Lambda the Ultimate

A Dialogue on Infinity, between a mathematician and a philosopher. Alexandre Borovik and David Corfield.

A new blog... From the first post:

The project concentrates on one of the principal purposes of the Exploring the Infinite Program:

To understand the nature of and the role played by conceptualizations of infinity in mathematics.

It will be shaped as a dialogue between a mathematician (AB) and a philosopher (DC) and will address one of the central paradoxes of mathematics:

why are most uses of infinity in mathematics restricted to the recycling of a small number of “canonical” and ubiquitous structures?

...To put the study of infinity on a firm basis, we first have to discuss the issue of the identity and “sameness” of mathematical objects: infinity of what?

This is pretty far out for LtU, but I suspect it will interest some more philosophically inclined readers. They will look at a number of disciplines, including computer science.

(I feel like maybe even "Theory" is not theoretical for this. Therefore I am also calling it "Fun".)

Generics of a Higher Kind. Adriaan Moors, Frank Piessens, and Martin Odersky.

With Java 5 and C# 2.0, first-order parametric polymorphism was introduced in mainstream object-oriented programming languages under the name of generics. Although the first-order variant of generics is very useful, it also imposes some restrictions: it is possible to abstract over a type, but the resulting type constructor cannot be abstracted over. This can lead to code duplication. We removed this restriction in Scala, by allowing type constructors as type parameters and abstract types. This paper presents the design and implementation of the resulting type constructor polymorphism. It combines type constructor polymorphism with implicit parameters to yield constructs similar to, and at times more expressive than, Haskell’s constructor type classes. The paper also studies interactions with other object-oriented language constructs, and discusses the gains in expressiveness.

Many readers will already be aware that Scala has added support for higher-kinded generics, related to Haskell's type constructor classes. I believe Scala is the first language to provide this capability in an OO "generics" framework. This ECOOP submission presents this work, with many practical examples.

(Consider this penance for my last post...)