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A platform for Java, Scala, Groovy and jRuby would be implemented in what language?

As an experiment I am working on a small platform for Java applications (client server, P2P etc.) which I would like to be able to use from both Java and Scala. And possibly also from Groovy, jRuby etc.
I know that Scala can call easily into Java, but that Java cannot as easily call back into Scala. I don't know how this is working in jRuby and Groovy.
My initial thought was to implement the platform in Java, and then see if I could make it available to other languages. However, the platform may include starting threads which call components that implement certain Java interfaces. Would it be possible to pass e.g. a factory implemented in Scala, but which implements a Java interface, to a Java component and have that Java component call the Scala factory?
What are your recommendations in general for implementing such a cross language platform?

I am by no means an expert and have never done such a cross-language project (just minor Java/Scala).
But I would suggest implementing it in the language:
you know best
makes you most productive
ensures the most maintainability
In my case it would be Scala.
So what I would do is define the API in the form of Java interfaces, which I would then implement in Scala (probably I would need to convert Scala/Java collections back-and-forth, but that would be an implementation detail).
That way you make sure that other JVM languages can interact with your API, and you implement it in whatever language you are best.

Java can call Scala as easy at the other way around,
With eclipse you need to install 'Scala IDE' from the 'eclipse market place'
and configure the compiler to 'Scala Then Java' option in Properties->'Scala Compiler'-> 'Build Manager'-> compileorder.
P.s. you also need to add Scala nature to the project.

Would it be possible to pass e.g. a factory implemented in Scala, but which implements a Java interface, to a Java component and have that Java component call the Scala factory?
Even if it were so, switching to Scala would not solve the problem, as then jRuby would have even more problems to access that component.
Actually, all listed languages declare interoperability with Java, but not with other languages. So first design goal is, your platform should be Java-compatible in all its API, though some components could be written in other languages - but so that it is cannot be seen by API users. The easiest way to make it so is to write all in Java. Besides, I recommend Java because features of "more advanced" languages has their reverse side - one innocent-looking line of code can consume enormous amounts of CPU time or memory.

Java without JVM

Just wondering if there are any Java implementations that work without a JVM. The reason I'm interested is, well, simply because I'm curious, and I was wondering if there were any "lightweight" Java implementations (without all the Sun libs attached).
I'm also interested in embedding Java in C++, but embedding the JVM in C++ seems rather ridiculous to me. I just want to exploit some of the Java language features in my C++ apps, but not exploit all the frivolous Java APIs.
EDIT:
I see from a lot of the answers I've gotten that I need to clarify...
I recently got in to developing node.js applications, which uses JavaScript. JavaScript in istelf is a language spec, it doesn't automatically come with the DOM, window.open, etc., although it did for a while. I'm wondering if there's something similar to Google's v8, except not for JavaScript, but for Java. In the end, I don't care if I can't write Hello World apps with it, I just want to be able to embed Java in a C++ application the way I can embed JavaScript in a C++ application with v8 or SpiderMonkey. If I could do that, then I could implement console output in C/C++ and then make that implementation callable from Java.

Do you want the Java VM alone without the API(STandard Library) ?
The JRE is composed by the JVM (Virtual MAchine) and the Standard Library, I have doubt that you can find a java implementation without the JVM ... You could find a compiler that compile java source code into native code(take a look at GCJ), but not a Java implementation without the VM.
Take a look at this wikipedia page to see some alternative Java implementations .

There's GCJ (GNU Compiler for Java), but the project has been deprecated since OpenJDK was open sourced.

there are light weight java processors designed for use in small devices for example JOP

As others have hinted, the "JVM" is the mechanism that knows how to load classes, interpret "bytecodes", and manage storage. It does not inherently include any of the java.lang... stuff, except that a few classes (String, Class, et al) are needed to represent classes and other basic data structures in the JVM.
As a result, Java without a JVM is just a bunch of meaningless bits.
There are (or were) compiled versions of Java that do/did not need the interpreter (though a reasonably compact interpreter is quite easy to build). A primitive class loader and some sort of storage management are still necessary, but class loading can be kept simple and for short-lived apps (or those that live with special restrictions) the storage manager need not do garbage collection.
As pstanton suggests, there are "lightweight" Java (or "Java-like") implementations that are suited for small devices.

IMHO, You need to re-exampine what it is you really want.
Java runtime consists of two main components
The JVM to run the code
The standard libraries which come with it.
You suggest you want to use Java, but you don't really have anything left without these.
For example, you cannot even write a "hello world" program without the libraries as String is a class in the JDK.

Best integrated scripting language for Java? (Stacktraces and debug)

I have a need for providing code snippets at runtime.
For this to work well, I basically need to call into the scripting language, and back into Java. For this to be usable in a debug scenario StackTraces must be usable too (so methods and linenumbers go directly to the script source like in modern JSP-pages) and Exceptions must bubble up correctly.
What scripting languages - where the source is read at runtime - can provide this? JSR-223 support is a bonus.

I think JRuby is best choice because:
Its performance as a scripting language is good.
It can execute in two mode (Compiled, Interpreted).
It supports Ruby on Rails and you can use JRuby for Rails applications in production environments.
You can invoke the classes of the Java Platform easily without any restriction.

I think Groovy would be the perfect fit in your case given it's super similarity and ease of integration with Java not to mention that it's pretty much the most mature JVM language out there with excellent support from the likes of SpringSource.
As an example of JSR support, Groovy has it.

JVM/CLR Source-compatible Language Options

I have an open source Java database migration tool (http://www.liquibase.org) which I am considering porting to .Net.
The majority of the tool (at least from a complexity side) is around logic like "if you are adding a primary key and the database is Oracle use this SQL. If database is MySQL use this SQL. If the primary key is named and the database is Postgres use this SQL".
I could fork the Java codebase and covert it (manually and/or automatically), but as updates and bug fixes to the above logic come in I do not want to have to apply it to both versions. What I would like to do is move all that logic into a form that can be compiled and used by both Java and .Net versions naively.
The code I am looking to convert does not contain any advanced library usage (JDBC, System.out, etc) that would vary significantly from Java to .Net, so I don't think that will be an issue (at worst it can be designed around).
So what I am looking for is:
A language in which I can code common parts of my app in and compile it into classes usable by the "standard" languages on the target platform
Does not add any runtime requirements to the system
Nothing so strange that it scares away potential contributors
I know Python and Ruby both have implementations on for the JVM and CLR. How well do they fit my requirements? Has anyone been successful (or unsuccesful) using this technique for cross-platform applications? Are there any gotcha's I need to worry about?

Check out the Fantom programming language. It has its own Java-like/C#-like syntax but can target either the Java VM or .NET CLR.
Their "Why Fantom" page gives a high-level overview of their approach to portability versus dynamic languages running on a VM.

You might have some luck using IKVM.NET. I'm not sure on its exact status, but it's worth a try if you're insistent on running Java code on the .NET Framework. It includes a .NET implementation of the Java base class library, so it seems reasonably complete.
The only other option I might suggest is porting the code to the J# language, a full .NET language (although not first class in the sense that C# or VB.NET is). The language was designed so that the differences with Java were minimal.

If you are thinking about an emdedded approach, you might look at Lua.

Accessing .NET/dll libraries/components from Java?

Are there inexpensive or free gateways from .NET to Java? I'm looking at some data acquisition hardware which has drivers for C/C++ and .NET -- I really don't want to do any programming in .NET.
Update: I haven't done what I originally wanted to do, but I've done something similar, using JNA to encapsulate some functions from a DLL, in order to control a USB hardware device from Java. (the DLL comes from the device manufacturer) It works really nicely. Thanks!

You could also try to use JNA for accessing the native library. JNA provides Java programs easy access to native shared libraries (DLLs on Windows) without writing anything but Java code—no JNI or native code is required. If their API is fairly straight foward, this might be the path of least resistance.
See their getting started guide where they call some native code (printf and GetSystemTime).

Well, there's JNBridge and EZ JCom, just from a Google search.
You could also use IKVM which is a slightly different approach.
(Any reason for not wanting to learn .NET, out of interest? It's a nice platform, and C# is a lovely language...)

If they have C++ versions of the drivers then you could write a wrapper around it using JNI and then load that in Java. JNI can be a bit of a pain, but it would let you use the C++ version of their drivers and not have to deal with .Net at all if you don't want.

I am partial to the recommendation to jump in the deep end with C# since it is so similar to Java. I did this and used IKVM to compile my favorite Java libs. to .NET assemblies and you get [nearly] all the core java runtime classes to boot, so if you tire of trying to find just the right C# collection type, you can always go back to java.util. (No generic collections though. Not sure why.)
Depending on what platform you're on, you have several choices for free IDEs too. For windows you can get Visual Studio Express for free but I also use SharpDevelop. You can also get the Mono IDE on Linux (and a few flavours of Unix, I think ?).
The C# learning curve is shallow if you already know Java. I only blew off 1.5 limbs on landmines that came out of nowhere for reasons I still don't understand, but workarounds were easy to come by. The worst thing about it was the darn developer docs which are AWFUL on account of being so slow. I really miss the snappiness of JavaDoc. Not only are the online docs incredibly slow, the problem is compounded by someones's iffy decision to put class summaries, constructors and methods/properties all on seperate pages so it just takes forever. Someone said to get the docs installer and install docs locally for a slightly improved experience. Not a bad idea I suppose.

I am author of jni4net, open source interprocess bridge between JVM and CLR. It's build on top of JNI and PInvoke. No C/C++ code needed. I hope it will help you.

If you have a Java application, the JNI mentioned by the others will be the way to go. You write some wrapper classes, and that's it.
If writing the wrappes is a too big task (depending on the number of methods you have to wrap), have a look at SWIG . I think it generates wrappers automatically, but I never actually used it.
If you want to code in the Java language, but you don't care if your program will run on the JRE/JVM, then you might as well use Microsoft J#. Basically, it's writing Java-Code wich is compiled to .NET-Bytecode and can use the .NET classes of the driver as well as your existing Java classes. With J# you will run into problems if your existing Java-code is newer than Java 1.4, look at this question on how to solve them.
From that point on, you could later add code in J#, C# or any other .NET language. However, you won't get back to the JRE/JVM easily.