Synthetic Domain Theory and Models of Linear Abadi & Plotkin Logic

In a recent article [4] 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 [4,5]. Based on recent work by Simpson and Rosolini [22] we construct a family of parametric LAPLstructures using synthetic domain theory and use the results of loc. cit. and results about LAPLstructures 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.