I'm working on an assignment involving Racket and I was hoping somebody could lead me into the right direction.
I must calculate the norm of a list without recursion or using a loop and without defining any helper functions.
Is this possible? The only thing that comes to mind is to somehow use the built-in map functions
(define (norm lst)
(apply + (map square lst)))
Related
In Racket (and other Schemes, from what I can tell), the only way I know of to check whether two things are not equal is to explicitly apply not to the test:
(not (= num1 num2))
(not (equal? string1 string2))
It's obviously (not (that-big-of-deal?)), but it's such a common construction that I feel like I must be overlooking a reason why it's not built in.
One possible reason, I suppose, is that you can frequently get rid of the not by using unless instead of when, or by switching the order of the true/false branches in an if statement. But sometimes that just doesn't mimic the reasoning that you're trying to convey.
Also, I know the negated functions are easy to define, but so is <=, for example, and that is built in.
What are the design decisions for not having things like not-equal?, not-eqv?, not-eq? and != in the standard library?
First, you are correct that it is (not (that-big-of-a-deal?))1
The reason Racket doesn't include it out of the box is likely just because it adds a lot of extra primitives without much benefit. I will admit that a lot of languages do have != for not equal, but even in Java, if you want to do a deep equality check using equals() (analogous to equal? in Racket), you have to manually invert the result with a ! yourself.
Having both <= and > (as well as >= and <) was almost certainly just convenient enough to cause the original designers of the language to include it.
So no, there isn't any deep reason why there is not any shortcut for having a not-eq? function built into Racket. It just adds more primitives and doesn't happen to add much benefit. Especially as you still need not to exist on its own anyway.
1I love that pun by the way. Have some imaginary internet points.
I do miss not having a not= procedure (or ≠ as mentioned in #soegaard's comment), but not for the reasons you think.
All the numeric comparison operators are variadic. For example, (< a b c d) is the same as (and (< a b) (< b c) (< c d)). In the case of =, it checks whether all arguments are numerically equal. But there is no procedure to check whether all arguments are all unequal—and that is a different question from whether not all arguments are equal (which is what (not (= a b c d)) checks).
Yes, you can simulate that procedure using a fold. But still, meh.
Edit: Actually, I just answered my own question in this regard: the reason for the lack of a variadic ≠ procedure is that you can't just implement it using n-1 pairwise comparisons, unlike all the other numeric comparison operators. The straightforward approach of doing n-1 pairwise comparisons would mean that (≠ 1 2 1 2) would return true, and that's not really helpful.
I'll leave my original musings in place for context, and for others who wonder similar things.
Almost all of the predicates are inherited by Scheme, the standard #!racket originally followed. They kept the number of procedures to a minimum as a design principle and left it to the user to make more complex structures and code. Feel free to make the ones you'd like:
(define not-equal? (compose1 not equal?))
(define != (compose1 not =))
; and so on
You can put it in a module and require it. Keep it by convention so that people who read you code knows after a minute that everything not-<known predicate> and !-<known-predicate> are (compose not <known-predicate>)
If you want less work and you are not after using the result in filter then making a special if-not might suffice:
(define-syntax-rule (if-not p c a) (if p a c))
(define (leafs tree)
(let aux ((tree tree) (acc 0))
(if-not (pair? tree)
(+ acc 1) ; base case first
(aux (cdr tree)
(aux (car tree) acc)))))
But it's micro optimizations compared to what I would have written:
(define (leafs tree)
(let aux ((tree tree) (acc 0))
(if (not (pair? tree))
(+ acc 1) ; base case first
(aux (cdr tree)
(aux (car tree) acc)))))
To be honest if I were trying to squeeze out a not I would just have switched them manually since then optimizing speed thrumps optimal readability.
I find that one easily can define != (for numbers) using following macro:
(define-syntax-rule (!= a b)
(not(= a b)))
(define x 25)
(!= x 25)
(!= x 26)
Output:
#f
#t
That may be the reason why it is not defined in the language; it can easily be created, if needed.
This is my first asked question here, so I will do my best to make you understand my need. I'm trying to do a function which should resolve any polynomial equation in scheme language, but I am a beginner so I can't do it properly...
I've tried to detect all the unknow and make different function for the substraction, the multiply, the addition and the division but I am stuck at this. I can't make a function who while said the nature of the calcul...
So please, help me guys please.
Sorry forgot to write it :
(define (addition? L1)
(if (memq '+' L1))
#T
(else (error))
)
(define (count L1 x n)
(cond [(null? L1) n]
[(eq? (car L1) x)
(count (cdr L1) x (+ n 1))]
[else
(count (cdr L1) x n)]))
(define (polynome L1)
(compter L1))
`
You solve this as you would solve any problem:
Make a data representation of your objects. Make accessors, constructors so that using the model is more precise.
Use the knowledge on how to do the transformation manually by making an algorithm that does this using the data representation. Start with the simple cases and reuse those to make the more complex ones. Divide and conquer. Solving two simpler problems than one big is always better.
Test to see if it works. If it doesn't refine or go to step 2.
To recap. you need to know how to solve polynomial equations in order to solve this. You'll need to know how to program in the target programming language. You need to know how to divide a complex problem into smaller simpler problems.
If you don't know Scheme I suggest you start do simpler problems first.
It isn't clear whether you are looking for a symbolic or a numeric approach. If you are looking for a symbolic approach, then perhaps you can find some inspiration in the source of racket-cas.
https://github.com/soegaard/racket-cas/blob/master/racket-cas/racket-cas.rkt
Note that if we are talking about polynomials of one real variable and the coeffecients are real, there is only a general solution formula if the degree is smaller than 5.
For general, numeric root finding see bracket:
https://github.com/soegaard/bracket/blob/master/numeric/root-finding.rkt
I've read and somewhat understand Use of lambda for cons/car/cdr definition in SICP. My problem is understanding the why behind it. My first problem was staring and staring at
(define (cons x y)
(lambda (m) (m x y)))
and not understanding how this function actually did any sort of consing. Consing as I learned it from various Lisp/Scheme books is putting stuff in lists, i.e.,
(cons 1 ()) => (1)
how does
(define (cons x y)
(lambda (m) (m x y)))
do anything like consing? But as the light went on in my head: cons was only sort of a placeholder for the eventual definitions of car and cdr. So car is
(define (car z)
(z (lambda (p q) p)))
and it anticipates an incoming z. But what is this z? When I saw this use:
(car (cons 1 2))
it finally dawned on me that, yes, the cons function in its entirety is z, i.e., we're passing cons to car! How weird!
((lambda (m) (m 1 2)) (lambda (p q) p)) ; and then
((lambda (p q) p) 1 2)
which results in grabbing the first expression since the basic car operation can be thought of as an if statement where the boolean is true, thus, grab the first one.
Yes, all lists can be thought of as cons-ed together expressions, but what have we won by this strangely backward definition? It's as if any initial, stand-alone definition of cons is not germane. It's as if uses of something define that something, as if there's no something until its uses circumscribe it. Is this the primary use of closures? Can someone give me some other examples?
but what have we won by this strangely backward definition?
The point of the exercise is to demonstrate that data structures can be defined completely in terms of functions; that data structures are not necessary as a primitive construct in a language -- if you have functions (that are closures), that's sufficient. This shows the power of functions, and is probably mind-boggling to someone from outside of functional programming.
It's not that in a real project we would actually define data structures this way. It would be more efficient to use language-provided data structure constructs. But it's important to know that we can do it this way. In computer science, it's useful to be able to "reduce" one construct (data structures) into another construct (functions) so that if we prove something about the second construct, it applies to the first one too.
In Scheme, the function (map fn list0 [list1 .. listN]) comes with the restriction that the lists must have the same number of elements. Coming from Python, I'm missing the freedom of Python list comprehensions, which look a lot like map above, but without this restriction.
I'm tempted to implement an alternative "my-map", which allows for lists of differing size, iterating through the first N elements of all lists, where N is the length of the shortest list.
For example, let num be 10 and lst be (1 2 3). With my-map, I hope to write expressions like:
(my-map + (circular-list num) lst)))
And get:
(11 12 13)
I have an easier time reading this than the more conventional
(map + (lambda (arg) (+ num arg)) lst)
or
(map + (make-list (length lst) num) lst)
Two questions:
As a Scheme newbie, am I overlooked important reasons for the restriction on `map`?
Does something like `my-map` already exist in Scheme or in the SRFIs? I did take a look at srfi-42, but either it's not what I'm looking for, or it was, and it wasn't obvious.
First, note that map does allow empty lists, but of course if there's one empty list then all of them should be empty.
Second, have a look at the srfi-1 version of map -- it is specifically different from the R5RS version as follows:
This procedure is extended from its R5RS specification to allow the arguments to be of unequal length; it terminates when the shortest list runs out.
Third, most Scheme programmers would very much prefer
(map (lambda (arg) (+ num arg)) lst)
My guess is that Scheme is different from Python in a way that makes lambda expressions become more and more readable as you get used to the language.
And finally, there are some implementations that come with some form of a list comprehension. For example, in Racket you can write:
(for/list ([arg lst]) (+ num arg))
Is it possible to do so? Let's say I want to get the last element of a list, I would create a variable i = 0, and increment it until it equals to length. Any idea? An example would be greatly appreciated.
Thanks,
There are several ways to declare a variable; the cleanest one is let:
(let ((x some-expr))
; code block that uses x
But you don't need this to get the last element of a list. Just use recursion:
(define (last xs)
(if (null? (cdr xs))
(car xs)
(last (cdr xs))))
Note: if you want, you can use a variable to cache cdr's result:
(define (last xs)
(let ((tail (cdr xs)))
(if (null? tail)
(car xs)
(last tail))))
Yes, it's possible to define local variables in scheme, either using let or define inside a function. Using set!, it's also possible to reassign a variable like you imagine.
That being said, you should probably not solve your problem this way. In Scheme it's generally good practice to avoid set! when you don't need to (and in this case you definitely don't need to). Further iterating over a list using indices is usually a bad idea as scheme's lists are linked lists and as such random access O(n) (making the last function as you want to implement it O(n^2)).
So a simple recursive implementation without indices would be more idiomatic and faster than what you're planning to do and as such preferable.