Why does this Lisp function keep giving me a stack overflow? - lisp

This function here:
(defun test (a)
(if (equal a nil) 0)
(if (listp (car a)) (print "a")
(print "b"))
(test (cdr a))
)
I want it to return 0 if a is nil which is the base case. then if the element in the front of the list is a list, print the letter a otherwise print b then call function again. Why doesn't the base case prevent the infinite loop?

Your code ends up with a stack overflow because you recurse into test regardless of the result of the nil-check.
(defun test (a)
(if (equal a nil) 0) ; <-- problem is partly here...
(if (listp (car a))
(print "a")
(print "b"))
(test (cdr a))) ; <-- ...and partly down here
Even if (equal a nil) evaluates to T and the surrounding if therefore evaluates to 0, you basically ignore this result, because the next step you do is checking if a is a list regardless of the outcome of the previous nil-check. Eventually you call test again without taking the result of your comparisons into consideration.
Keep in mind that the result of a function in Lisp is the result of the last evaluated expression, meaning that if you want your function to return 0 you have to make 0 the last evaluated expression.
The following code behaves as you specified:
(defun test (a)
(if (null a)
0
(progn
(if (listp (car a))
(print "a")
(print "b"))
(test (cdr a)))))
Note that you can use null to do a nil-check.
If a is not nil, then and only then, a is examined further. For this purpose progn lets you evaluate a sequence of expressions and eventually evaluates to the result of its last expression.

The other answers have explained your problem very well; just 2 notes:
cond
At least one style guide advises againt the use of if and prefers cond; this would have avoided the "fall-through problem":
(defun test (a)
(cond
((equal a nil) 0)
(t (if (listp (car a))
(print "a")
(print "b"))
(test (cdr a)))))
return
You can return early from a function; your code would have worked with a return-from clause:
(defun test (a)
(if (equal a nil) (return-from test 0))
(if (listp (car a))
(print "a")
(print "b"))
(test (cdr a)))

Because your base case is still followed by the printing and recursion. It didn't return straight afterwards.
Perhaps you wanted this:
(defun test (a)
(if (null a)
0
(progn (if (listp (car a))
(print "a")
(print "b"))
(test (cdr a)))))

Related

Did anybody write when-let-cond?

I was thinking about a cond with a twist
(let ((a 0))
(let* ((result nil))
(tagbody
(let ((b1 (+ 0 a)))
(when (eq b1 1)
(print "1")
(setf result b1)
(go finish)))
(let ((b2 (+ 0 a)))
(when (eq b2 2)
(print "2")
(setf result b2)
(go finish)))
(when T
(print "else")
(setf result a))
(format t "=== ~A~%" a)
finish)
result))
where when test-form is wrapped in let. On one hand this seems to fit into a problem I am working on, but also seems overcomplicated. Can it be simplified with a macro? What would be the best way to simplify it if I had lots of test-forms?
Part of the problem in trying to do it that way is restricting the let blocks to only one test-form and its body.
But I wonder if I am going down the wrong path. Playing with an imaginary variant of when-let suggests there is no benefit of going down this path.
Trying cond
The version using cond appears to be more compact.
(let ((a 3))
(let* ((b1 (+ 0 a))
(b2 (+ 0 a)))
(cond
((eq b1 1)
(print "1")
b1)
((eq b2 2)
(print "2")
b2)
(T (print "else")
a))))
All boils down to the variables defined in the let* which in real life example would be used to avoid calculating the same value twice and improve readability. What should I do?
I'd prefer to think more in terms of blocks and returning values from them, instead working with goto and variables. If one really needs separate let-bound variables and their own scope:
(prog ((a 0))
(let ((b1 (+ 0 a)))
(when (eql b1 1)
(print "1")
(return b1)))
(let ((b2 (+ 0 a)))
(when (eql b2 2)
(print "2")
(return b2)))
(return
(progn
(print "else")
(return a))))
Somebody did now. I wanted it to be compatible with cond which raises a trouble: if you want the binding clauses to be like
(cond/binding
...
((var expr) <use var>)
...)
But you want to allow just general test clauses, then a function with one argument is ambiguous: should
(cond/binding
...
((car x) ...)
...)
call car or bind car? To make this work then you need to bind a useless variable in that case:
(cond/binding
...
((useless (car x)) <useless not used here>)
...)
And that means you either need to insert ignore or ignorable declarations all over the place, or live with compiler warnings.
So, well, I decided it would be better to go the other way: you have to say when you want to bind a variable. And you do that by a clause like:
(cond/binding
...
((bind var expr) <var is bound here>)
...)
And note that bind is magic in the syntax (so this means you can't call a function called bind, but that's OK as I already use bind as a keyword in other macros.
The macro also tries hard (well, hard given I basically just typed it in and it's had no testing) to actually behave like cond: returning multiple values, for instance.
So this:
(cond/binding
((f x y z) t)
((bind x 3) (print x) (values x t))
(t (values nil nil))
(1))
expands to
(block #:cond/binding
(when (f x y z)
(return-from #:cond/binding (progn t)))
(let ((x 3))
(when x
(return-from #:cond/binding
(progn (print x) (values x t)))))
(when t
(return-from #:cond/binding (progn (values nil nil))))
(let ((r 1))
(when r
(return-from #:cond/binding r))))
(where all the blocks are the same block).
So, here:
(defmacro cond/binding (&body clauses)
;; Like COND but it can bind variables. All clauses are (should be)
;; like COND, except that a clause of the form ((bind var <expr>)
;; ...) will bind a variable. Note that bind has to be literally
;; the symbol BIND: it's magic in the syntax.
(let ((bn (make-symbol "COND/BINDING")))
`(block ,bn
,#(mapcar
(lambda (clause)
(unless (consp clause)
(error "bad clause ~S" clause))
(case (length clause)
(1
`(let ((r ,(car clause)))
(when r (return-from ,bn r))))
(otherwise
(destructuring-bind (test/binding &body forms) clause
(typecase test/binding
(cons
(case (car test/binding)
((bind)
(unless (and (= (length test/binding) 3)
(symbolp (second test/binding)))
(error "bad binding clause ~S" test/binding))
(destructuring-bind (var expr) (rest test/binding)
`(let ((,var ,expr))
(when ,var
(return-from ,bn
(progn ,#forms))))))
(otherwise
`(when ,test/binding
(return-from ,bn
(progn ,#forms))))))
(t
`(when ,test/binding
(return-from ,bn
(progn ,#forms)))))))))
clauses))))
Caveat emptor.
If I understand you problem correctly, then you can use or and rely on the fact that when is evaluated to nil if the condition is not true, e.g.,
(defun example (a)
(or
(let ((b1 (+ 0 a)))
(when (eql b1 1)
(print "1")
b1))
(let ((b2 (+ 0 a)))
(when (eql b2 2)
(print "2")
b2))
(progn
(print "else")
a)))
Using macrolet is the best solution so far. That allows me to bypass the limitations of when-let and not all bindins in the let form have to evaluate to true.
(let ((a 3))
(let ((result nil))
(macrolet ((ret-go (res)
`(progn
(setf result ,res)
(go finish))))
(tagbody
(let ((b1 (+ 0 a)))
(when (eq b1 1)
(print "1")
(ret-go b1)))
(let ((b2 (+ 0 a)))
(when (eq b2 2)
(print "2")
(ret-go b2)))
(when T
(print "else")
(setf result a))
(format t "=== ~A~%" a)
finish)
result)))

Common LISP: Make Your Own Union Function

I'm trying to make my own union function and realizing how much I dislike LISP. The goal is to give the function two lists and it will return a set theoretic union of the two. My attempted solution has grown increasingly complex with the same result: NIL. I can't change that from being the result no matter what I do.
I was thinking of building a separate list in my "removeDuplicates" function below, but then idk how I'd return that with recursion. I think what's happening is my "removeDuplicates" function eventually returns an empty list (as intended) but then an empty list is return at every level of the stack when the recursion unfurls (starts returning values up the stack) but I could be wrong. I've always had trouble understanding recursion in detail. The code is below.
(defun rember (A LAT)
(cond
((null LAT) ())
((EQ (car LAT) A) (cdr LAT))
(T (cons (car LAT)(rember A (cdr LAT))))
)
)
(defun my_member (A LAT)
(cond
((null LAT) nil)
((EQ (car LAT) A) T)
(T (my_member A (cdr LAT)))
)
)
(defun removeDuplicates (L)
(cond
((null L) '())
((my_member (car L) (cdr L)) (rember (car L) L) (removeDuplicates (cdr L)))
(T (removeDuplicates (cdr L)))
)
)
(defun my_union (A B)
(setq together(append A B))
(removeDuplicates together)
)
I'm aware most people are not a fan of this format of LISP code, but I prefer it. It allows me to see how parentheses line up better than if you just put all the closing parentheses together at the end of functions and condition blocks.
If I run (my_union '(a b) '(b c)) for example, the result is NIL.
When you call removeDuplicates recursively in the last condition, you're not combining the result with the car of the list, so you're discarding that element.
You're also not using the result of rember.
(defun removeDuplicates (L)
(cond
((null L) '())
((my_member (car L) (cdr L))
(cons (car L)
(removeDuplicates
(rember (car L) (cdr L))
))
)
(T (cons (car L) (removeDuplicates (cdr L))))
)
)
Here's a simple, obvious, union function:
(defun union/tfb (&rest lists)
;; compute the union of any number of lists, implicitly using EQL
(labels ((union/spread (l1 ls)
;; UNION/SPREAD just exists to avoid the impedance
;; mismatch in argument convention
(if (null ls)
l1
(let ((result l1))
(destructuring-bind (l2 . more) ls
(dolist (e l2 (union/spread result more))
(pushnew e result)))))))
(union/spread (first lists) (rest lists))))
I think this is reasonably natural CL, although of course the whole point of using a language like CL is avoiding endless wheel-reinvention like this.
So the rules of the game perhaps say you're not allowed to use PUSHNEW: well, you can easily can replace it with a conditional involving MEMBER:
(defun union/tfb (&rest lists)
;; compute the union of any number of lists, implicitly using EQL
(labels ((union/spread (l1 ls)
;; UNION/SPREAD just exists to avoid the impedance
;; mismatch in argument convention
(if (null ls)
l1
(let ((result l1))
(destructuring-bind (l2 . more) ls
(dolist (e l2 (union/spread result more))
;; Really use PUSHNEW for this
(unless (member e result)
(setf result (cons e result)))))))))
(union/spread (first lists) (rest lists))))
And perhaps you are also not allowed to use MEMBER: well you can easily write a predicate which does what you need:
(defun union/tfb (&rest lists)
;; compute the union of any number of lists, implicitly using EQL
(labels ((union/spread (l1 ls)
;; UNION/SPREAD just exists to avoid the impedance
;; mismatch in argument convention
(if (null ls)
l1
(let ((result l1))
(destructuring-bind (l2 . more) ls
(dolist (e l2 (union/spread result more))
;; Really use MEMBER for this, and in fact
;; PUSHNEW
(unless (found-in-p e result)
(setf result (cons e result))))))))
(found-in-p (e list)
;; is e found in LIST? This exists only because we're not
;; meant to use MEMBER
(cond ((null list) nil)
((eql e (first list)) t)
(t (found-in-p e (rest list))))))
(union/spread (first lists) (rest lists))))
If you want the result to be a set with unique elements even if the first list is not you can trivially do that (note CL's UNION does not promise this, and you can get the same result with the earlier version of UNION/TFB by (union/tfb '() ...)):
(defun union/tfb (&rest lists)
;; compute the union of any number of lists, implicitly using EQL
(labels ((union/spread (l1 ls)
;; UNION/SPREAD just exists to avoid the impedance
;; mismatch in argument convention
(if (null ls)
l1
(let ((result l1))
(destructuring-bind (l2 . more) ls
(dolist (e l2 (union/spread result more))
;; Really use MEMBER for this, and in fact
;; PUSHNEW
(unless (found-in-p e result)
(setf result (cons e result))))))))
(found-in-p (e list)
;; is e found in LIST? This exists only because we're not
;; meant to use MEMBER
(cond ((null list) nil)
((eql e (first list)) t)
(t (found-in-p e (rest list))))))
(union/spread '() lists)))
Finally if the rules prevent you using iterative constructs and assignment you can do that too:
(defun union/tfb (&rest lists)
;; compute the union of any number of lists, implicitly using EQL
(labels ((union/spread (l1 ls)
;; UNION/SPREAD just exists to avoid the impedance
;; mismatch in argument convention
(if (null ls)
l1
(union/loop l1 (first ls) (rest ls))))
(union/loop (result l more)
;; UNION/LOOP is just an iteration
(if (null l)
(union/spread result more)
(destructuring-bind (e . remainder) l
(union/loop (if (found-in-p e result)
result
(cons e result))
remainder more))))
(found-in-p (e list)
;; is e found in LIST? This exists only because we're not
;; meant to use MEMBER
(cond ((null list) nil)
((eql e (first list)) t)
(t (found-in-p e (rest list))))))
(union/spread '() lists)))
The final result of all these changes is something which is, perhaps, very pure, but is not natural CL at all: something like it might be more natural in Scheme (albeit not gratuitously replacing MEMBER with a home-grown predicate like this).
One way to test your Common Lisp code is to ask your interpreter to TRACE functions:
(trace removeDuplicates my_member rember)
To avoid having too many traces, use small examples.
First, let's try with an empty list; this is an example from the REPL ("read eval print loop"), tested with SBCL, while in the "SO" package (StackOverflow); the trace is printed a bit indented, a is numbered according to the depth of the recursion. Here the call is not recursive and terminates right away:
SO> (removeduplicates nil)
0: (SO::REMOVEDUPLICATES NIL)
0: REMOVEDUPLICATES returned NIL
NIL
This works, let's try an example with a singleton list, where there is obviously no duplicate:
SO> (removeduplicates '(1))
0: (SO::REMOVEDUPLICATES (1))
1: (SO::MY_MEMBER 1 NIL)
1: MY_MEMBER returned NIL
1: (SO::REMOVEDUPLICATES NIL)
1: REMOVEDUPLICATES returned NIL
0: REMOVEDUPLICATES returned NIL
NIL
removeDuplicate calls my_member, which correctly returns nil, followed by a recursive call to removeDuplicates with nil, which correctly returns nil. There is however a problem because then, the outermost call returns nil too, which is incorrect.
Looking at the trace, we have to look back at the code to find a place where my_member is called, followed by a recursive call to removeDuplicates. There is only one place wher my_member is called, as a test to the second clause in the cond;
Since the result is nil for that test, the next clause is tried, in that case the default case:
(cond
...
;; this is the call to my_member (= nil)
((my_member (car L) (cdr L)) ...)
;; this is the recursive call
(t (removeDuplicates (cdr L))))
The value of the cond is the one given by the last (removeDuplicates (cdr L)), which just does not retain the existing elements in front of L. If you were mutating a sequence, you could just recurse down the subsequence and ignore the previous elements: in that case the caller would still hold a reference to the original sequence, which would get its element removed by a side-effect of your functions. But here you are following a strictly immutable approach, and you have to recontruct a list as a return value.
In other words, removeDuplicates is expressed as: return a new list which contains the same elements as the original list, but without duplicates.
So you have to add (car L) in front of (removeDuplicates (cdr L)).
(defun removeDuplicates (L)
(cond
((null L) '())
((my_member (car L) (cdr L)) (rember (car L) L) (removeDuplicates (cdr L)))
(T (cons (car L)
(removeDuplicates (rest L))))))
Let's test:
SO> (removeduplicates '())
0: (SO::REMOVEDUPLICATES NIL)
0: REMOVEDUPLICATES returned NIL
NIL
SO> (removeduplicates '(1))
0: (SO::REMOVEDUPLICATES (1))
1: (SO::MY_MEMBER 1 NIL)
1: MY_MEMBER returned NIL
1: (SO::REMOVEDUPLICATES NIL)
1: REMOVEDUPLICATES returned NIL
0: REMOVEDUPLICATES returned (1)
(1)
You can test with a longer list (without duplicates), the result is correct, but the trace is longer.
Now, let's add duplicates:
SO> (removeduplicates '(1 2 2 1))
0: (SO::REMOVEDUPLICATES (1 2 2 1))
1: (SO::MY_MEMBER 1 (2 2 1))
2: (SO::MY_MEMBER 1 (2 1))
3: (SO::MY_MEMBER 1 (1))
3: MY_MEMBER returned T
2: MY_MEMBER returned T
1: MY_MEMBER returned T
1: (SO::REMBER 1 (1 2 2 1))
1: REMBER returned (2 2 1)
1: (SO::REMOVEDUPLICATES (2 2 1))
2: (SO::MY_MEMBER 2 (2 1))
2: MY_MEMBER returned T
2: (SO::REMBER 2 (2 2 1))
2: REMBER returned (2 1)
2: (SO::REMOVEDUPLICATES (2 1))
3: (SO::MY_MEMBER 2 (1))
4: (SO::MY_MEMBER 2 NIL)
4: MY_MEMBER returned NIL
3: MY_MEMBER returned NIL
3: (SO::REMOVEDUPLICATES (1))
4: (SO::MY_MEMBER 1 NIL)
4: MY_MEMBER returned NIL
4: (SO::REMOVEDUPLICATES NIL)
4: REMOVEDUPLICATES returned NIL
3: REMOVEDUPLICATES returned (1)
2: REMOVEDUPLICATES returned (2 1)
1: REMOVEDUPLICATES returned (2 1)
0: REMOVEDUPLICATES returned (2 1)
(2 1)
The result is correct (order does not matter).
So far, our tests are good.
You might not have identified the other problem in that function, namely that all calls to rember are useless, and frankly this is not necessarily easy to spot with the trace. But looking at the code, it should be clear if you write code to have little side-effects that the following clause calls (rember ...) for nothing:
((my_member (car L) (cdr L)) (rember (car L) L) (removeDuplicates (cdr L)))
A cond clause has for syntax (TEST . BODY), where BODY is a sequence of expressions that evaluates like a PROGN: the value of a PROGN is the value of its last clause, all intermediate clauses are only used for their side-effects. For example:
(progn
(print "I am here")
(* 10 3))
Here above, the call to PRINT returns a value, but it is discarded: the value of the enclosing PROGN is 30.
In your code, rember does no side-effect, and its return value is discarded. Just remove it:
(defun removeDuplicates (L)
(cond
((null L) '())
((my_member (car L) (cdr L))
(removeDuplicates (cdr L)))
(T (cons (first L)
(removeDuplicates (rest L))))))
I would write the same code as follows, personally:
(defun remove-duplicate-elements (list)
(when list
(let ((head (first list))
(tail (remove-duplicate-elements (rest list))))
(if (member head tail) tail (cons head tail)))))
Here is a remove-dupes that removes duplicates from a list in O(n) time using a hash table. It supports a custom equality function (which must be eq, eql, equal or `equalp) and a custom test function, so that any aspect of an item can be treated as the key.
(defun remove-dupes (list &key (test #'eql) (key #'identity))
(let ((hash (make-hash-table :test test)))
(loop for item in list
for item-key = (funcall key item)
for seen = (gethash item-key hash)
unless seen collect item and
do (setf (gethash item-key hash) t))))
For instance, suppose we have the assoc list ((a . 1) (a . 2) (b . 3) (c . 4) (b . 4)). We'd like to remove duplicates by car:
[1]> (remove-dupes '((a . 1) (a . 2) (b . 3) (c . 4) (b . 4)) :key #'car)
((A . 1) (B . 3) (C . 4))
Only the leftmost A, B and C entries are reported; the duplicates are suppressed. Now let's do it by cdr:
[2]> (remove-dupes '((a . 1) (a . 2) (b . 3) (c . 4) (b . 4)) :key #'cdr)
((A . 1) (A . 2) (B . 3) (C . 4))
The (b . 4) got culled due to the duplicated 4 value.
But, why do all this, when Common Lisp provides a remove-duplicates function (not to mention union).
remove-duplicates is more general than what I have here: it handles sequences, rather than just lists, so it works on vectors and strings. It has more keyword parameters.

Check for proper list in Common Lisp

Is there a standard function in Common Lisp that can check against improper lists (i.e. circular and dotted lists) without signaling an error? list-length can check against circular lists (it returns nil for them), but signals type-error when given a dotted list.
Scheme's list? traverses the whole list to make sure it is not dotted or circular; Common Lisp's listp only checks that it's given nil or a cons cell.
Here's the simplest I could come up with:
(defun proper-list-p (x)
(not (null (handler-case (list-length x) (type-error () nil)))))
Since several implementations have been suggested and many unexpected problems have been found, here's a test suite for aspiring proper-list-p writers:
(defun circular (xs)
(let ((xs (copy-list xs)))
(setf (cdr (last xs)) xs)
xs))
(assert (eql t (proper-list-p '())))
(assert (eql t (proper-list-p '(1))))
(assert (eql t (proper-list-p '(1 2))))
(assert (eql t (proper-list-p '(1 2 3))))
(assert (not (proper-list-p 1)))
(assert (not (proper-list-p '(1 . 2))))
(assert (not (proper-list-p '(1 2 . 3))))
(assert (not (proper-list-p '(1 2 3 . 4))))
(assert (not (proper-list-p (circular '(1)))))
(assert (not (proper-list-p (circular '(1 2)))))
(assert (not (proper-list-p (circular '(1 2 3)))))
(assert (not (proper-list-p (list* 1 (circular '(2))))))
(assert (not (proper-list-p (list* 1 2 (circular '(3 4))))))
There is no standard function to do this, perhaps because such a function was seen as rather expensive if it was to be correct, but, really, this just seems like am omission from the language to me.
A minimal (not very performant) implementation, which does not rely on handling errors (Python people think that's a reasonable way to program, I don't, although this is a stylistic choice), is, I think
(defun proper-list-p (l)
(typecase l
(null t)
(cons
(loop for tail = l then (cdr tail)
for seen = (list tail) then (push tail seen)
do (cond ((null tail)
(return t))
((not (consp tail))
(return nil))
((member tail (rest seen))
(return nil)))))))
This takes time quadratic in the length of l, and conses proportional to the length of l. You can obviously do better using an hashtable for the occurs check, and you can use a tortoise-&-hare algorithm do avoid the occurs check (but I'm not sure what the complexity of that is off the top of my head).
I am sure there are much better functions than this in libraries. In particular Alexandria has one.
While thinking about this question, I also wrote this function:
(defun classify-list (l)
"Classify a possible list, returning four values.
The first value is a symbol which is
- NULL if the list is empty;
- LIST if the list is a proper list;
- CYCLIC-LIST if it contains a cycle;
- IMPROPER-LIST if it does not end with nil;
- NIL if it is not a list.
The second value is the total number of conses in the list (following
CDRs only). It will be 0 for an empty list or non-list.
The third value is the cons at which the cycle in the list begins, or
NIL if there is no cycle or the list isn't a list.
The fourth value is the number if conses in the cycle, or 0 if there is no cycle.
Note that you can deduce the length of the leading element of the list
by subtracting the total number of conses from the number of conses in
the cycle: you can then use NTHCDR to pull out the cycle."
;; This is written as a tail recursion, I know people don't like
;; that in CL, but I wrote it for me.
(typecase l
(null (values 'null 0 nil 0 0))
(cons
(let ((table (make-hash-table)))
(labels ((walk (tail previous-tail n)
(typecase tail
(null
(values 'list n nil 0))
(cons
(let ((m (gethash tail table nil)))
(if m
(values 'cyclic-list n tail (- n m))
(progn
(setf (gethash tail table) n)
(walk (cdr tail) tail (1+ n))))))
(t
(values 'improper-list n previous-tail 0)))))
(walk l nil 0))))
(t (values nil 0 nil 0))))
This can be used to get a bunch of information about a list: how long it is, if it is proper, if not if it's cyclic, and where the cycle is. Beware that in the cases of cyclic lists this will return circular structure as its third value. I believe that you need to use an occurs check to do this – tortoise & hare will tell you if a list is cyclic, but not where the cycle starts.
in addition, something slightly less verbose, than the accepted answer:
(defun improper-tail (ls)
(do ((x ls (cdr x))
(visited nil (cons x visited)))
((or (not (consp x)) (member x visited)) x)))
(defun proper-list-p (ls)
(null (improper-tail ls)))
or just like this:
(defun proper-list-p (ls)
(do ((x ls (cdr x))
(visited nil (cons x visited)))
((or (not (consp x)) (member x visited)) (null x))))
seen to pass all the op's test assertions
After our hopeless attempts with tailp, here, sth which uses the
sharp-representation of circular lists :) .
With regex (to detect circular sublist)
(setf *print-circle* t)
(ql:quickload :cl-ppcre)
(defun proper-listp (lst)
(or (null lst) ; either a `'()` or:
(and (consp lst) ; a cons
(not (cl-ppcre::scan "#\d+=(" (princ-to-string lst)))) ; not circular
(null (cdr (last lst)))))) ; not a dotted list
Without regex (cannot detect circular sublists)
(defun proper-listp (lst)
(or (null lst) ; either a `'()` or:
(and (consp lst) ; a cons
(not (string= "#" (subseq (princ-to-string lst) 0 1))) ; not circular
(null (cdr (last lst)))))) ; not a dotted list
(tailp l (cdr l)) is t for circular lists but nil for non-circular lists.
Credits to #tfp and #RainerJoswig who taught me this here .
So, your function would be:
(defun proper-listp (lst)
(or (null lst) ; either a `'()` or:
(and (consp lst) ; a cons
(not (tailp lst (cdr lst))) ; not circular
(null (cdr (last lst)))))) ; not a dotted list
By the way, I use proper-listp by purpose. Correct would be - by convetion proper-list-p. However, this name is already occupied in the CLISP implementation by SYSTEM::%PROPER-LIST-Pwhy the definition of the function raises a continuable error.
Conclusion of our discussion in the comment section:
The behavior of tailp for circular lists is undefined. Therefore this answer is wrong! Thank you #Lassi for figuring this out!

Mutual Recursion in Common Lisp

This is the Common Lisp code:
(defun take (L)
(if (null L) nil
(cons (car L) (skip (cdr L)))))
(defun skip (L)
(if (null L) nil
(cons (car L) (take (cdr L)))))
The idea here is that, "take" will give all the odd sequence elements in the input list and "skip" will give all the even sequence elements in the input list. However, in both cases the entire list is returned.
What is the error in this code? Is this something to do with how CL handles lists, because the similar code in SML gives the desired output.
fun take(lst) =
if lst = nil then nil
else hd(lst)::skip(tl(lst))
and
skip(lst) =
if lst = nil then nil
else hd(lst)::take(tl(lst));
To expound on what Sylwester has said, your skip is wrong in both Lisp and SML. It should be
(defun take (L) ; even-indexed elements of a list L
(if (not (null L))
(cons (car L) (skip (cdr L)))))
(defun skip (L) ; odd-indexed elements of a list L
(if (not (null L))
(take (cdr L))))
and
fun take(lst) =
if lst = nil then nil
else hd(lst)::skip(tl(lst))
and
skip(lst) =
if lst = nil then nil
else take(tl(lst));
The take and skip are identical so that is no mystery. skip should just tail call instead of cons-ing. It's the consing that makes the return here.
It's worth pointing out that indexing in Common Lisp (like many other programming languages) starts with 0, so the even-indexed elements of a list are the first, the third, the fifth, and so on, since those have indices 0, 2, 4, etc. It's also worth noting that in Common Lisp, you can take the rest of the empty list and get back the empty list. (You can't do this in every Lisp, though. E.g., in Scheme it's an error to call cdr on something that's not a pair.) This means that you can implement even-elements and odd-elements rather easily. even-elementsjust returns a list of the first element, and the odd elements of the rest of the list. odd-elements returns the even-elements of the rest of the list:
(defun even-elements (list)
(if (endp list) list
(list* (first list) (odd-elements (rest list)))))
(defun odd-elements (list)
(even-elements (rest list)))
These behave in the expected fashion:
CL-USER> (even-elements '(0 1 2 3 4 5))
(0 2 4)
CL-USER> (odd-elements '(0 1 2 3 4 5))
(1 3 5)
Of course, if you note that the call to (odd-elements x) is just a call to (even-elements (rest x)), we could have implemented even-elements as follows, and had the same result:
(defun even-elements (list)
(if (endp list) list
(list* (first list) (even-elements (rest (rest list))))))

How does Lisp "prog" work in this example?

I'm a beginner in lisp and I need somebody to explain to me how the prog form works, step by step. What is the initial value of l1 ? Nil ?
The problem outputs T if the list has an even number of elements on the first level, nil if not.
(defun nr_par (l)
(prog ((l1 l))
ciclu
(cond
((null l1) (return T))
((null (cdr l1)) (return NIL))
((null (cddr l1)) (return T))
(T (setf l1 (cddr l1))
(go ciclu)))))
On console:
(nr_par '(1 2 3 4 5 6 7 8))
T
The program is straightforward, but not very idiomatic lisp (it is rather imperative instead of functional). Step by step goes as follows.
prog uses a series of variable bindings, in this case, l1 is assigned the value of l initially. Then, a series of statements in which a loop starts (again, not very lisp idiomatic).
This type of loops use a tag (ciclu) and a goto instruction (go), again, not recommended, but it is there. After that, the cond checks a series of cases. When the list is empty (null), you return true, in other cases, you check if the length is even or odd, and return the value in consequence.
In the case that the list is longer than one or two elements (neither of the cases is null), the l1 list is adjusted to point to the next of the next element of itself (the cddr function).
Finally, the go function turns the program back to the ciclu tag.
The program will finish when any of the cond clauses is met, returning either T or NIL.
See PROG in CLHS: L1 is var, L is init-form, so the initial value of L1 is the value of L.
As the CLHS page for prog says, it does three things: lets you have local vars and initialize them; lets you have tags as in tagbody and use go; and lets you use return as inside a block named NIL:
(defun nr_par (l)
(prog ((l1 l)) ; local binding(s)
ciclu
(if (null l1) (return T)) ; return
(if (null (cdr l1)) (return NIL))
(setf l1 (cddr l1))
(go ciclu))) ; go
(defun nr_par1 (l) ; directly equivalent
(labels ((ciclu (l1)
(if (null l1) (return-from ciclu T))
(if (null (cdr l1)) (return-from ciclu NIL))
(ciclu (cddr l1))))
(ciclu l)))
(defun nr_par2 (l) ; also equivalent
(do ((l1 l (cddr l1)))
(NIL) ; while T ...
(cond
((null l1) (return T))
((null (cdr l1)) (return NIL)))))
Function call is a glorified goto after all, isn't it?
See also Longest decreasing sequence in Lisp for an example representing several mutually-recursive functions hand-compiled into a prog with a bunch of GO statements.