Introduction to the book

This introductory chapter sets the stage for the following chapters. It first discusses the issue of foundational systems for constructive mathematical practice, and expresses the desire for a closer interplay between foundations and practice of constructive mathematics as they seem to have parted from each other in more recent times. It observes that a closer connection is already witnessed by some of the contributions to this book. With the intent of fostering the discussion on foundations, it suggests some ideas on (weak) foundational systems for constructive mathematics. Finally, it recalls the basic steps in the fields of constructive set and type theory, formal topology, and constructive analysis, and gives a presentation of the contributions in the volume to each field.