Ocaml hits most of the points on your list, if you can bring yourself to use a statically typed language.

> Support OO, imperative and functional paradigms

Yep. Objects aren't used all that often but they are fully supported and can do some things that are difficult in Java or C++ eg http://caml.inria.fr/pub/docs/manual-ocaml/manual007.html#to...

> Compile to fully optimized machine code with efficiency comparable to that of C

Not quite, but ocamlopt generates pretty damn fast code and, more importantly, has very predictable performance. Ocaml makes a pretty good systems language as demonstrated by the recent Mirage paper: http://anil.recoil.org/papers/2010-hotcloud-lamp.pdf

> Provide language support for numerical multidimensional arrays and linear algebra with a syntax comparable to Matlab

No, but this would make a good Jane Street summer project. Ocaml has extensible syntax via camlp4 and bindings to R, GSL and Matlab (no octave bindings for some reason).

> Support list comprehensions

Yes, as a syntax extension. http://batteries.forge.ocamlcore.org/doc.preview:batteries-b...

> Provide map,list and set types similar to those of Python

The syntax is not as nice but apart from that:

http://caml.inria.fr/pub/docs/manual-ocaml/libref/Map.Make.h...

http://caml.inria.fr/pub/docs/manual-ocaml/libref/Hashtbl.ht...

http://caml.inria.fr/pub/docs/manual-ocaml/libref/List.html

http://caml.inria.fr/pub/docs/manual-ocaml/libref/Set.S.html

> Support dynamic typing

Nope. You can circumvent the type system using Obj but its generally not advisable.

> Support optional static typing, and contracts

Static typing - yes. Contracts - see eg

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.157...

http://perso.eleves.bretagne.ens-cachan.fr/~dagand/opis/opis...

> Provide standard libraries with breadth of functionality comparable to those of Java but simpler API's (more like Python)

No. Ocaml Batteries is a start but nowhere near as broad as Python or Java.

> Provide a mechanism for efficient compile-time parametrization of algorithms, like C++ templates

Not just compile time specialization but multi-stage compilation via MetaOcaml. See eg http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.73....

> Support free-form (ie. whitespace independent) syntax

Yep, although there are some issues with the syntax eg dangling-else-like problems with nested matches.

> Provide a high quality cross-platform GUI toolkit with support for OpenGL

Well tested bingdings to Tk, Gtk and OpenGL.

> Provide an interactive graphical environment for experimentation and data analysis

None that I know of. I tend to use matplotlib and opengl interactively from the repl but its not up to the standards of mathematica etc.

> Provide a dataset abstraction similar to R data frames

I dont think so. I haven't used R much so I don't know exactly what features are missing.

> Be supported by a high-quality IDE and debugger

There are a couple of IDEs but none of them seem to be very well polished. Ocaml-mode and emacs is generally the way to go.

The time-travelling ocaml debugger is pretty amazing. You can also compile with support for gdb for low level debugging.