Interesting that you mention IJulia. My concern with it is that when you are trying to develop a new technique or algorithm, the idea of introducing extra layers of code running in another system (in this case IPython) seems like a lot to deal with. Maybe I'm just a wimp ;)
But it's not running through Python at all (as I understand it). The kernel is all implemented in Julia. It just uses the IPython frontend and architecture.
See this post on the implementation of IHaskell[1] for more details. My understanding is that IJulia uses the same concepts. Notably, when running IJulia, you can't even use %%magics to change back to Python mode.
1. http://andrew.gibiansky.com/blog/ipython/ipython-kernels/
(Also, it's firmly endorsed by the language creators. Stefan recently gave a talk using IJulia).
Thanks for the explanation and link. I think you are correct in that it doesn't appear to be using any Python. The demo I saw was given by Fernando Perez [http://www.youtube.com/watch?feature=player_embedded&v=F4rFu...] where he demonstrated a cross language example which, whilst technically impressive, wasn't something I felt I would attempt. Like I said I'm probably just a wimp.
First class arrays and array literals. It's a wonderful thing… like Matlab but very smartly designed.
The type dispatch system makes so much sense for mathematical work. It's simply how math is done. And Stefan Karpinski (co-creator) often compares it to linguistic grammars, too, which may be a stretch but I think there's some truth to it. It just feels right. And it makes things very extensible, right down to the core language.
And the core language is indeed mostly Julia itself. Compared to NumPy where things are often implemented in C or Cython. I've tried to hack on some Cython things in NumPy and was immediately turned off. It was so hard to debug and run interactively.
Julia's interactivity is wonderful. The IJulia project brings over some of the best user experience of NumPy (in my opinion)… which is not NumPy but IPython.
And the community is so very great and supporting. The package system is such a great asset and really lowers the bar to entry.