There are several paths:

1. JS as an assembly language. This is what emscripten[0], a LLVM bytecode-to-JS does, by following the asm.js specification[1]. This is for CPU-intensive tasks, not DOM manipulation. You can use any language that has a LLVM frontend.

2. JS as a target language, from a specific, new language. Those include cleaner variants that keep the same semantics (CoffeeScript, TypeScript, maybe Dart, ...) or more innovative ones, such as Elm[2], which is written in Haskell too. I'd say that a big innovation that makes the life easier is FRP (which is at the heart of Elm or React.js).

I fail yet to see what advantages PureScript brings compared to Elm.

0: https://github.com/kripken/emscripten 1: http://asmjs.org 2: http://elm-lang.org/