Isomorphisms of Types

1. Front Matter

   Pages i-10

   PDF

2. Introduction

   • Roberto Di Cosmo

   Pages 11-55

3. Confluence Results

   • Roberto Di Cosmo

   Pages 57-84

4. Strong normalization for subsystems of λ² βηπ✻

   • Roberto Di Cosmo

   Pages 85-99

5. First-Order Isomorphic Types

   • Roberto Di Cosmo

   Pages 101-117

6. Second-Order Isomorphic Types

   • Roberto Di Cosmo

   Pages 119-163

7. Isomorphisms for ML

   • Roberto Di Cosmo

   Pages 165-204

8. Related works, Future perspectives

   • Roberto Di Cosmo

   Pages 205-214

9. Back Matter

   Pages 215-235

   PDF

This is a book about isomorphisms 0/ types, arecent difficult research topic in type theory that turned out to be able to have valuable practical applications both for programming language design and far more human­ centered information retrieval in software libraries. By means of a deep study of the syntax of the now widely known typed A-ca1culus, it is possible to identify some simple equations between types that on one hand allow to improve the design of the ML language, and on the other hand provide the basis for building radically new information retrieval systems for functional software libraries. We present in this book both the theoretical aspects of these researches and a fully functional implementation of some of their applications in such a way to provide interesting material both for the theoretician looking for proofs and for the practitioner interested in implementation details. In order to make it possible for these different types of readers to use this book effectively, some special signs are used to designate material that is particularly technical or applied or that represents a digression. When the symbol appears at the beginning of a section or a subsection, it warns that the material contained in such section is particularly technical with respect to the general level of the chapter or section where it is located. This material is generally reserved to theoreticians and does not need to be read by the casual reader.

• Mathematica
• Permutation
• calculus
• logic
• mathematical logic
• optimization
• programming
• programming language

• Ecole Normale Supérieure, LIENS-DMI, Paris Cedex 05, France

  Roberto Cosmo

Policies and ethics