic intuitionistic / linear lambda calculus. In Proceedings of the Twenty-first Conference on the Mathematical Foundations of Programming Semantics, 2005. To appear].Based on recent work by Simpson and Rosolini [G. Rosolini and A. Simpson. Using synthetic domain theory to prove operational properties of a polymorphic programming language based on strictness. Manuscript, 2004] we construct a family of parametric LAPL-structures using synthetic domain theory and use the results of loc. cit. and results about LAPL-structures to prove operational consequences of parametricity for a strict version of the Lily programming language. In particular we can show that one can solve domain equations in the strict version of Lily up to ground contextual equivalence.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have