Tuesday, April 10

Tutorial Day on Domain Theory

This year's Tutorial Day for MFPS is devoted to Domain Theory. This subject is a fundamental tool for modeling programming languages, and has also begun to offer new insights into other areas. Four lectures about domains will be given as part of the Tutorial Day:

• 9:00 - 10:45 Classical Domain Theory by Achim Jung (Birmingham)
  
  In this lecture, I intend to present some of the core elements of classical domain theory, such as the fixpoint property of continuous functions and the construction of solutions for recursive domain equations. The principal aim is to provide background and intuitions in the concrete setting of directed-complete posets for the more abstract approaches that will be presented in the subsequent lectures. No previous knowledge of domains will be assumed.
  
  
• 11 - 12:45 Beyond Classical Domain Theory by Alex Simpson (Edinburgh)
  
  Classical domain theory provides mathematical structures suitable for modelling many aspects of computation. However, it also has its limitations. Surprisingly, some of these limitations can be overcome by taking a more simple-minded approach to domains, according to which a domain is simply a (special) set, and a morphism of domains is just a set-theoretic function. There is, however, one complication: for such an approach to be consistent, one has to work within an intuitionistic set theory.
  
  The aim of this tutorial is to convey something of the naturalness, flexibility and power of the "synthetic" domain theory that results. Re naturalness, I will motivate the use of intuitionistic set theory from an intuitive point of view. (No prior experience of intuitionistic set theory will be assumed.) Re flexibility, I will describe the wide range of constructions that the synthetic approach supports, including free algebras (for modelling computational effects) and relationally parametric models of polymorphism. Re power, I will show how all this combines to provide a machinery capable of proving operational properties of programs.
  
  
• 12:45 - 2pm Lunch
  
  
• 2 - 3:45 Synthetic Computability by Andrej Bauer (Slovenia)
  
  In this tutorial we show how to elegantly develop the basics of computability theory with simple set-theoretic and domain-theoretic ideas and constructions. Computability is never mentioned explicitly, instead we work in an intuitionistic set theory extended with suitable (classically inconsistent) axioms. The usual theorems of computability theory are expressed as statements of set-theoretic, domain-theoretic and topological nature.
  
  Classical theorems of computability theory are then just interpretations of our theorems in an appropriate realizability model (which will be presented in a separate tutorial).
  
  
• 4 - 5:45 Realizability Models by Giuseppe Rosolini (Genoa)
  
  This final tutorial is intended to provide a mathematically sound interpretation for the powerful and elegant intuitionistic theories that have been put forth in the previous lectures.
  
  The model is an extension of Kleene's "realizability interpretation" for intuitionistic arithmetic and has been extensively studied in the form of the effective topos. We shall present the model in different, though equivalent, forms in an attempt to convey more than just a sound interpretation for the synthetic theories. Only knowledge of the basics of category theory will be required.
  
  If time permits, we shall also explain how (some of) the results of the previous tutorials have computational content when read in the model.

These tutorial lectures are being organized by Professors Bauer and Rosolini. No particular background is assumed, and the lectures will be accessible to graduate students as well as researchers in neighboring areas. The lectures are free of charge, and open to all interested parties. They will begin at 9am. The lectures will take place in the Dominion Learning Center Auditorium of the Audubon Zoo, which is located at the back of Audubon Park in uptown New Orleans.

Mathematical Foundations of Programming Semantics
Conference Program

Wednesday, April 11

Thursday, April 12

Friday, April 13

Saturday, April 14