Can a language have Lisp's powerful macros without the parentheses?
Sure, the question is whether the macro is convenient to use and how powerful they are.
Let's first look how Lisp is slightly different.
Lisp syntax is based on data, not text
Lisp has a two-stage syntax.
A) first there is the data syntax for s-expressions
examples:
(mary called tim to tell him the price of the book)
(sin ( x ) + cos ( x ))
s-expressions are atoms, lists of atoms or lists.
B) second there is the Lisp language syntax on top of s-expressions.
Not every s-expression is a valid Lisp program.
(3 + 4)
is not a valid Lisp program, because Lisp uses prefix notation.
(+ 3 4)
is a valid Lisp program. The first element is a function - here the function +.
S-expressions are data
The interesting part is now that s-expressions can be read and then Lisp uses the normal data structures (numbers, symbols, lists, strings) to represent them.
Most other programming languages don't have a primitive representation for internalized source - other than strings.
Note that s-expressions here are not representing an AST (Abstract Syntax Tree). It's more like a hierarchical token tree coming out of a lexer phase. A lexer identifies the lexical elements.
The internalized source code now makes it easy to calculate with code, because the usual functions to manipulate lists can be applied.
Simple code manipulation with list functions
Let's look at the invalid Lisp code:
(3 + 4)
The program
(defun convert (code)
(list (second code) (first code) (third code)))
(convert '(3 + 4)) -> (+ 3 4)
has converted an infix expression into the valid Lisp prefix expression. We can evaluate it then.
(eval (convert '(3 + 4))) -> 7
EVAL evaluates the converted source code. eval takes as input an s-expression, here a list (+ 3 4).
How to calculate with code?
Programming languages now have at least three choices to make source calculations possible:
base the source code transformations on string transformations
use a similar primitive data structure like Lisp. A more complex variant of this is a syntax based on XML. One could then transform XML expressions. There are other possible external formats combined with internalized data.
use a real syntax description format and represent the source code internalized as a syntax tree using data structures that represent syntactic categories. -> use an AST.
For all these approaches you will find programming languages. Lisp is more or less in camp 2. The consequence: it is theoretically not really satisfying and makes it impossible to statically parse source code (if the code transformations are based on arbitrary Lisp functions). The Lisp community struggles with this for decades (see for example the myriad of approaches that the Scheme community has tried). Fortunately it is relatively easy to use, compared to some of the alternatives and quite powerful. Variant 1 is less elegant. Variant 3 leads to a lot complexity in simple AND complex transformations. It usually also means that the expression was already parsed with respect to a specific language grammar.
Another problem is HOW to transform the code. One approach would be based on transformation rules (like in some Scheme macro variants). Another approach would be a special transformation language (like a template language which can do arbitrary computations). The Lisp approach is to use Lisp itself. That makes it possible to write arbitrary transformations using the full Lisp language. In Lisp there is not a separate parsing stage, but at any time expressions can be read, transformed and evaluated - because these functions are available to the user.
Lisp is kind of a local maximum of simplicity for code transformations.
Other frontend syntax
Also note that the function read reads s-expressions to internal data. In Lisp one could either use a different reader for a different external syntax or reuse the Lisp built-in reader and reprogram it using the read macro mechanism - this mechanism makes it possible to extend or change the s-expression syntax. There are examples for both approaches to provide a different external syntax in Lisp.
For example there are Lisp variants which have a more conventional syntax, where code gets parsed into s-expressions.
Why is the s-expression-based syntax popular among Lisp programmers?
The current Lisp syntax is popular among Lisp programmers for two reasons:
1) the data is code is data idea makes it easy to write all kinds of code transformations based on the internalized data. There is also a relatively direct way from reading code, over manipulating code to printing code. The usual development tools can be used.
2) the text editor can be programmed in a straight forward way to manipulate s-expressions. That makes basic code and data transformations in the editor relatively easy.
Originally Lisp was thought to have a different, more conventional syntax. There were several attempts later to switch to other syntax variants - but for some reasons it either failed or spawned different languages.
Absolutely. It's just a couple orders of magnitude more complex, if you have to deal with a complex grammar. As Peter Norvig noted:
Python does have access to the
abstract syntax tree of programs, but
this is not for the faint of heart. On
the plus side, the modules are easy to
understand, and with five minutes and
five lines of code I was able to get
this:
>>> parse("2 + 2")
['eval_input', ['testlist', ['test', ['and_test', ['not_test', ['comparison',
['expr', ['xor_expr', ['and_expr', ['shift_expr', ['arith_expr', ['term',
['factor', ['power', ['atom', [2, '2']]]]], [14, '+'], ['term', ['factor',
['power', ['atom', [2, '2']]]]]]]]]]]]]]], [4, ''], [0, '']]
This was rather a disapointment to me. The Lisp parse of the equivalent expression is (+ 2 2). It seems that only a real expert would want to manipulate Python parse trees, whereas Lisp parse trees are simple for anyone to use. It is still possible to create something similar to macros in Python by concatenating strings, but it is not integrated with the rest of the language, and so in practice is not done.
Since I'm not a super-genius (or even a Peter Norvig), I'll stick with (+ 2 2).
Here's a shorter version of Rainer's answer:
In order to have lisp-style macros, you need a way of representing source-code in data structures. In most languages, the only "source code data structure" is a string, which doesn't have nearly enough structure to allow you to do real macros on. Some languages offer a real data structure, but it's too complex, like Python, so that writing real macros is stupidly complicated and not really worth it.
Lisp's lists and parentheses hit the sweet spot in the middle. Just enough structure to make it easy to handle, but not too much so you drown in complexity. As a bonus, when you nest lists you get a tree, which happens to be precisely the structure that programming languages naturally adopt (nearly all programming languages are first parsed into an "abstract syntax tree", or AST, before being actually interpreted/compiled).
Basically, programming Lisp is writing an AST directly, rather than writing some other language that then gets turned into an AST by the computer. You could possibly forgo the parens, but you'd just need some other way to group things into a list/tree. You probably wouldn't gain much from doing so.
Parentheses are irrelevant to macros. It's just Lisp's way of doing things.
For example, Prolog has a very powerful macros mechanism called "term expansion". Basically, whenever Prolog reads a term T, if tries a special rule term_expansion(T, R). If it is successful, the content of R is interpreted instead of T.
Not to mention the Dylan language, which has a pretty powerful syntactic macro system, which features (among other things) referential transparency, while being an infix (Algol-style) language.
Yes. Parentheses in Lisp are used in the classic way, as a grouping mechanism. Indentation is an alternative way to express groups. E.g. the following structures are equivalent:
A ((B C) D)
and
A
B
C
D
Have a look at Sweet-expressions. Wheeler makes a very good case that the reason things like infix notation have not worked before is that typical notation also tries to add precedence, which then adds complexity, which causes difficulties in writing macros.
For this reason, he proposes infix syntax like {1 + 2 + 3} and {1 + {2 * 3}} (note the spaces between symbols), that are translated to (+ 1 2) and (+ 1 (* 2 3)) respectively. He adds that if someone writes {1 + 2 * 3}, it should become (nfx 1 + 2 * 3), which could be captured, if you really want to provide precedence, but would, as a default, be an error.
He also suggests that indentation should be significant, proposes that functions could be called as fn(A B C) as well as (fn A B C), would like data[A] to translate to (bracketaccess data A), and that the entire system should be compatible with s-expressions.
Overall, it's an interesting set of proposals I'd like to experiment with extensively. (But don't tell anyone at comp.lang.lisp: they'll burn you at the stake for your curiosity :-).
Code rewriting in Tcl in a manner recognizably similar to Lisp macros is a common technique. For example, this is (trivial) code that makes it easier to write procedures that always import a certain set of global variables:
proc gproc {name arguments body} {
set realbody "global foo bar boo;$body"
uplevel 1 [list proc $name $arguments $realbody]
}
With that, all procedures declared with gproc xyz rather than proc xyz will have access to the foo, bar and boo globals. The whole key is that uplevel takes a command and evaluates it in the caller's context, and list is (among other things) an ideal constructor for substitution-safe code fragments.
Erlang's parse transforms are similar in power to Lisp macros, though they are much trickier to write and use (they are applied to the entire source file, rather than being invoked on demand).
Lisp itself had a brief dalliance with non-parenthesised syntax in the form of M-expressions. It didn't take with the community, though variants of the idea found their way into modern Lisps, so you get Lisp's powerful macros without the parentheses ... in Lisp!
Yes, you can definitely have Lisp macros without all the parentheses.
Take a look at "sweet-expressions", which provides a set of additional abbreviations for traditional s-expressions. They add indentation, a way to do infix, and traditional function calls like f(x), but in a way that is backwards-compatible (you can freely mix well-formatted s-expressions and sweet-expressions), generic, and homoiconic.
Sweet-expressions were developed on http://readable.sourceforge.net and there is a sample implementation.
For Scheme there is a SRFI for sweet-expressions, SRFI-110: http://srfi.schemers.org/srfi-110/
No, it's not necessary. Anything that gives you some sort of access to a parse tree would be enough to allow you to manipulate the macro body in hte same way as is done in Common Lisp. However, as the manipulation of the AST in lisp is identical to the manipulation of lists (something that is bordering on easy in the lisp family), it's possibly not nearly as natural without having the "parse tree" and "written form" be essentially the same.
I think this was not mentioned.
C++ templates are Turing-complete and perform processing at compile-time.
There is the well-known expression templates mechanism that allow transformations,
not from arbitrary code, but at least, from the subset of c++ operators.
So imagine you have 3 vectors of 1000 elements and you must perform:
(A + B + C)[0]
You can capture this tree in a expression template and arbitrarily manipulate it
at compile-time.
With this tree, at compile time, you can transform the expression.
For example, if that expression means A[0] + B[0] + C[0] for your domain, you could
avoid the normal c++ processing which would be:
Add A and B, adding 1000 elements.
Create a temporary for the result, and add with the 1000 elements of C.
Index the result to get the first element.
And replace with another transformed expression template tree that does:
Capture A[0]
Capture B[0]
Capture C[0]
Add all 3 results together in the result to return with += avoiding temporaries.
It is not better than lisp, I think, but it is still very powerful.
Yes, it is certainly possible. Especially if it is still a Lisp under the bonnet:
http://www.meta-alternative.net/pfront.pdf
http://www.meta-alternative.net/pfdoc.pdf
Boo has a nice "quoted" macro syntax that uses [| |] as delimiters, and has certain substitutions which are actually verified syntactically by the compiler pipeline using $variables. While simple and relatively painless to use, it's much more complicated to implement on the compiler side than s-expressions. Boo's solution may have a few limitations that haven't affected my own code. There's also an alternate syntax that reads more like ordinary OO code, but that falls into the "not for the faint of heart" category like dealing with Ruby or Python parse trees.
Javascript's template strings offer yet another approach to this sort of thing. For instance, Mark S. Miller's quasiParserGenerator implements a grammar syntax for parsers.
Go ahead and enter the Elixir programming language.
Elixir is a functional programming language that feels like Lisp with respect to macros, but it is on Ruby's clothes, and runs on top of the Erlang VM.
For those who do not like the parenthesis, but wish their language has powerful macros, Elixir is a great choice.
You can write macros in R (it have more like Algol Syntax) that have notion of delayed expression like in LISP macros. You can call substitute() or quote() to not evaluate the delayed expression but get actual expression and traverse its source code like in LISP. Even structure of the expression source code is like in LISP. Operators are first item in list. e.g.: input$foo which is getting property foo from list input as expression is written as ['$', 'input', 'foo'] just like in LISP.
You can check the ebook Metaprogramming in R that also show how to create Macros in R (not something you would normally do but it's possible). It's based on Article from 2001 Programmer’s Niche: Macros in R that explain how to write LIPS macros in R.
Related
I tried really hard to find answer to this question on google engine.
But I wonder how these high level programming languages are created in principle of automata or is automata theory not included in defining the languages?
Language design tends to have two important levels:
Lexical analysis - the definition of what tokens look like. What is a string literal, what is a number, what are valid names for variables, functions, etc.
Syntactic analysis - the definition of how tokens work together to make meaningful statements. Can you assign a value to a literal, what does a block look like, what does an if statement look like, etc.
The lexical analysis is done using regular languages, and generally tokens are defined using regular expressions. It's not that a DFA is used (most regex implementations are not DFAs in practice), but that regular expressions tend to line up well with what most languages consider tokens. If, for example, you wanted a language where all variable names had to be palindromes, then your language's token specification would have to be context-free instead.
The input to the lexing stage is the raw characters of the source code. The alphabet would therefore be ASCII or Unicode or whatever input your compiler is expecting. The output is a stream of tokens with metadata, such as string-literal (value: hello world) which might represent "hello world" in the source code.
The syntactic analysis is typically done using a subset of context-free languages called LL or LR parsers. This is because the implementation of CFG (PDAs) are nondeterministic. LL and LR parsing are ways to make deterministic decisions with respect to how to parse a given expression.
We use CFGs for code because this is the level on the Chomsky hierarchy where nesting occurs (where you can express the idea of "depth", such as with an if within an if). Higher or lower levels on the hierarchy are possible, but a regular syntax would not be able to express nesting easily, and context-sensitive syntax would probably cause confusion (but it's not unheard of).
The input to the syntactic analysis step is the token stream, and the output is some form of executable structure, typically a parse tree that is either executed immediately (as in interpretted languages) or stored for later optimization and/or execution (as in compiled languages) or something else (as in intermediate-compiled languages like Java). The alphabet of the CFG is therefore the possible tokens specified by the lexical analysis step.
So this whole thing is a long-winded way of saying that it's not so much the automata theory that's important, but rather the formal languages. We typically want to have the simplest language class that meets our needs. That typically means regular tokens and context-free syntax, but not always.
The implementation of the regular expression need not be an automaton, and the implementation of the CFG cannot be a PDA, because PDAs are nondeterministic, so we define deterministic parsers on reasonable subsets of the CFG class instead.
More generally we talk about Theory of computation.
What has happened through the history of programming languages is that it has been formally proven that higher-level constructs are equivalent to the constructs in the abstract machines of the theory.
We prefer the higher-level constructs in modern languages because they make programs easier to write, and easier to understand by other people. That in turn leads to easier peer-review and team-play, and thus better programs with less bugs.
The Wikipedia article about Structured programming tells part of the history.
As to Automata theory, it is still present in the implementation of regular expression engines, and in most programming situations in which a good solution consists in transitioning through a set of possible states.
I am currently working on writing my own language(shameless plug), which is centered around flexibility. I am trying to make almost any part of the language syntax exchangeable through things like extensions/plugins. While writing the whole thing, it has got me thinking. I am wondering how that sort of flexibility could affect the language.
I know that Lisp is often referred to as one of the most extensible languages due to its extensive macro system. I do understand that concept of macros, but I am yet to find a language that allows someone to change the way it is parsed. To my knowledge, almost every language has an extremely concrete syntax as defined by some long specification.
My question is how could having a flexible syntax affect the intuitiveness and usability of the language? I know the basic "people might be confused when the syntax changes" and "semantic analysis will be hard". Those are things that I am already starting to compensate for. I am looking for a more conceptual answer on the pros and cons of having a flexible syntax.
The topic of language design is still quite foreign to me, so I apologize if I am asking an obvious or otherwise stupid question!
Edit:
I was just wanting to clarify the question I was asking. Where exactly does flexibility in a language's syntax stand, in terms of language theory? I don't really need examples or projects/languages with flexibility, I want to understand how it can affect the language's readability, functionality, and other things like that.
Perl is the most flexible language I know. That a look at Moose, a postmodern object system for Perl 5. It's syntax is very different than Perl's but it is still very Perl-ish.
IMO, the biggest problem with flexibility is precedence in infix notation. But none I know of allow a datatype to have its own infix syntax. For example, take sets. It would be nice to use ⊂ and ⊇ in their syntax. But not only would a compiler have to recognize these symbols, it would have to be told their order of precedence.
Common Lisp allows to change the way it's parsed - see reader macros. Racket allows to modify its parser, see racket languages.
And of course you can have a flexible, dynamically extensible parsing alongside with powerful macros if you use the right parsing techniques (e.g., PEG). Have a look at an example here - mostly a C syntax, but extensible with both syntax and semantic macros.
As for precedence, PEG goes really well together with Pratt.
To answer your updated question - there is surprisingly little research done on programming languages readability anyway. You may want to have a look at what Dr. Blackwell group was up to, but it's still far from conclusive.
So I can only share my hand-wavy anecdotes - flexible syntax languages facilitates eDSL construction, and, in my opinion, eDSLs is the only way to eliminate unnecessary complexity from code, to make code actually maintainable in a long term. I believe that non-flexible languages are one of the biggest mistakes made by this industry, and it must be corrected at all costs, ASAP.
Flexibility allows you to manipulate the syntax of the language. For example, Lisp Macros can enable you to write programs that write programs and manipulate your syntax at compile-time to valid Lisp expressions. For example the Loop Macro:
(loop for x from 1 to 5
do(format t "~A~%" x))
1
2
3
4
5
NIL
And we can see how the code was translated with macroexpand-1:
(pprint(macroexpand-1 '(loop for x from 1 to 5
do (format t "~a~%" x))))
We can then see how a call to that macro is translated:
(LET ((X 1))
(DECLARE (TYPE (AND REAL NUMBER) X))
(TAGBODY
SB-LOOP::NEXT-LOOP
(WHEN (> X '5) (GO SB-LOOP::END-LOOP))
(FORMAT T "~a~%" X)
(SB-LOOP::LOOP-DESETQ X (1+ X))
(GO SB-LOOP::NEXT-LOOP)
SB-LOOP::END-LOOP)))
Language Flexibility just allows you to create your own embedded language within a language and reduce the length of your program in terms of characters used. So in theory, this can make a language very unreadable since we can manipulate the syntax. For example we can create invalid code that's translated to valid code:
(defmacro backwards (expr)
(reverse expr))
BACKWARDS
CL-USER> (backwards ("hello world" nil format))
"hello world"
CL-USER>
Clearly the above code can become complex since:
("hello world" nil format)
is not a valid Lisp expression.
Thanks to SK-logic's answer for pointing me in the direction of Alan Blackwell. I sent him an email asking his stance on the matter, and he responded with an absolutely wonderful explanation. Here it is:
So the person who responded to your StackOverflow question, saying
that flexible syntax could be useful for DSLs, is certainly correct.
It actually used to be fairly common to use the C preprocessor to
create alternative syntax (that would be turned into regular syntax in
an initial compile phase). A lot of the early esolangs were built this
way.
In practice, I think we would have to say that a lot of DSLs are
implemented as libraries within regular programming languages, and
that the library design is far more significant than the syntax. There
may be more purpose for having variety in visual languages, but making
customisable general purpose compilers for arbitrary graphical syntax
is really hard - much worse than changing text syntax features.
There may well be interesting things that your design could enable, so
I wouldn’t discourage experimentation. However, I think there is one reason why
customisable syntax is not so common. This is related to the famous
programmer’s editor EMACS. In EMACS, everything is customisable - all
key bindings, and all editor functions. It’s fun to play with, and
back in the day, many of us made our own personalised version that
only we knew how to operate. But it turned out that it was a real
hassle that everyone’s editor worked completely differently. You could
never lean over and make suggestions on another person’s session, and
teams always had to know who was logged in order to know whether the
editor would work. So it turned out that, over the years, we all just
started to use the default distribution and key bindings, which made
things easier for everyone.
At this point in time, that is just about enough of an explanation that I was looking for. If anyone feels as though they have a better explanation or something to add, feel free to contact me.
I'm writing a small tool for generating php checks from javascript code, and I would like to know if anyone knows of a standard way of transforming functional code into imperative code?
I found this paper: Defunctionalization at Work it explains defunctionalization pretty well.
Lambdalifting and defunctionalization somewhat answered the question, but what about datastructures, we are still parsing lists as if they are all linkedlists. Would there be a way of transforming the linkedlists of functional languages into other high-level datastructures like c++ vectors or java arraylists?
Here are a few additions to the list of #Artyom:
you can convert tail recursion into loops and assignments
linear types can be used to introduce assignments, e.g. y = f x can be replaced with x := f x if x is linear and has the same type as y
at least two kinds of defunctionalization are possible: Reynolds-type defunctionalization when you replace a high-order application with a switch full of first-order applications, and inlining (however, recursive functions is not always possible to inline)
Perhaps you are interested in removing some language elements (such as higher-order functions), right?
For eliminating HOFs from a program, there are techniques such as defunctionalization. For removing closures, you can use lambda-lifting (aka closure conversion). Is this something you are interested in?
I think you need to provide a concrete example of code you have, and the target code you intend to produce, so that others may propose solutions.
Added:
Would there be a way of transforming the linkedlists of functional languages into other high-level datastructures like c++ vectors or java arraylists?
Yes. Linked lists are represented with pointers in C++ (a structure "node" with two fields: one for the "payload", another for the "next" pointer; empty list is then represented as a NULL pointer, but sometimes people prefer to use special "sentinel values"). Note that, if the code in the source language does not rely on the representation of singly linked lists (in the source language implementation), you can also implement the "cons"/"nil" operations using a vector in the target language (not sure if this suits your needs, though). The idea here is to give an alternative implementations for the familiar operations.
No, there is not.
The reason is that there is no such concrete and well defined thing like functional code or imperative code.
Such transformations exist only for concrete instances of your abstraction: for example, there are transformations from Haskell code to LLVM bytecode, F# code to CLI bytecode or Frege code to Java code.
(I doubt if there is one from Javascript to PHP.)
Depends on what you need. The usual answer is "there is no such tool", because the result will not be usable. However look at this from this standpoint:
The set of Assembler instructions in a computer defines an imperative machine. Hence the compiler needs to do such a translation. However I assume you do not want to have assembler code but something more readable.
Usually these kinds of heavy program transformations are done manually, if one is interested in the result, or automatically if the result will never be looked at by a human.
I'm trying to do some research for a new project, and I need to create objects dynamically from random data.
For this to work, I need a language / compiler that doesn't have problems with weird uncompilable code lying around.
Basically, I need the random code to compile (or be interpreted) as much as possible - Meaning that the uncompilable parts will be ignored, and only the compilable parts will create the objects (which could be ran).
Object Oriented-ness is not a must, but is a very strong advantage.
I thought of ASM, but it's very messy, and I'd probably need a more readable code
Thanks!
It sounds like you're doing something very much like genetic programming; even if you aren't, GP has to solve some of the same problems—using randomness to generate valid programs. The approach to this that is typically used is to work with a syntax tree: rather than storing x + y * 3 - 2, you store something like the following:
Then, instead of randomly changing the syntax, one can randomly change nodes in the tree instead. And if x should randomly change to, say, +, you can statically know that this means you need to insert two children (or not, depending on how you define +).
A good choice for a language to work with for this would be any Lisp dialect. In a Lisp, the above program would be written (- (+ x (* y 3)) 2), which is just a linearization of the syntax tree using parentheses to show depth. And in fact, Lisps expose this feature: you can just as easily work with the object '(- (+ x (* y 3)) 2) (note the leading quote). This is a three-element list, whose first element is -, second element is another list, and third element is 2. And, though you might or might not want it for your particular application, there's an eval function, such that (eval '(- (+ x (* y 3)) 2)) will take in the given list, treat it as a Lisp syntax tree/program, and evaluate it. This is what makes Lisps so attractive for doing this sort of work; Lisp syntax is basically a reification of the syntax-tree, and if you operate at the syntax-tree level, you can work on code as though it was a value. Lisp won't help you read /dev/random as a program directly, but with a little interpretation layered on top, you should be able to get what you want.
I should also mention, though I don't know anything about it (not that I know much about ordinary genetic programming) the existence of linear genetic programming. This is sort of like the assembly model that you mentioned—a linear stream of very, very simple instructions. The advantage here would seem to be that if you are working with /dev/random or something like it, the amount of interpretation needed is very small; the disadvantage would be, as you mentioned, the low-level nature of the code.
I'm not sure if this is what you're looking for, but any programming language can be made to function this way. For any programming language P, define the language Palways as follows:
If p is a valid program in P, then p is a valid program in Palways whose meaning is the same as its meaning in P.
If p is not a valid program in P, then p is a valid program in Palways whose meaning is the same as a program that immediately terminates.
For example, I could make the language C++always so that this program:
#include <iostream>
using namespace std;
int main() {
cout << "Hello, world!" << endl;
}
would compile as "Hello, world!", while this program:
Hahaha! This isn't legal C++ code!
Would be a legal program that just does absolutely nothing.
To solve your original problem, just take any OOP language like Java, Smalltalk, etc. and construct the appropriate Javaalways, Smalltalkalways, etc. language from it. Again, I'm not sure if this is at all what you're looking for, but it could be done very easily.
Alternatively, consider finding a grammar for any OOP language and then using that grammar to produce random syntactically valid programs. You could then filter those programs down by using the Palways programming language for that language to eliminate syntactically but not semantically valid programs.
Divide the ASCII byte values into 9 classes (division modulo 9 would help). Then assign then to Brainfuck codewords (see http://en.wikipedia.org/wiki/Brainfuck). Then interpret as Brainfuck.
There you go, any sequence of ASCII characters is a program. Not that it's going to do anything sensible... This approach has a much better chance, compared to templatetypedef's answer, to get a nontrivial program from a random byte sequence.
Text Editors
You could try feeding random character strings to an editor like Emacs or VI. Many (most?) characters will perform an editing action but some will do nothing (other than beep, perhaps). You would have to ensure that the random code mutator never generates the character sequence that exits the editor. However, this experience would be much like programming a Turing machine -- the code is not too readable.
Mathematica
In Mathematica, undefined symbols and other expressions evaluate to themselves, without error. So, that language might be a viable choice if you can arrange for the random code mutator to always generate well-formed expressions. This would be readily achievable since the basic Mathematica syntax is trivial, making it easy to operate on syntactic units rather than at the character level. It would be even easier if the mutator were written in Mathematica itself since expression-munging is Mathematica's forte. You could define a mini-language of valid operations within a Mathematica package that does not import the system-defined symbols. This would allow you to generate well-formed expressions to your heart's content without fear of generating a dangerous expression, like DeleteFile[FileNames["*.*", "/", Infinity]].
I believe Common Lisp should suit your needs. I always have some code in my SLIME/Emacs session that wouldn't compile. You can always tweak things, redefine functions in run-time. It is actually very good for prototyping.
A few years ago it took me quite a while to learn. But nowadays we have quicklisp and everything is so much easier.
Here I describe my development environment:
Install lisp on my linux machine
PS: I want to give an example, where Common Lisp was useful for me:
Up to maybe 2004 I used to write small programs in C (the keep it simple Unix way).
The last 3 years I had to get lots of different hardware running. Motorized stages, scientific cameras, IO cards.
The cameras turned out to be quite annoying. Usually you have to cool them down to -50 degree celsius or so and (in some SDKs) they don't like it when you close them. But this
is exactly how my C development cycle worked: write (30s), compile (1s), run (0.1s), repeat.
Eventually I decided to just use Common Lisp. Often it is straight forward to define the foreign function interfaces to talk to the SDKs and I can do this without ever leaving the running Lisp image. I start the editor in the morning define the open-device function, to talk to the device and after 3 hours I have enough of the functions implemented to set gain, temperature, region of interest and obtain the video.
Then I can often put the SDK manual away and just use the camera.
I used the same interactive programming approach when I have to parse some webpage or some weird XML.
I am a big fan of Stephen Wolfram, but he is definitely one not shy of tooting his own horn. In many references, he extols Mathematica as a different symbolic programming paradigm. I am not a Mathematica user.
My questions are: what is this symbolic programming? And how does it compare to functional languages (such as Haskell)?
When I hear the phrase "symbolic programming", LISP, Prolog and (yes) Mathematica immediately leap to mind. I would characterize a symbolic programming environment as one in which the expressions used to represent program text also happen to be the primary data structure. As a result, it becomes very easy to build abstractions upon abstractions since data can easily be transformed into code and vice versa.
Mathematica exploits this capability heavily. Even more heavily than LISP and Prolog (IMHO).
As an example of symbolic programming, consider the following sequence of events. I have a CSV file that looks like this:
r,1,2
g,3,4
I read that file in:
Import["somefile.csv"]
--> {{r,1,2},{g,3,4}}
Is the result data or code? It is both. It is the data that results from reading the file, but it also happens to be the expression that will construct that data. As code goes, however, this expression is inert since the result of evaluating it is simply itself.
So now I apply a transformation to the result:
% /. {c_, x_, y_} :> {c, Disk[{x, y}]}
--> {{r,Disk[{1,2}]},{g,Disk[{3,4}]}}
Without dwelling on the details, all that has happened is that Disk[{...}] has been wrapped around the last two numbers from each input line. The result is still data/code, but still inert. Another transformation:
% /. {"r" -> Red, "g" -> Green}
--> {{Red,Disk[{1,2}]},{Green,Disk[{3,4}]}}
Yes, still inert. However, by a remarkable coincidence this last result just happens to be a list of valid directives in Mathematica's built-in domain-specific language for graphics. One last transformation, and things start to happen:
% /. x_ :> Graphics[x]
--> Graphics[{{Red,Disk[{1,2}]},{Green,Disk[{3,4}]}}]
Actually, you would not see that last result. In an epic display of syntactic sugar, Mathematica would show this picture of red and green circles:
But the fun doesn't stop there. Underneath all that syntactic sugar we still have a symbolic expression. I can apply another transformation rule:
% /. Red -> Black
Presto! The red circle became black.
It is this kind of "symbol pushing" that characterizes symbolic programming. A great majority of Mathematica programming is of this nature.
Functional vs. Symbolic
I won't address the differences between symbolic and functional programming in detail, but I will contribute a few remarks.
One could view symbolic programming as an answer to the question: "What would happen if I tried to model everything using only expression transformations?" Functional programming, by contrast, can been seen as an answer to: "What would happen if I tried to model everything using only functions?" Just like symbolic programming, functional programming makes it easy to quickly build up layers of abstractions. The example I gave here could be easily be reproduced in, say, Haskell using a functional reactive animation approach. Functional programming is all about function composition, higher level functions, combinators -- all the nifty things that you can do with functions.
Mathematica is clearly optimized for symbolic programming. It is possible to write code in functional style, but the functional features in Mathematica are really just a thin veneer over transformations (and a leaky abstraction at that, see the footnote below).
Haskell is clearly optimized for functional programming. It is possible to write code in symbolic style, but I would quibble that the syntactic representation of programs and data are quite distinct, making the experience suboptimal.
Concluding Remarks
In conclusion, I advocate that there is a distinction between functional programming (as epitomized by Haskell) and symbolic programming (as epitomized by Mathematica). I think that if one studies both, then one will learn substantially more than studying just one -- the ultimate test of distinctness.
Leaky Functional Abstraction in Mathematica?
Yup, leaky. Try this, for example:
f[x_] := g[Function[a, x]];
g[fn_] := Module[{h}, h[a_] := fn[a]; h[0]];
f[999]
Duly reported to, and acknowledged by, WRI. The response: avoid the use of Function[var, body] (Function[body] is okay).
You can think of Mathematica's symbolic programming as a search-and-replace system where you program by specifying search-and-replace rules.
For instance you could specify the following rule
area := Pi*radius^2;
Next time you use area, it'll be replaced with Pi*radius^2. Now, suppose you define new rule
radius:=5
Now, whenever you use radius, it'll get rewritten into 5. If you evaluate area it'll get rewritten into Pi*radius^2 which triggers rewriting rule for radius and you'll get Pi*5^2 as an intermediate result. This new form will trigger a built-in rewriting rule for ^ operation so the expression will get further rewritten into Pi*25. At this point rewriting stops because there are no applicable rules.
You can emulate functional programming by using your replacement rules as function. For instance, if you want to define a function that adds, you could do
add[a_,b_]:=a+b
Now add[x,y] gets rewritten into x+y. If you want add to only apply for numeric a,b, you could instead do
add[a_?NumericQ, b_?NumericQ] := a + b
Now, add[2,3] gets rewritten into 2+3 using your rule and then into 5 using built-in rule for +, whereas add[test1,test2] remains unchanged.
Here's an example of an interactive replacement rule
a := ChoiceDialog["Pick one", {1, 2, 3, 4}]
a+1
Here, a gets replaced with ChoiceDialog, which then gets replaced with the number the user chose on the dialog that popped up, which makes both quantities numeric and triggers replacement rule for +. Here, ChoiceDialog as a built-in replacement rule along the lines of "replace ChoiceDialog[some stuff] with the value of button the user clicked".
Rules can be defined using conditions which themselves need to go through rule-rewriting in order to produce True or False. For instance suppose you invented a new equation solving method, but you think it only works when the final result of your method is positive. You could do the following rule
solve[x + 5 == b_] := (result = b - 5; result /; result > 0)
Here, solve[x+5==20] gets replaced with 15, but solve[x + 5 == -20] is unchanged because there's no rule that applies. The condition that prevents this rule from applying is /;result>0. Evaluator essentially looks the potential output of rule application to decide whether to go ahead with it.
Mathematica's evaluator greedily rewrites every pattern with one of the rules that apply for that symbol. Sometimes you want to have finer control, and in such case you could define your own rules and apply them manually like this
myrules={area->Pi radius^2,radius->5}
area//.myrules
This will apply rules defined in myrules until result stops changing. This is pretty similar to the default evaluator, but now you could have several sets of rules and apply them selectively. A more advanced example shows how to make a Prolog-like evaluator that searches over sequences of rule applications.
One drawback of current Mathematica version comes up when you need to use Mathematica's default evaluator (to make use of Integrate, Solve, etc) and want to change default sequence of evaluation. That is possible but complicated, and I like to think that some future implementation of symbolic programming will have a more elegant way of controlling evaluation sequence
As others here already mentioned, Mathematica does a lot of term rewriting. Maybe Haskell isn't the best comparison though, but Pure is a nice functional term-rewriting language (that should feel familiar to people with a Haskell background). Maybe reading their Wiki page on term rewriting will clear up a few things for you:
http://code.google.com/p/pure-lang/wiki/Rewriting
Mathematica is using term rewriting heavily. The language provides special syntax for various forms of rewriting, special support for rules and strategies. The paradigm is not that "new" and of course it's not unique, but they're definitely on a bleeding edge of this "symbolic programming" thing, alongside with the other strong players such as Axiom.
As for comparison to Haskell, well, you could do rewriting there, with a bit of help from scrap your boilerplate library, but it's not nearly as easy as in a dynamically typed Mathematica.
Symbolic shouldn't be contrasted with functional, it should be contrasted with numerical programming. Consider as an example MatLab vs Mathematica. Suppose I want the characteristic polynomial of a matrix. If I wanted to do that in Mathematica, I could do get an identity matrix (I) and the matrix (A) itself into Mathematica, then do this:
Det[A-lambda*I]
And I would get the characteristic polynomial (never mind that there's probably a characteristic polynomial function), on the other hand, if I was in MatLab I couldn't do it with base MatLab because base MatLab (never mind that there's probably a characteristic polynomial function) is only good at calculating finite-precision numbers, not things where there are random lambdas (our symbol) in there. What you'd have to do is buy the add-on Symbolab, and then define lambda as its own line of code and then write this out (wherein it would convert your A matrix to a matrix of rational numbers rather than finite precision decimals), and while the performance difference would probably be unnoticeable for a small case like this, it would probably do it much slower than Mathematica in terms of relative speed.
So that's the difference, symbolic languages are interested in doing calculations with perfect accuracy (often using rational numbers as opposed to numerical) and numerical programming languages on the other hand are very good at the vast majority of calculations you would need to do and they tend to be faster at the numerical operations they're meant for (MatLab is nearly unmatched in this regard for higher level languages - excluding C++, etc) and a piss poor at symbolic operations.