Ebook: Types for Proofs and Programs: International Workshop, TYPES 2000 Durham, UK, December 8–12, 2000 Selected Papers

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.

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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.
Content:
Front Matter....Pages I-VIII
Collection Principles in Dependent Type Theory....Pages 1-23
Executing Higher Order Logic....Pages 24-40
A Tour with Constructive Real Numbers....Pages 41-52
An Implementation of Type:Type....Pages 53-62
On the Logical Content of Computational Type Theory: A Solution to Curry’s Problem....Pages 63-78
Constructive Reals in Coq: Axioms and Categoricity....Pages 79-95
A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals....Pages 96-111
A Kripke-Style Model for the Admissibility of Structural Rules....Pages 112-124
Towards Limit Computable Mathematics....Pages 125-144
Formalizing the Halting Problem in a Constructive Type Theory....Pages 145-159
On the Proofs of Some Formally Unprovable Propositions and Prototype Proofs in Type Theory....Pages 160-180
Changing Data Structures in Type Theory: A Study of Natural Numbers....Pages 181-196
Elimination with a Motive....Pages 197-216
Generalization in Type Theory Based Proof Assistants....Pages 217-232
An Inductive Version of Nash-Williams’ Minimal-Bad-Sequence Argument for Higman’s Lemma....Pages 233-242
Back Matter....Pages 243-243

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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.
Content:
Front Matter....Pages I-VIII
Collection Principles in Dependent Type Theory....Pages 1-23
Executing Higher Order Logic....Pages 24-40
A Tour with Constructive Real Numbers....Pages 41-52
An Implementation of Type:Type....Pages 53-62
On the Logical Content of Computational Type Theory: A Solution to Curry’s Problem....Pages 63-78
Constructive Reals in Coq: Axioms and Categoricity....Pages 79-95
A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals....Pages 96-111
A Kripke-Style Model for the Admissibility of Structural Rules....Pages 112-124
Towards Limit Computable Mathematics....Pages 125-144
Formalizing the Halting Problem in a Constructive Type Theory....Pages 145-159
On the Proofs of Some Formally Unprovable Propositions and Prototype Proofs in Type Theory....Pages 160-180
Changing Data Structures in Type Theory: A Study of Natural Numbers....Pages 181-196
Elimination with a Motive....Pages 197-216
Generalization in Type Theory Based Proof Assistants....Pages 217-232
An Inductive Version of Nash-Williams’ Minimal-Bad-Sequence Argument for Higman’s Lemma....Pages 233-242
Back Matter....Pages 243-243
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