Extending Typed Racket, Part 1

The Typed Racket team is pleased to announce a number of new additions to our system. We'll be writing a few blog posts about them, all of which you can read here.
This post begins with the core of the Typed Racket type system. The fundamental idea at the heart of Typed Racket is called occurrence typing. This is the technique that allows us to typecheck existing Racket programs without requiring rewrites. Here's a simple example:

(if (number? x) (add1 x) 0)

The typechecker can figure out from the use of number? that the second occurrence of x is always going to be a number. This simple form of occurrence typing is enough to take Typed Racket a long way. But because we want to be able to handle all the sophisticated reasoning that programmers are already using to write their Racket programs, we have been working on extending the system further.
The new design of our system is described in a paper, Logical Types for Untyped Languages, in the upcoming International Conference on Functional Programming. The introduction provides an overview that's acessible to any Racket programmer, but here's the key example:

(cond
  [(and (number? x) (string? y)) — 1 —]
  [(number? x)                   — 2 —]
  [else                          — 3 —])

In expression 1, we know that x is a number and y is a string. In 2, we know that x is a number and y is not a string, by the logical properties of and and cond. This form of logical reasoning is enabled by the new foundation of the system, and makes the entire system significantly more expressive.
All of these improvements are available in the current version of Racket.