Passing a function as an parameter in scheme - functional-programming

I am trying to create a function (last) that takes an function ( f ) and a List as an parameter. The list is passed to the function (odd?) and if the last element in the list is odd it returns true(#t) else it returns false (#f) .But the following code is not working , what is the correct way to declare the function as an parameter .
(define (last f L)
(if (null? L) '() ( last f (cdr L)) ))
(last odd? '( 0 5 3 8 6 7))

Here'a how you can write a solution using just built-in functions, notice the correct syntax for passing a procedure as a parameter, and also be aware that it's a bad idea to name your function as last, it clashes with an existing procedure, the very same that you should use to solve the problem!
(define (my-last f L)
(f (last L)))
If you definitely have to write the function from scratch, then make sure that you understand what base cases are needed:
(define (my-last f L)
(cond ((null? L) #f)
((null? (cdr L)) (f (car L)))
(else (my-last f (cdr L)))))
Either way, it works as expected:
(my-last odd? '(0 5 3 8 6 7))
=> #t

For how you wrote the function, you have an extra parentheses set in the call. It should just be (last odd? '(0 5 3 8 6 7)) as someone suggested you in the comments.

Related

Question about foldl function in Racket. (Functional programming)

So I have this line of code:
(foldl cons '() '(1 2 3 4))
And the output I get when I run it is this:
'(4 3 2 1)
Can you please explain to me why I don’t get '(1 2 3 4) instead?
I read the documentation but I am still a bit confused about how foldl works. Also if I wanted to define foldl how would I specify in Racket that the function can take a variable amount of lists as arguments?
Thanks!
Yes. By the definition of left fold, the combining function is called with the first element of the list and the accumulated result so far, and the result of that call is passed (as the new, updated accumulated result so far) to the recursive invocation of foldl with the same combining function and the rest of the list:
(foldl cons '() '(1 2 3))
=
(foldl cons (cons 1 '()) '(2 3))
=
(foldl cons (cons 2 (cons 1 '())) '(3))
=
(foldl cons (cons 3 (cons 2 (cons 1 '()))) '())
=
(cons 3 (cons 2 (cons 1 '())))
And when the list is empty, the accumulated result so far is returned as the final result.
To your second question, variadic functions in Scheme are specified with the dot . in the argument list, like so:
(define (fold-left f acc . lists)
(if (null? (first lists)) ;; assume all have same length
acc
(apply fold-left ;; recursive call
f
(apply f (append (map first lists) ;; combine first elts
(list acc))) ;; with result so far
(map rest lists)))) ;; the rests of lists
Indeed,
(fold-left (lambda (a b result)
(* result (- a b)))
1
'(1 2 3)
'(4 5 6))
returns -27.

Reverse list in CLISP

I'm trying to write my own function to reverse list in LISP. The problem is input
(revert '(2 3 (4 5 (6))))
My code looks like this:
(defun revert (l)
(if (null l)
nil
(append (revert (cdr l)) (list (car l)))))
It returns
((4 5 (6)) 3 2)
instead of this:
(((6) 5 4) 3 2)
How can I fix it to work correctly?
Since you want to reverse sublists as well, you have to use REVERT on the CAR as well as CDR:
(defun revert (l)
(if (null l)
nil
(append (revert (cdr l))
(list (revert (car l))))))
This however requires you to handle the possibility that L might be an atom, which should be returned as is. Since NIL is also an atom you can just change the condition to check for ATOM instead of NULL.
(defun revert (list)
(if (atom list)
list
(append (revert (cdr list))
(list (revert (car list))))))
(revert '(2 3 (4 5 (6))))
;=> (((6) 5 4) 3 2)
In Common Lisp, it's preferred to use full words for names, so it's better to name l list. You could also name the function something like tree-reverse.

How do I call my funtion factory with a filter?

I made a function factory in Scheme which receives a binary function f, and call it to a list of 1 or more variables.
(define makeDoForAll
(lambda (f)
(define (helper a lst)
(if (null? lst)
a
(if (null? (cdr lst))
(f a (car lst))
(helper (f a (car lst))
(cdr lst)))))
(lambda (x . others)
(helper x others))))
I want to make a new function that uses this function factory to sum up all even numbers in a given list, so that (sumEvens 1 2 3 4 5) will output 6 for example.
How do I call the function factory while implementing the filter (even? x)?
Some remarks:
Nested if are best written as cond expressions.
It looks like you are implementing a fold function.
You could generate a closure that accepts a list and performs both filtering and addition, but the simplest way to do what you want is to filter the list first, and then sum the resulting elements:
(foldl + 0 (filter even? '(1 2 3 4 5)))
=> 6

What is "named let" and how do I use it to implement a map function?

I'm totally new to Scheme and I am trying to implement my own map function. I've tried to find it online, however all the questions I encountered were about some complex versions of map function (such as mapping functions that take two lists as an input).
The best answer I've managed to find is here: (For-each and map in Scheme). Here is the code from this question:
(define (map func lst)
(let recur ((rest lst))
(if (null? rest)
'()
(cons (func (car rest)) (recur (cdr rest))))))
It doesn't solve my problem though because of the usage of an obscure function recur. It doesn't make sense to me.
My code looks like this:
(define (mymap f L)
(cond ((null? L) '())
(f (car L))
(else (mymap (f (cdr L))))))
I do understand the logic behind the functional approach when programming in this language, however I've been having great difficulties with coding it.
The first code snippet you posted is indeed one way to implement the map function. It uses a named let. See my comment on an URL on how it works. It basically is an abstraction over a recursive function. If you were to write a function that prints all numbers from 10 to 0 you could write it liks this
(define (printer x)
(display x)
(if (> x 0)
(printer (- x 1))))
and then call it:
(printer 10)
But, since its just a loop you could write it using a named let:
(let loop ((x 10))
(display x)
(if (> x 0)
(loop (- x 1))))
This named let is, as Alexis King pointed out, syntactic sugar for a lambda that is immediately called. The above construct is equivalent to the snippet shown below.
(letrec ((loop (lambda (x)
(display x)
(if (> x 0)
(loop (- x 1))))))
(loop 10))
In spite of being a letrec it's not really special. It allows for the expression (the lambda, in this case) to call itself. This way you can do recursion. More on letrec and let here.
Now for the map function you wrote, you are almost there. There is an issue with your two last cases. If the list is not empty you want to take the first element, apply your function to it and then apply the function to the rest of the list. I think you misunderstand what you actually have written down. Ill elaborate.
Recall that a conditional clause is formed like this:
(cond (test1? consequence)
(test2? consequence2)
(else elsebody))
You have any number of tests with an obligatory consequence. Your evaluator will execute test1? and if that evaluated to #t it will execute the consequence as the result of the entire conditional. If test1? and test2? fail it will execute elsebody.
Sidenote
Everything in Scheme is truthy except for #f (false). For example:
(if (lambda (x) x)
1
2)
This if test will evaluate to 1 because the if test will check if (lambda (x) x) is truthy, which it is. It is a lambda. Truthy values are values that will evaluate to true in an expression where truth values are expected (e.g., if and cond).
Now for your cond. The first case of your cond will test if L is null. If that is evaluated to #t, you return the empty list. That is indeed correct. Mapping something over the empty list is just the empty list.
The second case ((f (car L))) literally states "if f is true, then return the car of L".
The else case states "otherwise, return the result mymap on the rest of my list L".
What I think you really want to do is use an if test. If the list is empty, return the empty list. If it is not empty, apply the function to the first element of the list. Map the function over the rest of the list, and then add the result of applying the function the first element of the list to that result.
(define (mymap f L)
(cond ((null? L) '())
(f (car L))
(else (mymap (f (cdr L))))))
So what you want might look look this:
(define (mymap f L)
(cond ((null? L) '())
(else
(cons (f (car L))
(mymap f (cdr L))))))
Using an if:
(define (mymap f L)
(if (null? L) '()
(cons (f (car L))
(mymap f (cdr L)))))
Since you are new to Scheme this function will do just fine. Try and understand it. However, there are better and faster ways to implement this kind of functions. Read this page to understand things like accumulator functions and tail recursion. I will not go in to detail about everything here since its 1) not the question and 2) might be information overload.
If you're taking on implementing your own list procedures, you should probably make sure they're using a proper tail call, when possible
(define (map f xs)
(define (loop xs ys)
(if (empty? xs)
ys
(loop (cdr xs) (cons (f (car xs)) ys))))
(loop (reverse xs) empty))
(map (λ (x) (* x 10)) '(1 2 3 4 5))
; => '(10 20 30 40 50)
Or you can make this a little sweeter with the named let expression, as seen in your original code. This one, however, uses a proper tail call
(define (map f xs)
(let loop ([xs (reverse xs)] [ys empty])
(if (empty? xs)
ys
(loop (cdr xs) (cons (f (car xs)) ys)))))
(map (λ (x) (* x 10)) '(1 2 3 4 5))
; => '(10 20 30 40 50)

Basic LISP recursion, enumerate values greater than 3

I need a recursive LISP function that enumerates the number of elements in any list of numbers > 3. I'm not allowed to use lets, loops or whiles and can only use basic CAR, CDR, SETQ, COND, CONS, APPEND, PROGN, LIST...
This is my attempt at the function:
(defun foo (lst)
(COND ((null lst) lst)
(T (IF (> (CAR lst) 3)
(1+ (foo (CDR lst)))
(foo (CDR lst)) ) ) ) )
The function call:
(foo '(0 1 2 3 4 5 6))
Your code is pretty close to correct, just a small mistake in the base case:
For the empty list you return the empty list. So if you have the list (6), you add 6 to foo of the empty list, which is the empty list. That does not work because you can't add a number to a list.
You can easily fix it by making foo return 0 instead of lst when lst is empty.
As a style note: Mixing cond and if like this, seems a bit redundant. I would write it like this, using only cond instead:
(defun foo (lst)
(cond
((null lst)
0)
((> (car lst) 3)
(1+ (foo (cdr lst))))
(T
(foo (cdr lst)))))
Some stylistic points:
There's no need to put some Lisp built-ins in uppercase. It's not 1958 anymore!
But if you are going to put built-ins in uppercase, why not DEFUN and NULL?
You have an if inside the last branch of your cond. This is redundant. Since the purpose of cond is testing conditions, why not use it?
There's no need to space out your closing parentheses like that. No-one counts parentheses these days, we have parenthesis-matching editors.
Lisp has separate namespaces for functions and values, so you don't have to call your argument lst to avoid conflicting with the built-in function list.
If you were programming this for real, of course you'd use count-if:
(count-if #'(lambda (x) (> x 3)) '(0 1 2 3 4 5 6))
==> 3
One save you can have on duplication of the recursive call:
(defun foo (l)
(if (null l) 0 ; if list is empty, return 0
(+ (if (> (car l) 3) 1 0) ; else +1 if condition is satisfactory
(foo (cdr l))))) ; plus the result from the rest

Resources