A Polymorphic Lambda-Calculus with Sized Higher-Order Types Summary: A Polymorphic Lambda-Calculus with Sized Higher-Order Types Andreas Abel June 19, 2006 2 Contents 1 Introduction 7 1.1 Why Termination? . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Approaches to Termination . . . . . . . . . . . . . . . . . . . . . 9 1.3 Why Type-Based Termination Matters . . . . . . . . . . . . . . . 10 1.4 Informal Account of Type-Based Termination . . . . . . . . . . . 12 1.4.1 A Semantical Account of Type-Based Termination . . . . 12 1.4.2 From Semantics to Syntax . . . . . . . . . . . . . . . . . . 14 1.5 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Sized Higher-Order Subtyping 19 2.1 Constructors and Polarized Kinds . . . . . . . . . . . . . . . . . 19 2.1.1 Polarities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.2 Kinds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.3 Constructors . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1.4 Kinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Collections: Computer Technologies and Information Sciences