Types for Proofs and Programs

This book constitutes the thoroughly refereed post-proceedings of the International Workshop of the TYPES Working Group, TYPES 2000, held in Durham, UK in December 2000. The 15 revised full papers presented were carefully reviewed and selected during two rounds of refereeing and revision. All current issues on type theory and type systems and their applications to programming, systems design, and proof theory are addressed.

Inhalt

Collection Principles in Dependent Type Theory.- Executing Higher Order Logic.- A Tour with Constructive Real Numbers.- An Implementation of Type:Type.- On the Logical Content of Computational Type Theory: A Solution to Curry's Problem.- Constructive Reals in Coq: Axioms and Categoricity.- A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals.- A Kripke-Style Model for the Admissibility of Structural Rules.- Towards Limit Computable Mathematics.- Formalizing the Halting Problem in a Constructive Type Theory.- On the Proofs of Some Formally Unprovable Propositions and Prototype Proofs in Type Theory.- Changing Data Structures in Type Theory: A Study of Natural Numbers.- Elimination with a Motive.- Generalization in Type Theory Based Proof Assistants.- An Inductive Version of Nash-Williams' Minimal-Bad-Sequence Argument for Higman's Lemma.