Statistics function for Lua? - math

I'm trying to calculate a Student-t probability. I really need the incomplete beta function for this, but I can't find any good function in Lua. Does it exist?
I've ported over the code from Numerical Recipes in C, and it works, but it's not open source license. I need something with a real license, like GPL, MIT, etc.

There's also Apophenia, at http://apophenia.info/ . It doesn't yet have Lua bindings, but I'd even be willing to work with you on developing one. It's plain C and its only complication for binding is the setup for variadic functions. Even this is not especially complicated; just push a lot of extra nils onto the stack as needed.

Lua Fun is a high-performance practical programming library designed for LuaJIT tracing just-in-time compiler. The library affords a set of extra than 50 programming primitives usually determined in languages like Standard ML, Haskell, Erlang, JavaScript, Python and even Lisp.

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Function programming language and bare metal code?

I find modern functional programming languages and the paradigm in general to be very interesting. A lot of functional programming languages are able to generate efficient native code either by using C as an intermediate language or with their own code generators. I'm talking about languages like Haskell, OCaml, LISP or Scheme (SBCL, Chiken, Gambit and etc). But knowing that functional programming languages requires a big runtime library, that is usually implemented in C (for garbage collection for example), I'd like to ask is it really possible to create bare metal code in such language and only using it without the need to go back to C (for example for OS development, or for running native code on embedded device without operating system)? Is there any functional programming language that doesn't depend on runtime (even if it would be a language subset)? Is there any functional language in which I can reimplement the runtime that it needs (for example languages like Ada, D, Nimrod, Pascal has runtimes that are written in the language itself)? What alternative functional languages do I have for bare metal development these days?
Why such hate for C? Functional languages have to use a lower-level language for producing machine-level code.
And you can also write C in a very pure functional way. C offers to the developer the freedom to follow any programming style she wishes.
You can easily follow the functional paradigm in C by applying principles that you have learned from other functional languages, i.e.:
No mutation.
No malloc.
Avoid state.
Model in terms of verbs rather than nouns.
Use recursion instead of iteration.
et.c.
There is a book with an intro to Functional C.
I'd like to ask is it really possible to create bare metal code in
such language and only using it without the need to go back to C
Bare metal/machine-level/object code are 1GL (1st generation programming languages) made of binary numbers, represented by 1s and 0s.
Most 3GL or 4GL that use a compiler can generate object code.
Is there any functional programming language that doesn't depend on
runtime (even if it would be a language subset)
Well, every application that runs on top of an OS has to use the OS's API. Nearly all popular OSes are written in C/C++. That includes Windows, Linux, MacOS, Android et.c.
So, when creating an app for an OS, you may have to depend on the OS's runtime environment (that is usually written in C/C++).
Is there any functional language in which I can reimplement the
runtime that it needs (for example languages like Ada, D, Nimrod,
Pascal has runtimes that are written in the language itself)
Yeap, you can write your own runtime library for any language you wish, but that's not an easy task to do.
What alternative functional languages do I have for bare metal
development these days?
I suggest that you choose your favorite functional language (Haskell, F#, Scala or whatever) and just forget about the runtime. There are many and good reason that it is written in C. And AFAIK that isn't going to change anytime soon.
By programming in Scala you use the JVM and with F# the CLR or the WinRT. Maybe these options could help you.
EDIT: If what you really want to ask is if it is possible to write an OS in a functional language, then the answer is yes.
House is an OS written in Haskell. The FFI provides the necessary functionality for (a) calling low-level routines for accessing hardware, and (b) managing memory explicitly.
MirageOS is in OCaml, and there have been OSs implemented in ML.
Generally, any "Turing Complete" programming language can be used to create an operating system, and most functional languages like LISP, Haskell, OCaml, and so on are Turing Complete.
I'm thinking there will be very few (if any) alternatives since the primitives will then be system dependent and your object file needs to have it's own GC. (functional languages need a runtime GC)
You can make your own domain specific language in your favorite functional language, perhaps Scheme, that utilize some sort of assembler, like Sassy, to eventually output raw machine code. But really this is just making your own compiler.
A much simpler option to use C as an intermediate. Many does this since most systems have a C compiler. Devices comes with reference implementations in C.
A different alternative is to make a system like SBCL cross compile to your architecture and use it as the runtime OS of your device.
BTW: SBCL has very little implemented in other languages than Common Lisp. The main part is probably the GC. The GC code could have been implemented in CL, but that would have made debugging far more complex and with a buggy GC you get all sorts of strange behaviour.

What are the main differences between CLISP, ECL, and SBCL?

I want to do some simulations with ACT-R and I will need a Common Lisp implementation. I have three Common Lisp implementations available: (1) CLISP [1], (2) ECL [1], and (3) SBCL [1]. As you might have gathered from the links I have read a bit about all three of them on Wikipedia. But I would like the opinion of some experienced users. More specifically I would like to know:
(i) What are the main differences between the three implementations (e.g.: What are they best at? Is any of them used only for specific purposes and might therefore not be suited for specific tasks?)?
(ii) Is there an obvious choice either based on the fact that I will be using ACT-R or based on general reasons?
As this could be interpreted as a subjective question
I checked What topics can I ask about here and What types of questions should I avoid asking? and if I read correctly it should not qualify as forbidden fruit.
I wrote a moderately-sized application and ran it in SBCL, CCL, ECL, CLISP, ABCL, and LispWorks. For my application, SBCL is far and away the fastest, and it's got a pretty good debugger. It's a bit strict about some warnings--you may end up coding in a slightly more regimented way, or turn off one or more warnings.
I agree with Sylwester: If possible, write to the standard, and then you can run your code in any implementation. You'll figure out through testing which is best for your project.
Since SBCL compiles so agressively, once in a while the stacktrace in the debugger is less informative than I'd like. This can probably be controlled with parameters, but I just rerun the same code in one of the other implementations. ABCL has an informative stacktrace, for example, as I recall. (It's also very slow, but if you want real Common Lisp and Java interoperability, it's the only option.)
One of the nice things about Common Lisp is how many high-quality implementations there are, most of them free.
For informal use--e.g. to learn Common Lisp, CCL or CLISP may be a better choice than SBCL.
I have never tried compiling to C using ECL. It's possible that it would beat SBCL on speed for some applications. I have no idea.
CLISP and LispWorks will not handle arbitrarily long argument lists (unless that's been fixed in the last couple of years, but I doubt it). This turned out to be a problem with my application, but would not be a problem for most code.
Doesn't ACT-R come out of Carnegie Mellon? What do its authors use? My guess would be CMUCL or SBCL, which is derived from CMUCL. (I only tried CMUCL briefly. Its interpreter is very slow, but I assume that compiled code is very fast. I think that most people choose SBCL over CMUCL, however.)
(It's possible that this question belongs on Programmers.SE.)
In general, SBCL is the default choice among open-source Lisps. It is solid, well-supported, produces fast code, and provides many goodies beyond what the standard mandates (concurrency primitives, profiling, etc.) Another implementation with similar properties is CCL.
CLISP is more suitable if you're not an engineer, or you want to quickly show Lisp to someone non-engineer. It's a pretty basic implementation, but quick to get running and user-friendly. A Lisp-calculator :)
ECL's major selling point is that it's embeddable, i.e. it is rather easy to make it work inside some C application, like a web-server etc. It's a good choice for geeks, who want to explore solutions on the boundary of Lisp and the outside world. If you're not intersted in such use case I wouldn't recommend you to try it, especially since it is not actively supported, at the moment.
Their names, their bugs and their non standard additions (using them will lock you in)
I use CLISP as REPL and testing during dev and usually SBCL for production. ECL i've never used.
I recommend you test your code with more than one implementation.

Do functional languages cope well with complexity?

I am curious how functional languages compare (in general) to more "traditional" languages such as C# and Java for large programs. Does program flow become difficult to follow more quickly than if a non-functional language is used? Are there other issues or things to consider when writing a large software project using a functional language?
Thanks!
Functional programming aims to reduce the complexity of large systems, by isolating each operation from others. When you program without side-effects, you know that you can look at each function individually - yes, understanding that one function may well involve understanding other functions too, but at least you know it won't interfere with some other piece of system state elsewhere.
Of course this is assuming completely pure functional programming - which certainly isn't always the case. You can use more traditional languages in a functional way too, avoiding side-effects where possible. But the principle is an important one: avoiding side-effects leads to more maintainable, understandable and testable code.
Does program flow become difficult to follow more quickly than if a >non-functional language is used?
"Program flow" is probably the wrong concept to analyze a large functional program. Control flow can become baroque because there are higher-order functions, but these are generally easy to understand because there is rarely any shared mutable state to worry about, so you can just think about arguments and results. Certainly my experience is that I find it much easier to follow an aggressively functional program than an aggressively object-oriented program where parts of the implementation are smeared out over many classes. And I find it easier to follow a program written with higher-order functions than with dynamic dispatch. I also observe that my students, who are more representative of programmers as a whole, have difficulties with both inheritance and dynamic dispatch. They do not have comparable difficulties with higher-order functions.
Are there other issues or things to consider when writing a large
software project using a functional language?
The critical thing is a good module system. Here is some commentary.
The most powerful module system I know of the unit system of PLT Scheme designed by Matthew Flatt and Matthias Felleisen. This very powerful system unfortunately lacks static types, which I find a great aid to programming.
The next most powerful system is the Standard ML module system. Unfortunately Standard ML, while very expressive, also permits a great many questionable constructs, so it is easy for an amateur to make a real mess. Also, many programmers find it difficult to use Standard ML modules effectively.
The Objective Caml module system is very similar, but there are some differences which tend to mitigate the worst excesses of Standard ML. The languages are actually very similar, but the styles and idioms of Objective Caml make it significantly less likely that beginners will write insane programs.
The least powerful/expressive module system for a functional langauge is the Haskell module system. This system has a grave defect that there are no explicit interfaces, so most of the cognitive benefit of having modules is lost. Another sad outcome is that while the Haskell module system gives users a hierarchical name space, use of this name space (import qualified, in case you're an insider) is often deprecated, and many Haskell programmers write code as if everything were in one big, flat namespace. This practice amounts to abandoning another of the big benefits of modules.
If I had to write a big system in a functional language and had to be sure that other people understood it, I'd probably pick Standard ML, and I'd establish very stringent programming conventions for use of the module system. (E.g., explicit signatures everywhere, opague ascription with :>, and no use of open anywhere, ever.) For me the simplicity of the Standard ML core language (as compared with OCaml) and the more functional nature of the Standard ML Basis Library (as compared with OCaml) are more valuable than the superior aspects of the OCaml module system.
I've worked on just one really big Haskell program, and while I found (and continue to find) working in Haskell very enjoyable, I really missed not having explicit signatures.
Do functional languages cope well with complexity?
Some do. I've found ML modules and module types (both the Standard ML and Objective Caml) flavors invaluable tools for managing complexity, understanding complexity, and placing unbreachable firewalls between different parts of large programs. I have had less good experiences with Haskell
Final note: these aren't really new issues. Decomposing systems into modules with separate interfaces checked by the compiler has been an issue in Ada, C, C++, CLU, Modula-3, and I'm sure many other languages. The main benefit of a system like Standard ML or Caml is the that you get explicit signatures and modular type checking (something that the C++ community is currently struggling with around templates and concepts). I suspect that these issues are timeless and are going to be important for any large system, no matter the language of implementation.
I'd say the opposite. It is easier to reason about programs written in functional languages due to the lack of side-effects.
Usually it is not a matter of "functional" vs "procedural"; it is rather a matter of lazy evaluation.
Lazy evaluation is when you can handle values without actually computing them yet; rather, the value is attached to an expression which should yield the value if it is needed. The main example of a language with lazy evaluation is Haskell. Lazy evaluation allows the definition and processing of conceptually infinite data structures, so this is quite cool, but it also makes it somewhat more difficult for a human programmer to closely follow, in his mind, the sequence of things which will really happen on his computer.
For mostly historical reasons, most languages with lazy evaluation are "functional". I mean that these language have good syntaxic support for constructions which are typically functional.
Without lazy evaluation, functional and procedural languages allow the expression of the same algorithms, with the same complexity and similar "readability". Functional languages tend to value "pure functions", i.e. functions which have no side-effect. Order of evaluation for pure function is irrelevant: in that sense, pure functions help the programmer in knowing what happens by simply flagging parts for which knowing what happens in what order is not important. But that is an indirect benefit and pure functions also appear in procedural languages.
From what I can say, here are the key advantages of functional languages to cope with complexity :
Functional programming hates side-effects.
You can really black-box the different layers
and you won't be afraid of parallel processing
(actor model like in Erlang is really easier to use
than locks and threads).
Culturally, functional programmer
are used to design a DSL to express
and solve a problem. Identifying the fundamental
primitives of a problem is a radically
different approach than rushing to the brand
new trendy framework.
Historically, this field has been led by very smart people :
garbage collection, object oriented, metaprogramming...
All those concepts were first implemented on functional platform.
There is plenty of literature.
But the downside of those languages is that they lack support and experience in the industry. Having portability, performance and interoperability may be a real challenge where on other platform like Java, all of this seems obvious. That said, a language based on the JVM like Scala could be a really nice fit to benefit from both sides.
Does program flow become difficult to
follow more quickly than if a
non-functional language is used?
This may be the case, in that functional style encourages the programmer to prefer thinking in terms of abstract, logical transformations, mapping inputs to outputs. Thinking in terms of "program flow" presumes a sequential, stateful mode of operation--and while a functional program may have sequential state "under the hood", it usually isn't structured around that.
The difference in perspective can be easily seen by comparing imperative vs. functional approaches to "process a collection of data". The former tends to use structured iteration, like a for or while loop, telling the program "do this sequence of tasks, then move to the next one and repeat, until done". The latter tends to use abstracted recursion, like a fold or map function, telling the program "here's a function to combine/transform elements--now use it". It isn't necessary to follow the recursive program flow through a function like map; because it's a stateless abstraction, it's sufficient to think in terms of what it means, not what it's doing.
It's perhaps somewhat telling that the functional approach has been slowly creeping into non-functional languages--consider foreach loops, Python's list comprehensions...

Compiled dynamic language

I search for a programming language for which a compiler exists and that supports self modifying code. I’ve heared that Lisp supports these features, but I was wondering if there is a more C/C++/D-Like language with these features.
To clarify what I mean:
I want to be able to have in some way access to the programms code at runtime and apply any kind of changes to it, that is, removing commands, adding commands, changing them.
As if i had the AstTree of my programm. Of course i can’t have that tree in a compiled language, so it must be done different. The compile would need to translate the self-modifying commands into their binary equivalent modifications so they would work in runtime with the compiled code.
I don’t want to be dependent on an VM, thats what i meant with compiled :)
Probably there is a reason Lisp is like it is? Lisp was designed to program other languages and to compute with symbolic representations of code and data. The boundary between code and data is no longer there. This influences the design AND the implementation of a programming language.
Lisp has got its syntactical features to generate new code, translate that code and execute it. Thus pre-parsed code is also using the same data structures (symbols, lists, numbers, characters, ...) that are used for other programs, too.
Lisp knows its data at runtime - you can query everything for its type or class. Classes are objects themselves, as are functions. So these elements of the programming language and the programs also are first-class objects, they can be manipulated as such. Dynamic language has nothing to do with 'dynamic typing'.
'Dynamic language' means that the elements of the programming language (for example via meta classes and the meta-object protocol) and the program (its classes, functions, methods, slots, inheritance, ...) can be looked at runtime and can be modified at runtime.
Probably the more of these features you add to a language, the more it will look like Lisp. Since Lisp is pretty much the local maximum of a simple, dynamic, programmable programming language. If you want some of these features, then you might want to think which features of your other program language you have to give up or are willing to give up. For example for a simple code-as-data language, the whole C syntax model might not be practical.
So C-like and 'dynamic language' might not really be a good fit - the syntax is one part of the whole picture. But even the C syntax model limits us how easy we can work with a dynamic language.
C# has always allowed for self-modifying code.
C# 1 allowed you to essentially create and compile code on the fly.
C# 3 added "expression trees", which offered a limited way to dynamically generate code using an object model and abstract syntax trees.
C# 4 builds on that by incorporating support for the "Dynamic Language Runtime". This is probably as close as you are going to get to LISP-like capabilities on the .NET platform in a compiled language.
You might want to consider using C++ with LLVM for (mostly) portable code generation. You can even pull in clang as well to work in C parse trees (note that clang has incomplete support for C++ currently, but is written in C++ itself)
For example, you could write a self-modification core in C++ to interface with clang and LLVM, and the rest of the program in C. Store the parse tree for the main program alongside the self-modification code, then manipulate it with clang at runtime. Clang will let you directly manipulate the AST tree in any way, then compile it all the way down to machine code.
Keep in mind that manipulating your AST in a compiled language will always mean including a compiler (or interpreter) with your program. LLVM is just an easy option for this.
JavaScirpt + V8 (the Chrome JavaScript compiler)
JavaScript is
dynamic
self-modifying (self-evaluating) (well, sort of, depending on your definition)
has a C-like syntax (again, sort of, that's the best you will get for dynamic)
And you now can compile it with V8: http://code.google.com/p/v8/
"Dynamic language" is a broad term that covers a wide variety of concepts. Dynamic typing is supported by C# 4.0 which is a compiled language. Objective-C also supports some features of dynamic languages. However, none of them are even close to Lisp in terms of supporting self modifying code.
To support such a degree of dynamism and self-modifying code, you should have a full-featured compiler to call at run time; this is pretty much what an interpreter really is.
Try groovy. It's a dynamic Java-JVM based language that is compiled at runtime. It should be able to execute its own code.
http://groovy.codehaus.org/
Otherwise, you've always got Perl, PHP, etc... but those are not, as you suggest, C/C++/D- like languages.
I don’t want to be dependent on an VM, thats what i meant with compiled :)
If that's all you're looking for, I'd recommend Python or Ruby. They can both run on their own virtual machines and the JVM and the .Net CLR. Thus, you can choose any runtime you want. Of the two, Ruby seems to have more meta-programming facilities, but Python seems to have more mature implementations on other platforms.

Is a functional language a good choice for a Flight Simulator? How about Lisp?

I have been doing object-oriented programming for a few years now, and I have not done much functional programming. I have an interest in flight simulators, and am curious about the functional programming aspect of Lisp. Flight simulators or any other real world simulator makes sense to me in an object-oriented paradigm.
Here are my questions:
Is object oriented the best way to represent a real world simulation domain?
I know that Common Lisp has CLOS (OO for lisp), but my question is really about writing a flight simulator in a functional language. So if you were going to write it in Lisp, would you choose to use CLOS or write it in a functional manner?
Does anyone have any thoughts on coding a flight simulator in lisp or any functional language?
UPDATE 11/8/12 - A similar SO question for those interested -> How does functional programming apply to simulations?
It's a common mistake to think of "Lisp" as a functional language. Really it is best thought of as a family of languages, probably, but these days when people say Lisp they usually mean Common Lisp.
Common Lisp allows functional programming, but it isn't a functional language per se. Rather it is a general purpose language. Scheme is a much smaller variant, that is more functional in orientation, and of course there are others.
As for your question is it a good choice? That really depends on your plans. Common Lisp particularly has some real strengths for this sort of thing. It's both interactive and introspective at a level you usually see in so-called scripting languages, making it very quick to develop in. At the same time its compiled and has efficient compilers, so you can expect performance in the same ballpark as other efficient compilers (with a factor of two of c is typical ime). While a large language, it has a much more consistent design than things like c++, and the metaprogramming capabilities can make very clean, easy to understand code for your particular application. If you only look at these aspects
common lisp looks amazing.
However, there are downsides. The community is small, you won't find many people to help if that's what you're looking for. While the built in library is large, you won't find as many 3rd party libraries, so you may end up writing more of it from scratch. Finally, while it's by no means a walled garden, CL doesn't have the kind of smooth integration with foreign libraries that say python does. Which doesn't mean you can't call c code, there are nice tools for this.
By they way, CLOS is about the most powerful OO system I can think of, but it is quite a different approach if you're coming from a mainstream c++/java/c#/etc. OO background (yes, they differ, but beyond single vs. multiple inh. not that much) you may find it a bit strange at first, almost turned inside out.
If you go this route, you are going to have to watch for some issues with performance of the actual rendering pipeline, if you write that yourself with CLOS. The class system has incredible runtime flexibility (i.e. updating class definitions at runtime not via monkey patching etc. but via actually changing the class and updating instances) however you pay some dispatch cost on this.
For what it's worth, I've used CL in the past for research code requiring numerical efficiency, i.e. simulations of a different sort. It works well for me. In that case I wasn't worried about using existing code -- it didn't exist, so I was writing pretty much everything from scratch anyway.
In summary, it could be a fine choice of language for this project, but not the only one. If you don't use a language with both high-level aspects and good performance (like CL has, as does OCaml, and a few others) I would definitely look at the possibility of a two level approach with a language like lua or perhaps python (lots of libs) on top of some c or c++ code doing the heavy lifting.
If you look at the game or simulator industry you find a lot of C++ plus maybe some added scripting component. There can also be tools written in other languages for scenery design or related tasks. But there is only very little Lisp used in that domain. You need to be a good hacker to get the necessary performance out of Lisp and to be able to access or write the low-level code. How do you get this knowhow? Try, fail, learn, try, fail less, learn, ... There is nothing but writing code and experimenting with it. Lisp is really useful for good software engineers or those that have the potential to be a good software engineer.
One of the main obstacles is the garbage collector. Either you have a very simple one (then you have a performance problem with random pauses) or you have a sophisticated one (then you have a problem getting it working right). Only few garbage collectors exist that would be suitable - most Lisp implementations have good GC implementations, but still those are not tuned for real-time or near real-time use. Exceptions do exist. With C++ you can forget the GC, because there usually is none.
The other alternative to automatic memory management with a garbage collector is to use no GC and manage memory 'manually'. This is used by some (even commercial) Lisp applications that need to support some real-time response (for example process control expert systems).
The nearest thing that was developed in that area was the Crash Bandicoot (and also later games) game for the Playstation I (later games were for the Playstation II) from Naughty Dog. Since they have been bought by Sony, they switched to C++ for the Playstation III. Their development environment was written in Allegro Common Lisp and it included a compiler for a Scheme (a Lisp dialect) variant. On the development system the code gets compiled and then downloaded to the Playstation during development. They had their own 3d engine (very impressive, always got excellent reviews from game magazines), incremental level loading, complex behaviour control for lots of different actors, etc. So the Playstation was really executing the Scheme code, but memory management was not done via GC (afaik). They had to develop all the technology on their own - nobody was offering Lisp-based tools - but they could, because their were excellent software developers. Since then I haven't heard of a similar project. Note that this was not just Lisp for scripting - it was Lisp all the way down.
One the Scheme side there is also a new interesting implementation called Ypsilon Scheme. It is developed for a pinball game - this could be the base for other games, too.
On the Common Lisp side, there have been Lisp applications talking to flight simulators and controlling aspects of them. There are some game libraries that are based on SDL. There are interfaces to OpenGL. There is also something like the 'Open Agent Engine'. There are also some 3d graphics applications written in Common Lisp - even some complex ones. But in the area of flight simulation there is very little prior art.
On the topic of CLOS vs. Functional Programming. Probably one would use neither. If you need to squeeze all possible performance out of a system, then CLOS already has some overheads that one might want to avoid.
Take a look at Functional Reactive Programming. There are a number of frameworks for this in Haskell (don't know about other languages), most of which are based around arrows. The basic idea is to represent relationships between time-varying values and events. So for example you would write (in Haskell arrow notation using no particular library):
velocity <- {some expression of airspeed, heading, gravity etc.}
position <- integrate <- velocity
The second line declares the relationship between position and velocity. The <- arrow operators are syntactic sugar for a bunch of library calls that tie everything together.
Then later on you might say something like:
groundLevel <- getGroundLevel <- position
altitude <- getAltitude <- position
crashed <- liftA2 (<) altitude groundLevel
to declare that if your altitude is less than the ground level at your position then you have crashed. Just as with the other variables here, "crashed" is not just a single value, its a time-varying stream of values. That is why the "liftA2" function is used to "lift" the comparison operator from simple values to streams.
IO is not a problem in this paradigm. Inputs are time varying values such as joystick X and Y, while the image on the screen is simply another time varying value. At the very top level your entire simulator is an arrow from the inputs to the outputs. Then you call a "run" function that converts the arrow into an IO action that runs the game.
If you write this in Lisp you will probably find yourself creating a bunch of macros that basically re-invent arrows, so it might be worth just finding out about arrows to start with.
I don't know anything about flight sims, and you haven't listed anything in particular they consist of, so this is mostly a guess about writing a FS in Lisp.
Why not:
Lisp excels at exploratory programming. I think that since FSs been around so long, and there are free and open-source examples, that it would not benefit as much from this type of programming.
Flight sims are mostly (I'm guessing) written in static, natively compiled languages. If you're looking for pure runtime performance, in Lisp this tends to mean type declarations and other not-so-Lispy constructs. If you don't get the performance you want with naive approaches, your optimized-Lisp might end up looking a lot like C, and Lisp isn't as good at C at writing C.
A lot of a FS, I'm guessing, is interfacing to a graphics library like OpenGL, which is written in C. Depending on how your FFI / OpenGL bindings are, this might, again, make your code look like C-in-Lisp. You might not have the big win that Lisp does in, say, a web app (which consists of generating a tree structure of plain text, which Lisp is great at).
Why:
I took a glance at the FlightGear source code, and I see a lot of structural boilerplate -- even a straight port might end up being half the size.
They use strings for keys all over the place (C++ doesn't have symbols). They use XML for semi-human-readable config files (C++ doesn't have a runtime reader). Simply switching to native Lisp constructs here could be big win for minimal effort.
Nothing looks at all complex, even the "AI". It's simply a matter of keeping everything organized, and Lisp will be great at this because it'll be a lot shorter.
But the neat thing about Lisp is that it's multi-paradigm. You can use OO for organizing the "objects", and FP for computation within each object. I say just start writing and see where it takes you.
I would first think of the nature of the simulation.
Some simulations require interaction like a flight simulator. I don't think functional programming may be a good choice for an interactive (read: CPU intensive/response-critical) applicaiton. Of course, if you have access to 8 PS3's wired together with Linux, you'll not care too much about performance.
For simulations like evolutionary/genetic programming where you set it up and let 'er rip, a functioonal lauguage may help model the problem domain better than an OO language. Not that I'm an expert in functional programming but the ease of coding recursion and the idea of lazy evaluation common in functional languages seems to me a good fit for the 'let her rip' sort of sims.
I wouldn't say functional programming lends itself particularly well to flight simulation. In general, functional languages can be very useful for writing scientific simulations, though this is a slightly specialised case. Really, you'd probably be better off with a standard imperative (preferably OOP) language like C++/C#/Java, as they would tend to have the better physics libraries as well as graphics APIs, both of which you would need to use very heavily. Also, the OOP approach might make it easier to represent your environment. Another point to consider is that (as far as I know) the popular flight simulators on the market today are written pretty much entirely in C++.
Essentially, my philosophy is that if there's no particularly good reason that you should need to use functional paradigms, then don't use a functional language (though there's nothing to stop you using functional constructs in OOP/mixed languages). I suspect you're going to have a lot less painful of a development process using the well-tested APIs for C++ and languages more commonly associated with game development (which has many commonalities with flight sim). Now, if you want to add some complex AI to the simulator, Lisp might seem like a rather more obvious choice, though even then I wouldn't at all jump for it. And finally, if you're really keen on using a functional language, I would recommend you go with one of the more general purpose ones like Python or even F# (both mixed imperative-functional languages really), as opposed to Lisp, which could end up getting rather ugly for such a project.
There are a few problems with functional languages, and that is they don't mesh well with state, but they do go well with process. So in a way it could be said they are action oriented. This means you'll be wasting your time simulating a plane, what you want to do is simulate the actions of flying a plane. Once you grim that you can probably get it to work.
Now as side point, haskell wouldn't be good IMHO, because it's too abstract for a "game", this sort of app is all about Input/Output, but Haskell is about avoiding IO, so it'll become a monad nightmare, and you'll be working against the language. Lisp is a better choice, or Lua or Javascript, they are also functional, but not purely functional, so for your case try Lisp. Anyways in any of these languages your graphics will be C or C++.
A serious issue however is there is very little documentation, and less tutorials about Functional languages and "games", of course scientific simulations is academically documented but those papers are quite dense, if you succeed maybe you could write you experiences, for others as it's a rather empty field right now

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