Realizability models for a linear dependent PCF

Recently, Dal Lago and Gaboardi have proposed a type system, named d`PCF as a framework for implicit computational complexity. d`PCF is a non-standard type system for PCF programs which is relatively complete with respect to complexity properties thanks to the use of linear types inspired by Bounded linear logic and dependent types à la Dependent ML. In this work, we adapt the framework of quantitative realizability in order to obtain a model for d`PCF. The quantitative realizability model aims at a better understanding of d`PCF type decorations and at the same time giving an abstract semantical proof of intensional soundness.