“Concepts ” are an essential language feature needed to support generic programming in the large. Concepts allow for succinct expression of bounds on type parameters of generic algorithms, enable systematic organization of problem domain abstractions, and make generic algorithms easier to use. In this paper we formalize the design of a type system and semantics for concepts that is suitable for non-type-inferencing languages. Our design shares much in common with the type classes of Haskell, though our primary influence is from best practices in the C ++ community, where concepts are used to document type requirements for templates in generic libraries. The technical development in this paper defines an extension to System F and a type-directed translation from the extension back to System F. The translation is proved sound; the proof is written in the human readable but machine checkable Isar language and has been automatically verified by the Isabelle proof assistant. This document was generated directly from the Isar theory files using Isabelle’s support for literate proofs.

First and foremost I thank my parents for all their love and for teaching me to enjoy learning. I especially thank my wife Katie for her support and understanding through this long and sometimes stressful process. I also thank Katie for insisting on good error messages for G! My advisor, Andrew Lumsdaine, deserves many thanks for his support and guidance and for keeping the faith as I undertook this long journey away from scientific computing and into the field of programming languages. I thank my thesis committee: R. Kent Dybvig, Daniel P. Friedman, Steven D. Johnson, and Amr Sabry for their advice and encouragement. A special thanks goes to Ronald Garcia, Christopher Mueller, and Douglas Gregor for carefully editing and catching the many many times when I accidentally skipped over the important stuff. Thanks to Jaakko and Jeremiah for hours of stimulating discussions and arguments concerning separate compilation and concept-based overloading. Thanks to David Abrahams for countless hours spent debating the merits of one design over another while jogging through the hinterlands of Norway. Thanks to Alexander Stepanov and David Musser for getting all this started, and thank you for the encouragement over the years. Thanks to Matthew Austern, his book Generic Programming in the STL was both an inspiration

Abstract. The past decade of experience has demonstrated that the generic programming methodology is highly effective for the design, implementation, and use of large-scale software libraries. The fundamental principle of generic programming is the realization of interfaces for entire sets of components, based on their essential syntactic and semantic requirements, rather than for any particular components. Many programming languages have features for describing interfaces between software components, but none completely support the approach used in generic programming. We have recently developed G, a language designed to provide first-class language support for generic programming and large-scale libraries. In this paper, we present an overview of G and analyze the interdependence between language features and libraries design in light of a complete implementation of the Standard Template Library using G. In addition, we discuss important issues related to modularity and encapsulation in large-scale libraries and how language support for validation of components in isolation can prevent many common problems in component integration. 1

Generics, in its basic form, is a programming language feature that enables the parameterization of software components with respect to type. For example, a List class can be parameterized on the type of its elements, enabling the same List class to be used for lists of integers, lists of strings, etc. Generics, in its more advanced form, enables parameterization with respect to types and operations on those types. The advanced form of generics facilitates generic

C++0x is the working title for the revision of the ISO standard of the C++ programming language that was originally planned for release in 2009 (but that will probably appear in 2011). The largest language extension in C++0x was “concepts”, that is, a collection of features for constraining template parameters. In September of 2008, the C++ standards committee voted the concepts extension into C++0x, but then in July of 2009, the committee voted the concepts extension back out of C++0x. This article is my account of the technical challenges and debates within the “concepts” effort in the years 2003 to 2009.