Summary: A Polymorphic Lambda­Calculus
with Sized Higher­Order Types
Andreas Abel
June 19, 2006

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Contents
1 Introduction 7
1.1 Why Termination? . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Approaches to Termination . . . . . . . . . . . . . . . . . . . . . 9
1.3 Why Type­Based Termination Matters . . . . . . . . . . . . . . . 10
1.4 Informal Account of Type­Based Termination . . . . . . . . . . . 12
1.4.1 A Semantical Account of Type­Based Termination . . . . 12
1.4.2 From Semantics to Syntax . . . . . . . . . . . . . . . . . . 14
1.5 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Sized Higher­Order Subtyping 19
2.1 Constructors and Polarized Kinds . . . . . . . . . . . . . . . . . 19
2.1.1 Polarities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.2 Kinds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München

Collections: Computer Technologies and Information Sciences