In my ongoing quest to recreate lodash in lisp as a way of getting familiar with the language I am trying to write a concat-list function that takes an initial list and an arbitrary number of additional lists and concatenates them.
I'm sure that this is just a measure of getting familiar with lisp convention, but right now my loop is just returning the second list in the argument list, which makes sense since it is the first item of other-lists.
Here's my non-working code (edit: refactored):
(defun concat-list (input-list &rest other-lists)
;; takes an arbitrary number of lists and merges them
(loop
for list in other-lists
append list into input-list
return input-list
)
)
Trying to run (concat-list '(this is list one) '(this is list two) '(this is list three)) and have it return (this is list one this is list two this is list three).
How can I spruce this up to return the final, merged list?
The signature of your function is a bit unfortunate, it becomes easier if you don't treat the first list specially.
The easy way:
(defun concat-lists (&rest lists)
(apply #'concatenate 'list lists))
A bit more lower level, using loop:
(defun concat-lists (&rest lists)
(loop :for list :in lists
:append list))
Going lower, using dolist:
(defun concat-lists (&rest lists)
(let ((result ()))
(dolist (list lists (reverse result))
(setf result (revappend list result)))))
Going even lower would maybe entail implementing revappend yourself.
It's actually good style in Lisp not to use LABELS based iteration, since a) it's basically a go-to like low-level iteration style and it's not everywhere supported. For example the ABCL implementation of Common Lisp on the JVM does not support TCO last I looked. Lisp has wonderful iteration facilities, which make the iteration intention clear:
CL-USER 217 > (defun my-append (&rest lists &aux result)
(dolist (list lists (nreverse result))
(dolist (item list)
(push item result))))
MY-APPEND
CL-USER 218 > (my-append '(1 2 3) '(4 5 6) '(7 8 9))
(1 2 3 4 5 6 7 8 9)
Some pedagogical solutions to this problem
If you just want to do this, then use append, or nconc (destructive), which are the functions which do it.
If you want to learn how do to it, then learning about loop is not how to do that, assuming you want to learn Lisp: (loop for list in ... append list) really teaches you nothing but how to write a crappy version of append using arguably the least-lispy part of CL (note I have nothing against loop & use it a lot, but if you want to learn lisp, learning loop is not how to do that).
Instead why not think about how you would write this if you did not have the tools to do it, in a Lispy way.
Well, here's how you might do that:
(defun append-lists (list &rest more-lists)
(labels ((append-loop (this more results)
(if (null this)
(if (null more)
(nreverse results)
(append-loop (first more) (rest more) results))
(append-loop (rest this) more (cons (first this) results)))))
(append-loop list more-lists '())))
There's a dirty trick here: I know that results is completely fresh so I am using nreverse to reverse it, which does so destructively. Can we write nreverse? Well, it's easy to write reverse, the non-destructive variant:
(defun reverse-nondestructively (list)
(labels ((r-loop (tail reversed)
(if (null tail)
reversed
(r-loop (rest tail) (cons (first tail) reversed)))))
(r-loop list '())))
And it turns out that a destructive reversing function is only a little harder:
(defun reverse-destructively (list)
(labels ((rd-loop (tail reversed)
(if (null tail)
reversed
(let ((rtail (rest tail)))
(setf (rest tail) reversed)
(rd-loop rtail tail)))))
(rd-loop list '())))
And you can check it works:
> (let ((l (make-list 1000 :initial-element 1)))
(time (reverse-destructively l))
(values))
Timing the evaluation of (reverse-destructively l)
User time = 0.000
System time = 0.000
Elapsed time = 0.000
Allocation = 0 bytes
0 Page faults
Why I think this is a good approach to learning Lisp
[This is a response to a couple of comments which I thought was worth adding to the answer: it is, of course, my opinion.]
I think that there are at least three different reasons for wanting to solve a particular problem in a particular language, and the approach you might want to take depends very much on what your reason is.
The first reason is because you want to get something done. In that case you want first of all to find out if it has been done already: if you want to do x and the language a built-in mechanism for doing x then use that. If x is more complicated but there is some standard or optional library which does it then use that. If there's another language you could use easily which does x then use that. Writing a program to solve the problem should be something you do only as a last resort.
The second reason is because you've fallen out of the end of the first reason, and you now find yourself needing to write a program. In that case what you want to do is use all of the tools the language provides in the best way to solve the problem, bearing in mind things like maintainability, performance and so on. In the case of CL, then if you have some problem which naturally involves looping, then, well, use loop if you want to. It doesn't matter whether loop is 'not lispy' or 'impure' or 'hacky': just do what you need to do to get the job done and make the code maintainable. If you want to print some list of objects, then by all means write (format t "~&~{~A~^, ~}~%" things).
The third reason is because you want to learn the language. Well, assuming you can program in some other language there are two approaches to doing this.
the first is to say 'I know how to do this thing (write loops, say) in languages I know – how do I do it in Lisp?', and then iterate this for all the thing you already know how to do in some other language;
the second is to say 'what is it that makes Lisp distinctive?' and try and understand those things.
These approaches result in very approaches to learning. In particular I think the first approach is often terrible: if the language you know is, say, Fortran, then you'll end up writing Fortran dressed up as Lisp. And, well, there are perfectly adequate Fortran compilers out there: why not use them? Even worse, you might completely miss important aspects of the language and end up writing horrors like
(defun sum-list (l)
(loop for i below (length l)
summing (nth i l)))
And you will end up thinking that Lisp is slow and pointless and return to the ranks of the heathen where you will spread such vile calumnies until, come the great day, the golden Lisp horde sweeps it all away. This has happened.
The second approach is to ask, well, what are the things that are interesting about Lisp? If you can program already, I think this is a much better approach to the first, because learning the interesting and distinctive features of a language first will help you understand, as quickly as possible, whether its a language you might actually want to know.
Well, there will inevitably be argument about what the interesting & distinctive features of Lisp are, but here's a possible, partial, set.
The language has a recursively-defined data structure (S expressions or sexprs) at its heart, which is used among other things to represent the source code of the language itself. This representation of the source is extremely low-commitment: there's nothing in the syntax of the language which says 'here's a block' or 'this is a conditiona' or 'this is a loop'. This low-commitment can make the language hard to read, but it has huge advantages.
Recursive processes are therefore inherently important and the language is good at expressing them. Some variants of the language take this to the extreme by noticing that iteration is simply a special case of recursion and have no iterative constructs at all (CL does not do this).
There are symbols, which are used as names for things both in the language itself and in programs written in the language (some variants take this more seriously than others: CL takes it very seriously).
There are macros. This really follows from the source code of the language being represented as sexprs and this structure having a very low commitment to what it means. Macros, in particular, are source-to-source transformations, with the source being represented as sexprs, written in the language itself: the macro language of Lisp is Lisp, without restriction. Macros allow the language itself to be seamlessly extended: solving problems in Lisp is done by designing a language in which the problem can be easily expressed and solved.
The end result of this is, I think two things:
recursion, in addition to and sometimes instead of iteration is an unusually important technique in Lisp;
in Lisp, programming means building a programming language.
So, in the answer above I've tried to give you examples of how you might think about solving problems involving a recursive data structure recursively: by defining a local function (append-loop) which then recursively calls itself to process the lists. As Rainer pointed out that's probably not a good way of solving this problem in Common Lisp as it tends to be hard to read and it also relies on the implementation to turn tail calls into iteration which is not garuanteed in CL. But, if your aim is to learn to think the way Lisp wants you to think, I think it is useful: there's a difference between code you might want to write for production use, and code you might want to read and write for pedagogical purposes: this is pedagogical code.
Indeed, it's worth looking at the other half of how Lisp might want you to think to solve problems like this: by extending the language. Let's say that you were programming in 1960, in a flavour of Lisp which has no iterative constructs other than GO TO. And let's say you wanted to process some list iteratively. Well, you might write this (this is in CL, so it is not very like programming in an ancient Lisp would be: in CL tagbody establishes a lexical environment in the body of which you can have tags – symbols – and then go will go to those tags):
(defun print-list-elements (l)
;; print the elements of a list, in order, using GO
(let* ((tail l)
(current (first tail)))
(tagbody
next
(if (null tail)
(go done)
(progn
(print current)
(setf tail (rest tail)
current (first tail))
(go next)))
done)))
And now:
> (print-list-elements '(1 2 3))
1
2
3
nil
Let's program like it's 1956!
So, well, let's say you don't like writing this sort of horror. Instead you'd like to be able to write something like this:
(defun print-list-elements (l)
;; print the elements of a list, in order, using GO
(do-list (e l)
(print e)))
Now if you were using most other languages you need to spend several weeks mucking around with the compiler to do this. But in Lisp you spend a few minutes writing this:
(defmacro do-list ((v l &optional (result-form nil)) &body forms)
;; Iterate over a list. May be buggy.
(let ((tailn (make-symbol "TAIL"))
(nextn (make-symbol "NEXT"))
(donen (make-symbol "DONE")))
`(let* ((,tailn ,l)
(,v (first ,tailn)))
(tagbody
,nextn
(if (null ,tailn)
(go ,donen)
(progn
,#forms
(setf ,tailn (rest ,tailn)
,v (first ,tailn))
(go ,nextn)))
,donen
,result-form))))
And now your language has an iteration construct which it previously did not have. (In real life this macro is called dolist).
And you can go further: given our do-list macro, let's see how we can collect things into a list:
(defun collect (thing)
;; global version: just signal an error
(declare (ignorable thing))
(error "not collecting"))
(defmacro collecting (&body forms)
;; Within the body of this macro, (collect x) will collect x into a
;; list, which is returned from the macro.
(let ((resultn (make-symbol "RESULT"))
(rtailn (make-symbol "RTAIL")))
`(let ((,resultn '())
(,rtailn nil))
(flet ((collect (thing)
(if ,rtailn
(setf (rest ,rtailn) (list thing)
,rtailn (rest ,rtailn))
(setf ,resultn (list thing)
,rtailn ,resultn))
thing))
,#forms)
,resultn)))
And now we can write the original append-lists function entirely in terms of constructs we've invented:
(defun append-lists (list &rest more-lists)
(collecting
(do-list (e list) (collect e))
(do-list (l more-lists)
(do-list (e l)
(collect e)))))
If that's not cool then nothing is.
In fact we can get even more carried away. My original answer above used labels to do iteration As Rainer has pointed out, this is not safe in CL since CL does not mandate TCO. I don't particularly care about that (I am happy to use only CL implementations which mandate TCO), but I do care about the problem that using labels this way is hard to read. Well, you can, of course, hide this in a macro:
(defmacro looping ((&rest bindings) &body forms)
;; A sort-of special-purpose named-let.
(multiple-value-bind (vars inits)
(loop for b in bindings
for var = (typecase b
(symbol b)
(cons (car b))
(t (error "~A is hopeless" b)))
for init = (etypecase b
(symbol nil)
(cons (unless (null (cddr b))
(error "malformed binding ~A" b))
(second b))
(t
(error "~A is hopeless" b)))
collect var into vars
collect init into inits
finally (return (values vars inits)))
`(labels ((next ,vars
,#forms))
(next ,#inits))))
And now:
(defun append-lists (list &rest more-lists)
(collecting
(looping ((tail list) (more more-lists))
(if (null tail)
(unless (null more)
(next (first more) (rest more)))
(progn
(collect (first tail))
(next (rest tail) more))))))
And, well, I just think it is astonishing that I get to use a programming language where you can do things like this.
Note that both collecting and looping are intentionally 'unhygenic': they introduce a binding (for collect and next respectively) which is visible to code in their bodies and which would shadow any other function definition of that name. That's fine, in fact, since that's their purpose.
This kind of iteration-as-recursion is certainly cool to think about, and as I've said I think it really helps you to think about how the language can work, which is my purpose here. Whether it leads to better code is a completely different question. Indeed there is a famous quote by Guy Steele from one of the 'lambda the ultimate ...' papers:
procedure calls may be usefully thought of as GOTO statements which also pass parameters
And that's a lovely quote, except that it cuts both ways: procedure calls, in a language which optimizes tail calls, are pretty much GOTO, and you can do almost all the horrors with them that you can do with GOTO. But GOTO is a problem, right? Well, it turns out so are procedure calls, for most of the same reasons.
So, pragmatically, even in a language (or implementation) where procedure calls do have all these nice characteristics, you end up wanting constructs which can express iteration and not recursion rather than both. So, for instance, Racket which, being a Scheme-family language, does mandate tail-call elimination, has a whole bunch of macros with names like for which do iteration.
And in Common Lisp, which does not mandate tail-call elimination but which does have GOTO, you also need to build macros to do iteration, in the spirit of my do-list above. And, of course, a bunch of people then get hopelessly carried away and the end point is a macro called loop: loop didn't exist (in its current form) in the first version of CL, and it was common at that time to simply obtain a copy of it from somewhere, and make sure it got loaded into the image. In other words, loop, with all its vast complexity, is just a macro which you can define in a CL which does not have it already.
OK, sorry, this is too long.
(loop for list in (cons '(1 2 3)
'((4 5 6) (7 8 9)))
append list)
I want to know if these two definitions of nth are equal:
I. is defined as macro:
(defmacro -nth (n lst)
(defun f (n1 lst1)
(cond ((eql n1 0) lst1)
(t `(cdr ,(f (- n1 1) lst1)))))
`(car ,(f n lst)))
II. is defined as a bunch of functions:
(defun f (n lst)
(cond ((eql n 0) lst)
(t `(cdr ,(f (- n 1) lst)))))
(defun f1 (n lst)
`(car ,(f n `',lst)))
(defun --nth (n lst)
(eval (f1 n lst)))
Am i get the right idea? Is macro definition is evaluating of expression, constructed in its body?
OK, let start from the beginning.
Macro is used to create new forms that usually depend on macro's input. Before code is complied or evaluated, macro has to be expanded. Expansion of a macro is a process that takes place before evaluation of form where it is used. Result of such expansion is usually a lisp form.
So inside a macro here are a several levels of code.
Not quoted code will be evaluated during macroexpansion (not at run-time!), in your example you define function f when macro is expanded (for what?);
Next here is quoted (with usual quote or backquote or even nested backquotes) code that will become part of macroexpansion result (in its literal form); you can control what part of code will be evaluated during macroexpansion and what will stay intact (quoted, partially or completely). This allows one to construct anything before it will be executed.
Another feature of macro is that it does not evaluate its parameters before expansion, while function does. To give you picture of what is a macro, see this (just first thing that came to mind):
(defmacro aif (test then &optional else)
`(let ((it ,test))
(if it ,then ,else)))
You can use it like this:
CL-USER> (defparameter *x* '((a . 1) (b . 2) (c . 3) (d . 4)))
*X*
CL-USER> (aif (find 'c *x* :key #'car) (1+ (cdr it)) 0)
4
This macro creates useful lexical binding, capturing variable it. After checking of a condition, you don't have to recalculate result, it's accessible in forms 'then' and 'else'. It's impossible to do with just a function, it has introduced new control construction in language. But macro is not just about creating lexical environments.
Macro is a powerful tool. It's impossible to fully describe what you can do with it, because you can do everything. But nth is not something you need a macro for. To construct a clone of nth you can try to write a recursive function.
It's important to note that LISP macro is most powerful thing in the programming world and LISP is the only language that has this power ;-)
To inspire you, I would recommend this article: http://www.paulgraham.com/avg.html
To master macro, begin with something like this:
http://www.gigamonkeys.com/book/macros-defining-your-own.html
Then may be Paul Graham's "On Lisp", then "Let Over Lambda".
There is no need for either a macro nor eval to make abstractions to get the nth element of a list. Your macro -nth doesn't even work unless the index is literal number. try this:
(defparameter test-list '(9 8 7 6 5 4 3 2 1 0))
(defparameter index 3)
(nth index test-list) ; ==> 6 (this is the LISP provided nth)
(-nth index test-list) ; ==> ERROR: index is not a number
A typical recursive solution of nth:
(defun nth2 (index list)
(if (<= index 0)
(car list)
(nth2 (1- index) (cdr list))))
(nth2 index test-list) ; ==> 6
A typical loop version
(defun nth3 (index list)
(loop :for e :in list
:for i :from index :downto 0
:when (= i 0) :return e))
(nth3 index test-list) ; ==> 6
Usually a macro is something you use when you see your are repeating yourself too much and there is no way to abstract your code further with functions. You may make a macro that saves you the time to write boilerplate code. Of course there is a trade off of not being standard code so you usually write the macro after a couple of times have written the boilerplate.
eval should never be used unless you really have to. Usually you can get by with funcall and apply. eval works only in the global scope so you loose closure variables.
I am new to lisp, and am learning as I go.
The standard common lisp break function 1. pops you into the debugger, and 2. if you choose to continue, returns nil.
It seems to me that a break function that popped you into the debugger but RETURNED ITS INPUT would be extremely useful. Then, you could just insert it transparently around a given s-expression to look at the state of the program at that point.
So I could do something like
CL-USER> (break-transparent (+ 1 2))
which would pop me into the debugger and let me look around and then would return
3
Is there such a thing in lisp, and, if not, is there a way to make such a thing? I am not good with macros yet.
Thanks,
EDIT:
Doug Currie kindly answered this below with a simple macro. Here is my slightly modified version for anyone else with this question that displays the argument to break-transparent front and center in the debugger window.
(defmacro break-transparent (exp)
`(let ((x ,exp)) (break "argument to break: ~:S" x) x))
You can write break-transparent as a macro that expands to:
(progn
(break)
(+ 1 2))
or if you really want to evaluate the expression before the break:
(let ((x (+ 1 2)))
(break)
x)
So,
(defmacro (break-transparent exp)
`(let ((x ,exp)) (break) x))
Since you've added the macro from the other answer to your question in a slightly modified version, here's a fixed version of that that doesn't add a new identifer that might interfere with an existing one:
(defmacro break-transparent (value)
(let ((g (gensym)))
`(let ((,g ,value))
(break "argument to break: ~:S" ,g)
,g)))
Can someone help me understand how push can be implemented as a macro? The naive version below evaluates the place form twice, and does so before evaluating the element form:
(defmacro my-push (element place)
`(setf ,place (cons ,element ,place)))
But if I try to fix this as below then I'm setf-ing the wrong place:
(defmacro my-push (element place)
(let ((el-sym (gensym))
(place-sym (gensym)))
`(let ((,el-sym ,element)
(,place-sym ,place))
(setf ,place-sym (cons ,el-sym ,place-sym)))))
CL-USER> (defparameter *list* '(0 1 2 3))
*LIST*
CL-USER> (my-push 'hi *list*)
(HI 0 1 2 3)
CL-USER> *list*
(0 1 2 3)
How can I setf the correct place without evaluating twice?
Doing this right seems to be a little more complicated. For instance, the code for push in SBCL 1.0.58 is:
(defmacro-mundanely push (obj place &environment env)
#!+sb-doc
"Takes an object and a location holding a list. Conses the object onto
the list, returning the modified list. OBJ is evaluated before PLACE."
(multiple-value-bind (dummies vals newval setter getter)
(sb!xc:get-setf-expansion place env)
(let ((g (gensym)))
`(let* ((,g ,obj)
,#(mapcar #'list dummies vals)
(,(car newval) (cons ,g ,getter))
,#(cdr newval))
,setter))))
So reading the documentation on get-setf-expansion seems to be useful.
For the record, the generated code looks quite nice:
Pushing into a symbol:
(push 1 symbol)
expands into
(LET* ((#:G906 1) (#:NEW905 (CONS #:G906 SYMBOL)))
(SETQ SYMBOL #:NEW905))
Pushing into a SETF-able function (assuming symbol points to a list of lists):
(push 1 (first symbol))
expands into
(LET* ((#:G909 1)
(#:SYMBOL908 SYMBOL)
(#:NEW907 (CONS #:G909 (FIRST #:SYMBOL908))))
(SB-KERNEL:%RPLACA #:SYMBOL908 #:NEW907))
So unless you take some time to study setf, setf expansions and company, this looks rather arcane (it may still look so even after studying them). The 'Generalized Variables' chapter in OnLisp may be useful too.
Hint: if you compile your own SBCL (not that hard), pass the --fancy argument to make.sh. This way you'll be able to quickly see the definitions of functions/macros inside SBCL (for instance, with M-. inside Emacs+SLIME). Obviously, don't delete those sources (you can run clean.sh after install.sh, to save 90% of the space).
Taking a look at how the existing one (in SBCL, at least) does things, I see:
* (macroexpand-1 '(push 1 *foo*))
(LET* ((#:G823 1) (#:NEW822 (CONS #:G823 *FOO*)))
(SETQ *FOO* #:NEW822))
T
So, I imagine, mixing in a combination of your version and what this generates, one might do:
(defmacro my-push (element place)
(let ((el-sym (gensym))
(new-sym (gensym "NEW")))
`(let* ((,el-sym ,element)
(,new-sym (cons ,el-sym ,place)))
(setq ,place ,new-sym)))))
A few observations:
This seems to work with either setq or setf. Depending on what problem you're actually trying to solve (I presume re-writing push isn't the actual end goal), you may favor one or the other.
Note that place does still get evaluated twice... though it does at least do so only after evaluating element. Is the double evaluation something you actually need to avoid? (Given that the built-in push doesn't, I'm left wondering if/how you'd be able to... though I'm writing this up before spending terribly much time thinking about it.) Given that it's something that needs to evaluate as a "place", perhaps this is normal?
Using let* instead of let allows us to use ,el-sym in the setting of ,new-sym. This moves where the cons happens, such that it's evaluated in the first evaluation of ,place, and after the evaluation of ,element. Perhaps this gets you what you need, with respect to evaluation ordering?
I think the biggest problem with your second version is that your setf really does need to operate on the symbol passed in, not on a gensym symbol.
Hopefully this helps... (I'm still somewhat new to all this myself, so I'm making some guesses here.)
I am working on a genetic programming hobby project.
I have a function/macro setup that, when evaluated in a setq/setf form, will generate a list that will look something like this.
(setq trees (make-trees 2))
==> (+ x (abs x))
Then it will get bound out to a lambda function #<FUNCTION :LAMBDA (X) ... > via strategic use of functions/macros
However, I want to get a bit more effective with this than manually assigning to variables, so I wrote something like this:
(setq sample
(let* ((trees (make-trees 2))
(tree-bindings (bind-trees trees))
(evaluated-trees (eval-fitness tree-bindings))))
(list (trees tree-bindings evaluated-trees)))
However, I get EVAL: trees has no value when I place this in a let form. My suspicion is that the macro expansions don't get fully performed in a LET as compared to a SETF, but that doesn't make sense to me.
What is the cause of this issue?
--- edit: yanked my code and put the whole file in a pastebin ---
Supposing that I decide that a setq isn't going to do it for me and I write a simple function to do it:
(defun generate-sample ()
(let ((twiggs (make-trees 2)))
(let ((tree-bindings (bind-trees twiggs)))
(let ((evaluated-trees (eval-fitness tree-bindings)))
(list twiggs tree-bindings evaluated-trees)))))
This yields an explosion of ...help file error messages (??!?)... and "eval: variable twiggs has no value", which stems from the bind-trees definition on SLIME inspection.
I am reasonably sure that I've completely hosed my macros. http://pastebin.org/673619
(Setq make-trees 2) sets the value of the variable make-trees to 2, then returns 2.
I do not see a reason for a macro in what you describe. Is it true that your make-trees creates a single random tree, which can be interpreted as a program? Just define this as a function with defun. I am thinking of something like this:
(defun make-tree (node-number)
(if (= node-number 1)
(make-leaf)
(cons (get-random-operator)
(mapcar #'make-tree
(random-partition (- node-number 1))))))
Let and setq do totally different things. Setq assigns a value to an existing variable, while let creates a new lexical scope with a number of lexical bindings.
I think that you should present more of your code; currently, your question does not make a lot of sense.
Update:
I will fix your snippet's indentation to make things clearer:
(setq sample
(let* ((trees (make-trees 2))
(tree-bindings (bind-trees trees))
(evaluated-trees (eval-fitness tree-bindings))))
(list (trees tree-bindings evaluated-trees)))
Now, as written before, let* establishes lexical bindings. These
are only in scope within its body:
(setq sample
(let* ((trees (make-trees 2))
(tree-bindings (bind-trees trees))
(evaluated-trees (eval-fitness tree-bindings)))
;; here trees, tree-bindings, and evaluated-trees are bound
) ; end of let* body
;; here trees, tree-bindings, and evaluated trees are not in scope anymore
(list (trees tree-bindings evaluated-trees)))
That last line is spurious, too. If those names were bound, it would
return a list of one element, which would be the result of evaluating
the function trees with tree-bindings and evaluated-trees as
arguments.
You might get what you want like this:
(setq sample
(let* ((trees (make-trees 2))
(tree-bindings (bind-trees trees))
(evaluated-trees (eval-fitness tree-bindings)))
(list trees tree-bindings evaluated-trees)))
Another update:
The purpose of macros is to eliminate repeated code when that elimination is not possible with functions. One frequent application is when dealing with places, and you also need them to define new control constructs. As long as you do not see that something cannot work as a function, do not use a macro for it.
Here is some code that might help you:
(defun make-tree-lambda (depth)
(list 'lambda '(x)
(new-tree depth)))
(defun make-tree-function (lambda-tree)
(eval lambda-tree))
(defun eval-fitness (lambda-form-list input-output-list)
"Determines how well the lambda forms approach the wanted function
by comparing their output with the wanted output in the supplied test
cases. Returns a list of mean quadratic error sums."
(mapcar (lambda (lambda-form)
(let* ((actual-results (mapcar (make-tree-function lambda-form)
(mapcar #'first input-output-list)))
(differences (mapcar #'-
actual-results
(mapcar #'second input-output-list)))
(squared-differences (mapcar #'square
differences)))
(/ (reduce #'+ squared-differences)
(length squared-differences))))
lambda-form-list))
(defun tree-fitness (tree-list input-output-list)
"Creates a list of lists, each inner list is (tree fitness). Input
is a list of trees, and a list of test cases."
(mapcar (lambda (tree fitness)
(list tree fitness))
tree-list
(eval-fitness (mapcar #'make-tree-lambda tree-list)
input-output-list)))