I have tried to write a procedure that gets an integer as parameter and returns true if the number is a palindrome and false otherwise and it seems to be that there is a problem with changing a global parameter's value whithin an internal function block.
(define index 0)
(define (palindrome? x)
(if (= (lenght x) 1)
#t
(if (last_equal_first x)
(palindrome? (remove x))
#f)))
(define (lenght x)
(define index **(+ index 1))**
(if (= (modulo x (ten_power index)) x)
index
(lenght x)))
(define (last_equal_first x)
(if (= (modulo x 10) (modulo x (/ (ten_power (lenght x)) 10)))
#t
#f))
I would like to know what can I do about it
thanks!
Well, one problem is that you're redefining index after it's been used, in the length function. define doesn't really do what you want here - you want set!.
However, I think you'll find another bug when you try to call the length function more than once - you never set index to 0 after the first time, so I believe your length function will only work once.
However, this seems like it might be a homework assignment. Would you like clear instructions on fixing these problems, or would you like clues that lead you to understand the algorithm more?
What that (define ...) statement does in lenght is create a new variable called "index" that is more locally scoped than the "index" you defined at the top. That's only the superficial problem---more importantly, it looks like you're trying to write C code using Scheme. In a simple homework assignment like this, you should not need to use global variables, nor should you ever have to change a variable once it's created. Many programmers have trouble shifting how they think when first learning functional programming.
The way you've written lenght is not so much recursion as just a glorified while loop! There is no point to recursion if (lenght x) only calls (lenght x) again. For example, here's how I would write digits to count how many base-10 digits are in a number:
(define digits
(lambda (n)
(letrec ([digit-helper (lambda (n index)
(if (= (modulo n (expt 10 index)) n)
index
(digit-helper n (add1 index))))])
(digit-helper n 0))))
Notice how I never change a variable once it's been created, but only create new variables each time. Since I need to keep track of index, I created helper function digit-helper that takes two arguments to mask the fact that digit only takes one argument.
Related
I feel that understanding this subtlety might help me to understand how scope works in Scheme.
So why does Scheme error out if you try to do something like:
(define (func n)
(define n (+ 1 n))
n)
It only errors out at runtime when calling the function.
The reason I find it strange is because Scheme does allow re-definitions, even inside functions. For example this gives no error and will always return the value 5 as expected:
(define (func n)
(define n 5)
n)
Additionally, Scheme also seems to support self-re-definition in global space. For instance:
(define a 5)
(define a (+ 1 a))
gives no error and results in "a" displaying "6" as expected.
So why does the same thing give a runtime error when it occurs inside a function (which does support re-definition)? In other words: Why does self-re-definition only not work when inside of a function?
global define
First off, top level programs are handled by a different part of the implementation than in a function and defining an already defined variable is not allowed.
(define a 10)
(define a 20) ; ERROR: duplicate definition for identifier
It might happen that it works in a REPL since it's common to redefine stuff, but when running programs this is absolutely forbidden. In R5RS and before what happened is underspecified and didn't care since be specification by violating it it no longer is a Scheme program and implementers are free to do whatever they want. The result is of course that a lot of underspecified stuff gets implementation specific behaviour which are not portable or stable.
Solution:
set! mutates bindings:
(define a 10)
(set! a 20)
define in a lambda (function, let, ...)
A define in a lambda is something completely different, handled by completely different parts of the implementation. It is handled by the macro/special form lambda so that it is rewritten to a letrec*
A letrec* or letrec is used for making functions recursive so the names need to be available at the time the expressions are evaluated. Because of that when you define n it has already shadowed the n you passed as argument. In addition from R6RS implementers are required to signal an error when a binding is evaluated that is not yet initialized and that is probably what happens. Before R6RS implementers were free to do whatever they wanted:
(define (func n)
(define n (+ n 1)) ; illegal since n hasn't got a value yet!
n)
This actually becomes:
(define func
(lambda (n)
(let ((n 'undefined-blow-up-if-evaluated))
(let ((tmpn (+ n 1)))
(set! n tmpn))
n)))
Now a compiler might see that it violates the spec at compile time, but many implementations doesn't know before it runs.
(func 5) ; ==> 42
Perfectly fine result in R5RS if the implementers have good taste in books.
The difference in the version you said works is that this does not violate the rule of evaluating n before the body:
(define (func n)
(define n 5)
n)
becomes:
(define func
(lambda (n)
(let ((n 'undefined-blow-up-if-evaluated))
(let ((tmpn 5)) ; n is never evaluated here!
(set! n tmpn))
n)))
Solutions
Use a non conflicting name
(define (func n)
(define new-n (+ n 1))
new-n)
Use let. It does not have its own binding when the expression gets evaluated:
(define (func n)
(let ((n (+ n 1)))
n))
I know this is maybe an oddball idea, but I thought might as well give it a try to ask here.
I was experimenting in Racket about state representation without local variables.
The idea was defining a function that prints it's parameter value and if called again gives me another value. Since pure functions called with the same parameter always produce the same result, my workaround-idea got me the following.
(define (counter n)
(displayln n)
(λ () (counter (add1 n)))) ; unapplied lambda so it doesn't go in a loop
Then I devised a function to call counter and its resulting lambdas a certain number of times.
(define (call proc n)
(unless (zero? n)
(let ([x (proc)])
(call x (sub1 n)))))
Which results in this:
> (call (counter 0) 5)
0
1
2
3
4
5
What is the name for the concept applied here? Propably it's something trivial what you need in real applications all the time, but since I have no experience in that respect yet so I can't pinpoint a name for it. Or maybe I just complicated something very simple, but nonetheless I would appreciate an answer so I can look further into it.
Sorry if my question is not clear enough, but english is not my first language and to ask about things I have no name for makes me feel kinda uncertain.
You're using closures to save state: a lambda form stores the environment in which it was defined, and you keep redefining the procedure (called x in your code), so each time it "remembers" a new value for n.
Another way to do the same would be to let the procedure itself keep track of the value - in other words, counter should remember the current n value between invocations. This is what I mean:
(define (counter initial)
(let ((n (sub1 initial)))
(lambda ()
(set! n (add1 n))
n)))
In the above code, the first invocation of counter returns a new lambda that closes over n, and each invocation of that lambda modifies n and returns its new value. Equivalently, we could use Racket-specific syntax for currying and the begin0 special form to achieve the same effect:
(define ((counter n))
(begin0
n
(set! n (add1 n))))
Either way, notice how the procedure "remembers" its previous value:
(define proc (counter 0))
(proc)
=> 0
(proc)
=> 1
And we would call it like this:
(define (call proc n)
(unless (zero? n)
(displayln (proc))
(call proc (sub1 n))))
(call (counter 0) 5)
=> 0
1
2
3
4
Also notice that the above fixes an off-by-one error originally in your code - the procedure was being called six times (from 0 to 5) and not five times as intended, that happened because call invokes counter five times, but you called counter one more time outside, when evaluating (counter 0).
In an effort to find a simple example of CPS which doesn't give me a headache , I came across this Scheme code (Hand typed, so parens may not match) :
(define fact-cps
(lambda(n k)
(cond
((zero? n) (k 1))
(else
(fact-cps (- n 1)
(lambda(v)
(k (* v n))))))))
(define fact
(lambda(n)
(fact-cps n (lambda(v)v)))) ;; (for giggles try (lambda(v)(* v 2)))
(fact 5) => 120
Great, but Scheme isn't Common Lisp, so I took a shot at it:
(defun not-factorial-cps(n k v)
(declare (notinline not-factorial-cps)) ;; needed in clisp to show the trace
(cond
((zerop n) (k v))
((not-factorial-cps (1- n) ((lambda()(setq v (k (* v n))))) v))))
;; so not that simple...
(defun factorial(n)
(not-factorial-cps n (lambda(v)v) 1))
(setf (symbol-function 'k) (lambda(v)v))
(factorial 5) => 120
As you can see, I'm having some problems, so although this works, this has to be wrong. I think all I've accomplished is a convoluted way to do accumulator passing style. So other than going back to the drawing board with this, I had some questions: Where exactly in the Scheme example is the initial value for v coming from? Is it required that lambda expressions only be used? Wouldn't a named function accomplish more since you could maintain the state of each continuation in a data structure which can be manipulated as needed? Is there in particular style/way of continuation passing style in Common Lisp with or without all the macros? Thanks.
The problem with your code is that you call the anonymous function when recurring instead of passing the continuation like in the Scheme example. The Scheme code can easily be made into Common Lisp:
(defun fact-cps (n &optional (k #'values))
(if (zerop n)
(funcall k 1)
(fact-cps (- n 1)
(lambda (v)
(funcall k (* v n))))))
(fact-cps 10) ; ==> 3628800
Since the code didn't use several terms or the implicit progn i switched to if since I think it's slightly more readable. Other than that and the use of funcall because of the LISP-2 nature of Common Lisp it's the identical code to your Scheme version.
Here's an example of something you cannot do tail recursively without either mutation or CPS:
(defun fmapcar (fun lst &optional (k #'values))
(if (not lst)
(funcall k lst)
(let ((r (funcall fun (car lst))))
(fmapcar fun
(cdr lst)
(lambda (x)
(funcall k (cons r x)))))))
(fmapcar #'fact-cps '(0 1 2 3 4 5)) ; ==> (1 1 2 6 24 120)
EDIT
Where exactly in the Scheme example is the initial value for v coming
from?
For every recursion the function makes a function that calls the previous continuation with the value from this iteration with the value from the next iteration, which comes as an argument v. In my fmapcar if you do (fmapcar #'list '(1 2 3)) it turns into
;; base case calls the stacked lambdas with NIL as argument
((lambda (x) ; third iteration
((lambda (x) ; second iteration
((lambda (x) ; first iteration
(values (cons (list 1) x)))
(cons (list 2) x)))
(cons (list 3) x))
NIL)
Now, in the first iteration the continuation is values and we wrap that in a lambda together with consing the first element with the tail that is not computed yet. The next iteration we make another lambda where we call the previous continuation with this iterations consing with the tail that is not computed yet.. At the end we call this function with the empty list and it calls all the nested functions from end to the beginning making the resulting list in the correct order even though the iterations were in oposite order from how you cons a list together.
Is it required that lambda expressions only be used? Wouldn't a named
function accomplish more since you could maintain the state of each
continuation in a data structure which can be manipulated as needed?
I use a named function (values) to start it off, however every iteration of fact-cps has it's own free variable n and k which is unique for that iteration. That is the data structure used and for it to be a named function you'd need to use flet or labels in the very same scope as the anonymous lambda functions are made. Since you are applying previous continuation in your new closure you need to build a new one every time.
Is there in particular style/way of continuation passing style in
Common Lisp with or without all the macros?
It's the same except for the dual namespace. You need to either funcall or apply. Other than that you do it as in any other language.
In my OO World, I have an instance of "weapon" class called "max-damage". I asked to create a random number for a variable called "damage".
It says: The amount of "damage" suffered should be a random integer no more than the "max-damage", and at least 1.
I need some help to create that random integer, thanks!
PS: I can't ask more questions, in order to ask this question, I have changed the previous one, sorry..
You got the syntax of filter wrong, it's necessary that you pass a procedure as the first argument. Concretely, the procedure is a predicate (meaning: it evaluates to a boolean value), and the output list will only keep the elements in the original list that evaluate to #t when passed to the procedure. This is what I mean:
(define (remove-divisible lst value)
(filter (lambda (x) (not (zero? (remainder x value))))
lst))
If using a lambda bothers you, it's always possible to define a helper procedure, like this:
(define (remove-divisible lst value)
(define (not-divisible? x)
(not (zero? (remainder x value))))
(filter not-divisible? lst))
I have to define a variadic function in Scheme that takes the following form:
(define (n-loop procedure [a list of pairs (x,y)]) where the list of pairs can be any length.
Each pair specifies a lower and upper bound. That is, the following function call: (n-loop (lambda (x y) (inspect (list x y))) (0 2) (0 3)) produces:
(list x y) is (0 0)
(list x y) is (0 1)
(list x y) is (0 2)
(list x y) is (1 0)
(list x y) is (1 1)
(list x y) is (1 2)
Obviously, car and cdr are going to have to be involved in my solution. But the stipulation that makes this difficult is the following. There are to be no assignment statements or iterative loops (while and for) used at all.
I could handle it using while and for to index through the list of pairs, but it appears I have to use recursion. I don't want any code solutions, unless you feel it is necessary for explanation, but does anyone have a suggestion as to how this might be attacked?
The standard way to do looping in Scheme is to use tail recursion. In fact, let's say you have this loop:
(do ((a 0 b)
(b 1 (+ a b))
(i 0 (+ i 1)))
((>= i 10) a)
(eprintf "(fib ~a) = ~a~%" i a))
This actually get macro-expanded into something like the following:
(let loop ((a 0)
(b 1)
(i 0))
(cond ((>= i 10) a)
(else (eprintf "(fib ~a) = ~a~%" i a)
(loop b (+ a b) (+ i 1)))))
Which, further, gets macro-expanded into this (I won't macro-expand the cond, since that's irrelevant to my point):
(letrec ((loop (lambda (a b i)
(cond ((>= i 10) a)
(else (eprintf "(fib ~a) = ~a~%" i a)
(loop b (+ a b) (+ i 1)))))))
(loop 0 1 0))
You should be seeing the letrec here and thinking, "aha! I see recursion!". Indeed you do (specifically in this case, tail recursion, though letrec can be used for non-tail recursions too).
Any iterative loop in Scheme can be rewritten as that (the named let version is how loops are idiomatically written in Scheme, but if your assignment won't let you use named let, expand one step further and use the letrec). The macro-expansions I've described above are straightforward and mechanical, and you should be able to see how one gets translated to the other.
Since your question asked how about variadic functions, you can write a variadic function this way:
(define (sum x . xs)
(if (null? xs) x
(apply sum (+ x (car xs)) (cdr xs))))
(This is, BTW, a horribly inefficient way to write a sum function; I am just using it to demonstrate how you would send (using apply) and receive (using an improper lambda list) arbitrary numbers of arguments.)
Update
Okay, so here is some general advice: you will need two loops:
an outer loop, that goes through the range levels (that's your variadic stuff)
an inner loop, that loops through the numbers in each range level
In each of these loops, think carefully about:
what the starting condition is
what the ending condition is
what you want to do at each iteration
whether there is any state you need to keep between iterations
In particular, think carefully about the last point, as that is how you will nest your loops, given an arbitrary number of nesting levels. (In my sample solution below, that's what the cur variable is.)
After you have decided on all these things, you can then frame the general structure of your solution. I will post the basic structure of my solution below, but you should have a good think about how you want to go about solving the problem, before you look at my code, because it will give you a good grasp of what differences there are between your solution approach and mine, and it will help you understand my code better.
Also, don't be afraid to write it using an imperative-style loop first (like do), then transforming it to the equivalent named let when it's all working. Just reread the first section to see how to do that transformation.
All that said, here is my solution (with the specifics stripped out):
(define (n-loop proc . ranges)
(let outer ((cur ???)
(ranges ranges))
(cond ((null? ranges) ???)
(else (do ((i (caar ranges) (+ i 1)))
((>= i (cadar ranges)))
(outer ??? ???))))))
Remember, once you get this working, you will still need to transform the do loop into one based on named let. (Or, you may have to go even further and transform both the outer and inner loops into their letrec forms.)