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In my ongoing quest to learn lisp, I'm running into a conceptual problem. It's somewhat akin to the question here, but maybe it's thematically appropriate to lisp that my question is a level of abstraction up.
As a rule, when should you create a macro vs. a function? It seems to me, maybe naively, that there would be very few cases where you must create a macro instead of a function, and that in most remainder cases, a function would generally suffice. Of these remainder cases, it seems like the main additional value of a macro would be in clarity of syntax. And if that's the case, then it seems like not just the decision to opt for macro use but also the design of their structures might be fundamentally idiosyncratic to the individual programmer.
Is this wrong? Is there a general case outlining when to use macros over functions? Am I right that the cases where a macro is required by the language are generally few? And lastly, is there a general syntactic form that's expected of macros, or are they generally used as shorthands by programmers?
I found a detailed answer, from Paul Graham's On Lisp, bold emphases added:
Macros can do two things that functions can’t: they can control (or prevent) the evaluation of their arguments, and they are expanded right into the calling context. Any application which requires macros requires, in the end, one or both of these properties.
...
Macros use this control in four major ways:
Transformation. The Common Lisp setf macro is one of a class of macros which pick apart their arguments before evaluation. A built-in access function will often have a converse whose purpose is to set what the access function retrieves. The converse of car is rplaca, of cdr, rplacd, and so on. With setf we can use calls to such access functions as if they were variables to be set, as in (setf (car x) ’a), which could expand into (progn (rplaca x ’a) ’a).
To perform this trick, setf has to look inside its first argument. To know that the case above requires rplaca, setf must be able to see that the first argument is an expression beginning with car. Thus setf, and any other operator which transforms its arguments, must be written as a macro.
Binding. Lexical variables must appear directly in the source code. The first argument to setq is not evaluated, for example, so anything built on setq must be a macro which expands into a setq, rather than a function which calls it. Likewise for operators like let, whose arguments are to appear as parameters in a lambda expression, for macros like do which expand into lets, and so on. Any new operator which is to alter the lexical bindings of its arguments must be written as a macro.
Conditional evaluation. All the arguments to a function are evaluated. In constructs like when, we want some arguments to be evaluated only under certain conditions. Such flexibility is only possible with macros.
Multiple evaluation. Not only are the arguments to a function all evaluated, they are all evaluated exactly once. We need a macro to define a construct like do, where certain arguments are to be evaluated repeatedly.
There are also several ways to take advantage of the inline expansion of macros. It’s important to emphasize that the expansions thus appear in the lexical context of the macro call, since two of the three uses for macros depend on that fact. They are:
Using the calling environment. A macro can generate an expansion containing a variable whose binding comes from the context of the macro call. The behavior of the following macro:
(defmacro foo (x) ‘(+ ,x y))
depends on the binding of y where foo is called.
This kind of lexical intercourse is usually viewed more as a source of contagion than a source of pleasure. Usually it would be bad style to write such a macro. The ideal of functional programming applies as well to macros: the preferred way to communicate with a macro is through its parameters. Indeed, it is so rarely necessary to use the calling environment that most of the time it happens, it happens by mistake...
Wrapping a new environment. A macro can also cause its arguments to be evaluated in a new lexical environment. The classic example is let, which could be implemented as a macro on lambda. Within the body of an expression like (let ((y 2)) (+ x y)), y will refer to a new variable.
Saving function calls. The third consequence of the inline insertion of macro expansions is that in compiled code there is no overhead associated with a macro call. By runtime, the macro call has been replaced by its expansion. (The same is true in principle of functions declared inline.)
...
What about those operators which could be written either way [i.e. as a function or a macro]?... Here are several points to consider when we face such choices:
THE PROS
Computation at compile-time. A macro call involves computation at two times: when the macro is expanded, and when the expansion is evaluated. All the macro expansion in a Lisp program is done when the program is compiled, and every bit of computation which can be done at compile-time is one bit that won’t slow the program down when it’s running. If an operator could be written to do some of its work in the macro expansion stage, it will be more efficient to make it a macro, because whatever work a smart compiler can’t do itself, a function has to do at runtime. Chapter 13 describes macros like avg which do some of their work during the expansion phase.
Integration with Lisp. Sometimes, using macros instead of functions will make a program more closely integrated with Lisp. Instead of writing a program to solve a certain problem, you may be able to use macros to transform the problem into one that Lisp already knows how to solve. This approach, when possible, will usually make programs both smaller and more efficient: smaller because Lisp is doing some of your work for you, and more efficient because production Lisp systems generally have had more of the fat sweated out of them than user programs. This advantage appears mostly in embedded languages, which are described starting in Chapter 19.
Saving function calls. A macro call is expanded right into the code where it appears. So if you write some frequently used piece of code as a macro, you can save a function call every time it’s used. In earlier dialects of Lisp, programmers took advantage of this property of macros to save function calls at runtime. In Common Lisp, this job is supposed to be taken over by functions declared inline.
By declaring a function to be inline, you ask for it to be compiled right into the calling code, just like a macro. However, there is a gap between theory and practice here; CLTL2 (p. 229) says that “a compiler is free to ignore this declaration,” and some Common Lisp compilers do. It may still be reasonable to use macros to save function calls, if you are compelled to use such a compiler...
THE CONS
Functions are data, while macros are more like instructions to the compiler. Functions can be passed as arguments (e.g. to apply), returned by functions, or stored in data structures. None of these things are possible with macros.
In some cases, you can get what you want by enclosing the macro call within a lambda-expression. This works, for example, if you want to apply or funcall certain macros:> (funcall #’(lambda (x y) (avg x y)) 1 3) --> 2. However, this is an inconvenience. It doesn’t always work, either: even if, like avg, the macro has an &rest parameter, there is no way to pass it a varying number of arguments.
Clarity of source code. Macro definitions can be harder to read than the equivalent function definitions. So if writing something as a macro would only make a program marginally better, it might be better to use a function instead.
Clarity at runtime. Macros are sometimes harder to debug than functions. If you get a runtime error in code which contains a lot of macro calls, the code you see in the backtrace could consist of the expansions of all those macro calls, and may bear little resemblance to the code you originally wrote.
And because macros disappear when expanded, they are not accountable at runtime. You can’t usually use trace to see how a macro is being called. If it worked at all, trace would show you the call to the macro’s expander function, not the macro call itself.
Recursion. Using recursion in macros is not so simple as it is in functions. Although the expansion function of a macro may be recursive, the expansion itself may not be. Section 10.4 deals with the subject of recursion in macros...
Having considered what can be done with macros, the next question to ask is: in what sorts of applications can we use them? The closest thing to a general description of macro use would be to say that they are used mainly for syntactic transformations. This is not to suggest that the scope for macros is restricted. Since Lisp programs are made from lists, which are Lisp data structures, “syntactic transformation” can go a long way indeed...
Macro applications form a continuum between small general-purpose macros like while, and the large, special-purpose macros defined in the later chapters. On one end are the utilities, the macros resembling those that every Lisp has built-in. They are usually small, general, and written in isolation. However, you can write utilities for specific classes of programs too, and when you have a collection of macros for use in, say, graphics programs, they begin to look like a programming language for graphics. At the far end of the continuum, macros allow you to write whole programs in a language distinctly different from Lisp. Macros used in this way are said to implement embedded languages.
Yes, the first rule is: don't use a macro where a function will do.
There are a few things you can't do with functions, for example conditional evaluation of code. Others become quite unwieldy.
In general I am aware of three recurring use cases for macros (which doesn't mean that there aren't any others):
Defining forms (e. g. defun, defmacro, define-frobble-twiddle)
These often have to take some code snippet, wrap it (e. g. in a lamdba form), and register it somewhere, maybe even multiple places. The users (programmers) should only concern themselves with the code snippet. This is thus mostly about removing boilerplate. Additionally, the macro can process the body, e. g. registering docstrings, handle declarations etc.
Example: Imagine that you are writing a sort of event mini-framework. Your event handlers are pure functions that take some input and produce an effect declaration (think re-frame from the Clojure world). You want these functions to be normal named functions so that you can just test them with the usual testing frameworks, but also register them in a lookup table for your event loop mechanism. You'd maybe want to have something like a define-handler macro:
(defvar *handlers* (make-hash-table)) ; internal for the framework
(defmacro define-handler (&whole whole name lambda-list &body body)
`(progn (defun ,#(rest whole))
(setf (gethash ,name *handlers*)
(lambda ,lambda-list ,#body)))) ; could also be #',name
Control constructs (e. g. case, cond, switch, some->)
These use conditional evaluation and convenient re-arrangement of the expression.
With- style wrappers
This is an idiom to provide unwind-protect functionality to some arbitrary resource. The difference to a general with construct (as in Clojure) is that the resource type can be anything, you don't have to reify it with something like a Closable interface.
Example:
(defmacro with-foo-bar-0 (&body body)
(let ((foo-bar (gensym "FOO-BAR")))
`(let (,foo-bar))
(shiftf ,foo-bar (aref (gethash :foo *buzz*) 0) 0)
(unwind-protect (progn ,#body)
(setf (aref (gethash :foo *buzz*) 0) ,foo-bar)))))
This sets something inside a nested data structure to 0, and ensures that it is reset to the value it had before on any, even non-local, exit.
[This is a much-reduced version of a longer, incomplete answer which I decided was not appropriate for SE.]
There are no cases where you must use a macro. Indeed, there are no cases where you must use a programming language at all: if you are happy to learn the order code for the machine you are using and competent with a keypunch then you can program that way.
Most of us are not happy doing that: we like to use programming languages. These have two obvious benefits and one less-obvious but far more important one. The two obvious benefits:
programming languages make programming easier;
programming languages make programs portable across machines.
The more important reason is that building languages is an enormously successful approach to problem solving for human beings. It's so successful that we do it all the time, without even thinking we are doing it. Every time we invent some new term for something we are in fact inventing a language; every time a mathematician invents some new bit of notation they are inventing a language. People like to sneer at these languages by calling them 'jargon', 'slang' or 'dialect' but, famously: a shprakh iz a dialekt mit an armey un flot (translated: a language is a dialect with an army and navy).
The same thing is true for programming languages as is true for natural languages, except that programming languages are designed to communicate both with other humans and with a machine, and the machine requires very precise instructions. This means that it can be rather hard to build programming languages, so people tend to stick with the languages they know.
Except that they don't: the approach of building a language to describe some problem is so powerful that people in fact do this anyway. But they don't know that they are doing it and they don't have the tools to do it so what they end up with tends to be a hideous monster stitched together from pieces of other things with the robustness and readability of custard. We've all dealt with such things. A common characteristic is 'language in a string' where one language appears within strings of another language, with constructs of this inner language being put together by string operations in the outer language. If you are really lucky this will go several levels deep (I have seen three).
These things are abominations, but they are still the best way of dealing with large problem areas. Well, they are the best way if you live in a world where constructing a new programming language is so hard that only special clever people can do it
But it's hard only because if your only tool is C then everything looks like a PDP-11. If instead we used a tool which made the incremental construction of programming languages easy by allowing them to be defined in terms of simpler versions of themselves in a lightweight way, then we could just construct whole families of programming languages in which to talk about various problems, each of which would simply be a point in the space of possible languages. And anyone could do this: it would be a little bit harder than just writing functions, because working out grammar rules is a little bit harder than thinking up new words, but it would not be a lot harder.
And that's what macros do: they let you define programming languages to talk about a particular problem area in a way which is extremely lightweight. One such language is Common Lisp, but it's just one starting point in the space of Lisp-family languages: a point from which you can build the language you actually want (and people, of course, will belittle these languages by calling them 'dialects': well, a programming language is only a dialect with a standards committee).
Functions let you add to the vocabulary of the language you are building. Macros let you add to the grammar of the language. Between them they let you define a new language in which to talk about the problem area you are interested in. And doing that is the whole point of programming in Lisp: Lisp is about building languages to talk about problem areas.
An soon as you are little familiar to macros, you will wonder why you ever had this question. :-)
Macros are in no way alternatives to functions and neither vice versa. It just seems to be so, if you are working on the REPL, because macro expansion, compilation and running is happening within the moment you are pressing [enter].
Macros are running at compile time, so any macro-processing is finished, as son as your definition runs. There is no way to "call" a macro at the runtime of the definition that involves this very macro.
Macros just calculate S-exprs, that will be passed to the compiler.
Just think of a macro as something, that is coding for you.
This is easier to understand with little more code in your editor than with small definitions the REPL. Good luck!
Simple question - is the match form in Racket a macro? It certainly seems like it could be defined as a macro, but I thought it might be baked further into the implementation to make it faster or something...
Yes. See this paper if you're curious about how it's implemented. In general, all of the syntactic forms that are not listed on this page in the docs are built as macros.
match is not a macro. It is a regular Racket function.
EDIT:
I was totally wrong. Match is a macro. Here's the documentation. http://docs.racket-lang.org/reference/match.html
I have seen one answer of How does Lisp let you redefine the language itself?
Stack Overflow question (answered by Noah Lavine):
Macros aren't quite a complete redefinition of the language, at least as far as I know (I'm actually a Schemer; I could be wrong), because there is a restriction. A macro can only take a single subtree of your code, and generate a single subtree to replace it. Therefore you can't write whole-program-transforming macros, as cool as that would be.
After reading this I am curious about whether there are "whole-program-transforming macros" in Lisp or Scheme (or some other language).
If not then why?
It is not useful and never required?
Same thing could be achieved by some other ways?
It is not possible to implement it even in Lisp?
It is possible, but not tried or implemented ever?
Update
One kind of use case
e.g.
As in stumpwm code
here are some functions all in different lisp source files
uses a dynamic/global defvar variable *screen-list* that is defined in primitives.lisp , but used in screen.lisp, user.lisp, window.lisp.
(Here each files have functions, class, vars related to one aspect or object)
Now I wanted to define these functions under the closure where
*screen-list* variable available by let form, it should not be
dynamic/global variable, But without moving these all functions into
one place (because I do not want these functions to lose place from their
related file)
So that this variable will be accessible to only these functions.
Above e.g. equally apply to label and flet, so that it will further possible
that we could make it like that only required variable, function will be available,
to those who require it.
Note one way might be
implement and use some macro defun_with_context for defun where first argument is
context where let, flet variables definend.
But apart from it could it be achieved by reader-macro as
Vatine and Gareth Rees answered.
You quoted Noah Lavine as saying:
A macro can only take a single subtree of your code, and generate a single subtree to replace it
This is the case for ordinary macros, but reader macros get access to the input stream and can do whatever they like with it.
See the Hyperspec section 2.2 and the set-macro-character function.
In Racket, you can implement whole-program-transforming macros. See the section in the documentation about defining new languages. There are many examples of this in Racket, for example the lazy language and Typed Racket.
Off the top of my head, a few approaches:
First, you can. Norvig points out that:
We can write a compiler as a set of macros.
so you can transform an entire program, if you want to. I've only seen it done rarely, because typically the intersection between "things you want to do to every part of your program" and "things that you need macro/AST-type transformations for" is a pretty small set. One example is Parenscript, which transforms your Lisp code ("an extended subset of CL") into Javascript. I've used it to compile entire files of Lisp code into Javascript which is served directly to web clients. It's not my favorite environment, but it does what it advertises.
Another related feature is "advice", which Yegge describes as:
Great systems also have advice. There's no universally accepted name for this feature. Sometimes it's called hooks, or filters, or aspect-oriented programming. As far as I know, Lisp had it first, and it's called advice in Lisp. Advice is a mini-framework that provides before, around, and after hooks by which you can programmatically modify the behavior of some action or function call in the system.
Another is special variables. Typically macros (and other constructs) apply to lexical scope. By declaring a variable to be special, you're telling it to apply to dynamic scope (I think of it as "temporal scope"). I can't think of any other language that lets you (the programmer) choose between these two. And, apart from the compiler case, these two really span the space that I'm interested in as a programmer.
A typical approach is to write your own module system. If you just want access to all the code, you can have some sort of pre-processor or reader extension wrap source files with your own module annotation. If you then write your own require or import form, you will ultimately be able to see all the code in scope.
To get started, you could write your own module form that lets you define several functions which you then compile in some clever way before emitting optimized code.
There's always the choice of using compiler macros (they can do whole-function transformation based on a lew of criteria, but shouldn't change the value returned, as that would be confusing).
There's reader macros, they transform the input "as it is read" (or "before it is read", if you prefer). I haven't done much large-scale reader-macro hacking, but I have written some code to allow elisp sourec to be (mostly) read in Common Lisp, with quite a few subtle differences in syntactic sugar between the two.
I believe those sorts of macros are called code-walking macros. I haven't implemented a code walker myself, so I am not familiar with the limits.
In Common LISP, at least, you may wrap top-level forms in PROGN and they still retain their status as top-level forms (see CLTL2, section 5.3). Therefore, the limitation of a macro generating a single subtree is not much of a limitation since it could wrap any number of resulting subtrees within PROGN. This makes whole-program macros quite possible.
E.g.
(my-whole-program-macro ...)
= expands to =>
(progn
(load-system ...)
(defvar ...)
(defconstant ...)
(defmacro ...)
(defclass ...)
(defstruct ...)
(defun ...)
(defun ...)
...
)
Why would anyone prefer Scheme macros over Common Lisp macros (and I genuinely want to know too, I'm not trying to be a troll)?
My experience as a Lisp newb is that Common Lisp style macros are much easier to learn than Scheme's macros. I have yet to see any advantages to Scheme's macros, but of course that doesn't mean they don't exist.
I do know that Scheme macros are "hygenic", but I'm still not convinced this is worth the additional complexity. On the other hand though, there obviously are people that are convinced that this is necessary, otherwise there wouldn't be implementations of Scheme macros in Common Lisp.
To make a long story short, can someone defend Scheme's macros to me?
Scheme macros introduce two, essentially orthogonal, concepts: hygiene and pattern matching. Hygiene is less important in a lisp2 like Common Lisp. The pattern matching language captures many of the common macro idioms, but has the problem that it is essentially a different language from scheme. Probably the best introduction to scheme's macros, along with some of the rationale behind them is Shriram Krishnamurthi's PLAI chapters 36 and 37.
I suspect that the reason people write scheme style macro systems in common lisp is more for the pattern matching than for the hygiene.
Because they use a different, non-Scheme language, Scheme macros are less powerful than Common Lisp macros in the almost-formal sense: you can do arbitrary compile-time computation with them, but it's hairy and convoluted. It's a lot like the argument for not using set!: less-powerful set!free languages produces less buggy code in exchange for awkward handling of state. Any time you trade power for discipline, you are betting that you will be able to build more complex systems in the long run.
That's the best argument I've seen for Scheme macros over Common Lisp ones: if you are building a complex language on top of Scheme, you are less likely to introduce subtle macro bugs if you stick with the standard macro system.
Personally, I don't build big languages using macros, so I prefer Common Lisp macros. I find them much easier for small jobs and avoiding variable capture etc isn't a big deal on a small scale.
Scheme macros preserve referential transparency.
Quoting the "Guile Reference Manual" 6.10.2.2 Hygiene:
syntax-rules macros (..) preserve referential transparency. When you
read a macro definition, any free bindings in that macro are resolved
relative to the macro definition; and when you read a macro
instantiation, all free bindings in that expression are resolved
relative to the expression.
This property is sometimes known as hygiene, and it does aid in code
cleanliness. In your macro definitions, you can feel free to introduce
temporary variables, without worrying about inadvertently introducing
bindings into the macro expansion.
Standard scheme offers syntax-rules and syntax-case.
I've heard that Lisp lets you redefine the language itself, and I have tried to research it, but there is no clear explanation anywhere. Does anyone have a simple example?
Lisp users refer to Lisp as the programmable programming language. It is used for symbolic computing - computing with symbols.
Macros are only one way to exploit the symbolic computing paradigm. The broader vision is that Lisp provides easy ways to describe symbolic expressions: mathematical terms, logic expressions, iteration statements, rules, constraint descriptions and more. Macros (transformations of Lisp source forms) are just one application of symbolic computing.
There are certain aspects to that: If you ask about 'redefining' the language, then redefine strictly would mean redefine some existing language mechanism (syntax, semantics, pragmatics). But there is also extension, embedding, removing of language features.
In the Lisp tradition there have been many attempts to provide these features. A Lisp dialect and a certain implementation may offer only a subset of them.
A few ways to redefine/change/extend functionality as provided by major Common Lisp implementations:
s-expression syntax. The syntax of s-expressions is not fixed. The reader (the function READ) uses so-called read tables to specify functions that will be executed when a character is read. One can modify and create read tables. This allows you for example to change the syntax of lists, symbols or other data objects. One can also introduce new syntax for new or existing data types (like hash-tables). It is also possible to replace the s-expression syntax completely and use a different parsing mechanism. If the new parser returns Lisp forms, there is no change needed for the Interpreter or Compiler. A typical example is a read macro that can read infix expressions. Within such a read macro, infix expressions and precedence rules for operators are being used. Read macros are different from ordinary macros: read macros work on the character level of the Lisp data syntax.
replacing functions. The top-level functions are bound to symbols. The user can change the this binding. Most implementations have a mechanism to allow this even for many built-in functions. If you want to provide an alternative to the built-in function ROOM, you could replace its definition. Some implementations will raise an error and then offer the option to continue with the change. Sometimes it is needed to unlock a package. This means that functions in general can be replaced with new definitions. There are limitations to that. One is that the compiler may inline functions in code. To see an effect then one needs to recompile the code that uses the changed code.
advising functions. Often one wants to add some behavior to functions. This is called 'advising' in the Lisp world. Many Common Lisp implementations will provide such a facility.
custom packages. Packages group the symbols in name spaces. The COMMON-LISP package is the home of all symbols that are part of the ANSI Common Lisp standard. The programmer can create new packages and import existing symbols. So you could use in your programs an EXTENDED-COMMON-LISP package that provides more or different facilities. Just by adding (IN-PACKAGE "EXTENDED-COMMON-LISP") you can start to develop using your own extended version of Common Lisp. Depending on the used namespace, the Lisp dialect you use may look slighty or even radically different. In Genera on the Lisp Machine there are several Lisp dialects side by side this way: ZetaLisp, CLtL1, ANSI Common Lisp and Symbolics Common Lisp.
CLOS and dynamic objects. The Common Lisp Object System comes with change built-in. The Meta-Object Protocol extends these capabilities. CLOS itself can be extended/redefined in CLOS. You want different inheritance. Write a method. You want different ways to store instances. Write a method. Slots should have more information. Provide a class for that. CLOS itself is designed such that it is able to implement a whole 'region' of different object-oriented programming languages. Typical examples are adding things like prototypes, integration with foreign object systems (like Objective C), adding persistance, ...
Lisp forms. The interpretation of Lisp forms can be redefined with macros. A macro can parse the source code it encloses and change it. There are various ways to control the transformation process. Complex macros use a code walker, which understands the syntax of Lisp forms and can apply transformations. Macros can be trivial, but can also get very complex like the LOOP or ITERATE macros. Other typical examples are macros for embedded SQL and embedded HTML generation. Macros can also used to move computation to compile time. Since the compiler is itself a Lisp program, arbitrary computation can be done during compilation. For example a Lisp macro could compute an optimized version of a formula if certain parameters are known during compilation.
Symbols. Common Lisp provides symbol macros. Symbol macros allow to change the meaning of symbols in source code. A typical example is this: (with-slots (foo) bar (+ foo 17)) Here the symbol FOO in the source enclosed with WITH-SLOTS will be replaced with a call (slot-value bar 'foo).
optimizations, with so-called compiler macros one can provide more efficient versions of some functionality. The compiler will use those compiler macros. This is an effective way for the user to program optimizations.
Condition Handling - handle conditions that result from using the programming language in a certain way. Common Lisp provides an advanced way to handle errors. The condition system can also be used to redefine language features. For example one could handle undefined function errors with a self-written autoload mechanism. Instead of landing in the debugger when an undefined function is seen by Lisp, the error handler could try to autoload the function and retry the operation after loading the necessary code.
Special variables - inject variable bindings into existing code. Many Lisp dialects, like Common Lisp, provide special/dynamic variables. Their value is looked up at runtime on the stack. This allows enclosing code to add variable bindings that influence existing code without changing it. A typical example is a variable like *standard-output*. One can rebind the variable and all output using this variable during the dynamic scope of the new binding will go to a new direction. Richard Stallman argued that this was very important for him that it was made default in Emacs Lisp (even though Stallman knew about lexical binding in Scheme and Common Lisp).
Lisp has these and more facilities, because it has been used to implement a lot of different languages and programming paradigms. A typical example is an embedded implementation of a logic language, say, Prolog. Lisp allows to describe Prolog terms with s-expressions and with a special compiler, the Prolog terms can be compiled to Lisp code. Sometimes the usual Prolog syntax is needed, then a parser will parse the typical Prolog terms into Lisp forms, which then will be compiled. Other examples for embedded languages are rule-based languages, mathematical expressions, SQL terms, inline Lisp assembler, HTML, XML and many more.
I'm going to pipe in that Scheme is different from Common Lisp when it comes to defining new syntax. It allows you to define templates using define-syntax which get applied to your source code wherever they are used. They look just like functions, only they run at compile time and transform the AST.
Here's an example of how let can be defined in terms of lambda. The line with let is the pattern to be matched, and the line with lambda is the resulting code template.
(define-syntax let
(syntax-rules ()
[(let ([var expr] ...) body1 body2 ...)
((lambda (var ...) body1 body2 ...) expr ...)]))
Note that this is NOTHING like textual substitution. You can actually redefine lambda and the above definition for let will still work, because it is using the definition of lambda in the environment where let was defined. Basically, it's powerful like macros but clean like functions.
Macros are the usual reason for saying this. The idea is that because code is just a data structure (a tree, more or less), you can write programs to generate this data structure. Everything you know about writing programs that generate and manipulate data structures, therefore, adds to your ability to code expressively.
Macros aren't quite a complete redefinition of the language, at least as far as I know (I'm actually a Schemer; I could be wrong), because there is a restriction. A macro can only take a single subtree of your code, and generate a single subtree to replace it. Therefore you can't write whole-program-transforming macros, as cool as that would be.
However, macros as they stand can still do a whole lot of stuff - definitely more than any other language will let you do. And if you're using static compilation, it wouldn't be hard at all to do a whole-program transformation, so the restriction is less of a big deal then.
A reference to 'structure and interpretation of computer programs' chapter 4-5 is what I was missing from the answers (link).
These chapters guide you in building a Lisp evaluator in Lisp. I like the read because not only does it show how to redefine Lisp in a new evaluator, but also let you learn about the specifications of Lisp programming language.
This answer is specifically concerning Common Lisp (CL hereafter), although parts of the answer may be applicable to other languages in the lisp family.
Since CL uses S-expressions and (mostly) looks like a sequence of function applications, there's no obvious difference between built-ins and user code. The main difference is that "things the language provides" is available in a specific package within the coding environment.
With a bit of care, it is not hard to code replacements and use those instead.
Now, the "normal" reader (the part that reads source code and turns it into internal notation) expects the source code to be in a rather specific format (parenthesised S-expressions) but as the reader is driven by something called "read-tables" and these can be created and modified by the developer, it is also possible to change how the source code is supposed to look.
These two things should at least provide some rationale as to why Common Lisp can be considered a re-programmable programming language. I don't have a simple example at hand, but I do have a partial implementation of a translation of Common Lisp to Swedish (created for April 1st, a few years back).
From the outside, looking in...
I always thought it was because Lisp provided, at its core, such basic, atomic logical operators that any logical process can be built (and has been built and provided as toolsets and add-ins) from the basic components.
It is not so much that it can redefine itself as that its basic definition is so malleable that it can take any form and that no form is assumed/presumed into the structure.
As a metaphor, if you only have organic compounds you do organic chemistry, if you only have metal oxides you do metallurgy but if you have only elements you can do everything but you have extra initial steps to complete....most of which others have already done for you....
I think.....
Cool example at http://www.cs.colorado.edu/~ralex/papers/PDF/X-expressions.pdf
reader macros define X-expressions to coexist with S-expressions, e.g.,
? (cx <circle cx="62" cy="135" r="20"/>)
62
plain vanilla Common Lisp at http://www.AgentSheets.com/lisp/XMLisp/XMLisp.lisp
...
(eval-when (:compile-toplevel :load-toplevel :execute)
(when (and (not (boundp '*Non-XMLISP-Readtable*)) (get-macro-character #\<))
(warn "~%XMLisp: The current *readtable* already contains a #/< reader function: ~A" (get-macro-character #\<))))
... of course the XML parser is not so simple but hooking it into the lisp reader is.