apply first of a list of functions in Clojure - syntax

if i have a list of functions:
(def lst '(+ -))
and i wish to apply the first of that list (+) to a list of numbers, i would think its
(apply (first lst) '(1 2 3 4))
but apparently U am wrong? Syntax mistake I assume. How do I do this?
PS:
=>(first lst)
+
=>(apply (first lst) '(1 2 3 4))
4
both return without error, they just return what i WOULD expect in the first case, and what i would NOT expect in the second.

Since your list is quoted:
(def lst '(+ -))
; ^- quote!
its members are two symbols, not functions. A symbol in Clojure can be used as a function, but then it acts very much like a keyword (i.e. looks itself up in its argument):
('foo {'foo 1})
; => 1
The correct solution is to use a list -- or, more idiomatically, a vector -- of functions:
(def lst (list + -)) ; ok
; or...
(def lst `(~+ ~-)) ; very unusual in Clojure
; or...
(def lst [+ -]) ; the idiomatic solution
Then your apply example will work.
By the way, notice that a function, when printed back by the REPL, doesn't look like the symbol which names it:
user=> +
#<core$_PLUS_ clojure.core$_PLUS_#10c10de0>

Related

Update list in racket without hash

I have the 2 lists, '(1 2 3 4), and '(add1 sub1 add1). They do not have same length. The first list is numbers, the second list is functions. I want to apply the functions to each of element in the number list.
'(1 2 3 4) (add1 sub1 add1) -> '(2 3 4 5) '(sub1 add1)
It look very simple, but I find I can not update the lists. Because in Scheme there is no way to update lists without hash. I can only create new lists. So every time I have to create a new list for each function in the second list. Can someone help me code this question?
Alternatively you could use map and compose in combination.
This is much easier to read and understand.
(map (compose add1 sub1 add1) '(1 2 3 4))
;; '(2 3 4 5)
(compose add1 sub1 add1) chains the functions one after another
and map applies this chained/composed function on each element of the input list '(1 2 3 4).
Generalize to a function:
(define (map-functions funcs . args)
(apply map (apply compose funcs) args))
(map-functions (list add1 sub1 add1) '(1 2 3 4)) ;; '(2 3 4 5)
compose is inbuilt but one can define it like this (% in names to not to overwrite the existing compose.
;; first a compose to compose to functions
(define (%%compose f1 f2)
(lambda args
(f1 (apply f2 args))))
;; then, generalize it for as many functions as one wants (as a variadic function) using `foldl`
(define (%compose . funcs)
(foldl %%compose (car funcs) (cdr funcs)))
You're looking for a left fold. It looks like Racket calls it foldl, which will do the job, combined with map. Something like (Untested, because I don't have Racket installed):
(define functions (list add1 sub1 add1)) ; So you have functions instead of symbols like you get when using quote
(define numbers '(1 2 3 4))
(foldl (lambda (f lst) (map f lst)) numbers functions)
Basically, for each function in that list, it maps the function against the list returned by mapping the previous function (Starting with the initial list of numbers when there is no previous).
If you're stuck with a list of symbols and can't use the (list add1 ... trick to get references to the actual functions, one approach (And I hope there are better ones) is to use eval and some quasiquoting:
(foldl (lambda (f lst) (eval `(map ,f (quote ,lst)))) '(1 2 3 4) '(add1 sub1 add1))

How do non-binary foldl and foldr work in Racket?

I'm familiar with the underlying workings and differences of foldl and foldr over a single list. However, in Racket, you can use folds on multiple lists. For example, you can find the difference of elements in two lists by writing
; (mapMinus '(3 4) '(1 2)) => '(2 2)
(define (mapMinus lst0 lst1)
(foldl (λ (hd0 hd1 acc) (cons (- hd0 hd1) acc)) '() lst0 lst1))
How exactly do Racket's implementations of foldl and foldr work to handle multiple lists? The Racket source code for foldl is available on GitHub here, but I don't know Chez Scheme well enough to understand it.
A fold that operates over multiple lists simply applies its lambda element-wise on all of the lists, simultaneously. Perhaps a simplified implementation (with no error checking, etc.) of it will make things clearer; let's compare a standard implementation of foldr (which IMHO is slightly simpler to understand than foldl):
(define (foldr proc init lst)
(if (null? lst)
init
(proc (car lst)
(foldr proc init (cdr lst)))))
With an implementation that accepts multiple lists:
(define (foldr proc init . lst) ; lst is a list of lists
(if (null? (car lst)) ; all lists assumed to be of same length
init
; use apply because proc can have any number of args
(apply proc
; append, list are required for building the parameter list
; in the right way so it can be passed to (apply proc ...)
(append (map car lst)
; use apply again because it's a variadic procedure
(list (apply foldr proc init (map cdr lst)))))))
All the extra code in the multi-list version is for applying proc to multiple elements at the same time, getting the current element of each list (map car lst) and advancing over all the lists (map cdr lst).
Also the implementation needs to take into account that the procedure operates over a variable number of lists, assuming that the provided lambda receives the correct number of arguments (number of input lists + 1). It works as expected:
(foldr (lambda (e1 e2 acc)
(cons (list e1 e2) acc))
'()
'(1 2 3)
'(4 5 6))
=> '((1 4) (2 5) (3 6))
I think what you really are asking is how to create a variadic function in Scheme/Racket. The answer is given at https://docs.racket-lang.org/guide/define.html, but let me just give you a quick example:
(define (foo a b . xs)
(+ a b (length xs)))
would be equivalent to
def foo(a, b, *xs):
return a + b + len(xs)
in Python. xs here is a list value containing the rest of the arguments.
The second piece of puzzle is, how to apply a variadic function with a list value. For that, you can use apply. Read more at https://docs.racket-lang.org/guide/application.html#%28part._apply%29. Again, here's a quick example:
(define (foo a b c) (+ a b c))
(apply foo 1 '(2 3))
;; equivalent to (foo 1 2 3)
would be equivalent to
def foo(a, b, c): return a + b + c
foo(1, *[2, 3]) ;; equivalent to foo(1, 2, 3)
With these, creating a fold that accepts multiple arguments is just a programming exercise:
(define (my-fold proc accum required-first-list . list-of-optional-lists)
... IMPLEMENT FOLD HERE ...)
Note that if you read the source code of Racket (which uses Chez Scheme), you will see that it uses case-lambda instead of defining the function directly. case-lambda is just a way to make the code more efficient for common usage of fold (i.e., a fold with only one list).

Alternating Sum Using Foldr/Foldl (Racket)

Back again with another Racket question. New to higher order functions in general, so give me some leeway.
Currently trying to find the alternating sum using the foldr/foldl functions and not recursion.
e.g. (altsum '(1 3 5 7)) should equal 1 - 3 + 5 - 7, which totals to -4.
I've thought about a few possible ways to tackle this problem:
Get the numbers to add in one list and the numbers to subtract in another list and fold them together.
Somehow use the list length to determine whether to subtract or add.
Maybe generate some sort of '(1 -1 1 -1) mask, multiply respectively, then fold add everything.
However, I have no clue where to start with foldl/foldr when every operation is not the same for every item in the list, so I'm having trouble implementing any of my ideas. Additionally, whenever I try to add more than 2 variables in my foldl's anonymous class, I have no idea what variables afterward refer to what variables in the anonymous class either.
Any help or pointers would be greatly appreciated.
We can leverage two higher-order procedures here: foldr for processing the list and build-list for generating a list of alternating operations to perform. Notice that foldr can accept more than one input list, in this case we take a list of numbers and a list of operations and iterate over them element-wise, accumulating the result:
(define (altsum lst)
(foldr (lambda (ele op acc) (op acc ele))
0
lst
(build-list (length lst)
(lambda (i) (if (even? i) + -)))))
It works as expected:
(altsum '(1 3 5 7))
=> -4
Your idea is OK. You can use range to make a list of number 0 to length-1 and use the oddness of each to determine + or -:
(define (alt-sum lst)
(foldl (lambda (index e acc)
(define op (if (even? index) + -))
(op acc e))
0
(range (length lst))
lst))
As an alternative one can use SRFI-1 List Library that has fold that allows different length lists as well as infinite lists and together with circular-list you can have it alterate between + and - for the duration of lst.
(require srfi/1) ; For R6RS you import (srfi :1)
(define (alt-sum lst)
(fold (lambda (op n result)
(op result n))
0
(circular-list + -)
lst))
(alt-sum '(1 3 5 7))
; ==> -4

Scheme skip or continue during lambda map

I am building a function that takes a set of integers, and returns a subset of the odd integers. I am running into the problem that I need to skip over the even integers in my map, but right now my function returns #<void> instead.
(define (oddSubset set)
(map
(lambda (x)
(cond
((odd? x) x)))
s))
In use:
> (oddSubset '(1 2 3))
'(1 #<void> 3)
Is there logic I can use like "else, continue onto next element"?
Note: I am trying to rewrite the built in filter function
map does not have the possibility to skip, but you can use filter instead:
(filter odd? '(1 2 3 4 5 6)) ; ==> (1 3 5)
Or you can use fold-right
(fold-right (lambda (e acc)
(if (odd? e)
(cons e acc)
acc))
'()
'(1 2 3 4 5 6)) ; ==> (1 3 5)
I assume #!r6rs. Both fold-right and filter are in the library (rnrs lists (6)). There is also SRFI-1 which gives both of these procedures for a R5RS language.
In the none standard language #!racket uses the name foldr in place of fold-right.
map looks like a weird choice for this. By definition it maps a function onto each element in a list and returns the list of the results, so trying to "skip" elements seems unnatural.
filter is what you're looking for.
(filter odd? '(1 2 3))
'(1 3)
map applies a function on all elements. Each invocation of the function is supposed to be independant from the others. Even if you introduce a state with a closure, you can't avoid map to build a list of same size as your input.
You want to (re-)implement the filter function. If you want to do it by yourself, you should try to use foldl and foldr instead.
(cond
((odd? x) x))
map check each element in the list: if it is odd, then return that element. But you did not tell your program what to do when the element is not odd, so map return void.
To solve your problem: use filter instead, since map will return something for each element in the list.
If you want to know how to implement filter, try reading the second chapter of SICP

How to convert a list into its elements

This must be very easy to accomplish but I am new to racket and dont know how:
I have a list (1 2 3 4) and would like to convert it into (1)(2)(3)(4)
Or is there a way to build it as (1)(2)(3)(4). I am using
cons '(element) call-function
to build it inside a function (recursively)
Try this:
(map list '(1 2 3 4))
From your text, I see that you do '(element). Problem with that is that everything which is quoted is never anything but what you see. Thus if element happens to be a variable it won't be expanded because of the quote.
The right way to get a list with one element would be to use list. eg. (list element) to get whatever the variable element to be the one element in your list. However, you won't need this in a roll-your-own recursive procedure:
(define (listify lst)
(if (null? lst) ; if lst is null we are done
'() ; evaluate to the empty list
(cons (list (car lst)) ; else we make a list with the first element
(listify (cdr lst))))) ; and listify the rest of the list too
Most of the procedure now is facilitating going through the argument, but since it's a common thing to do we can use higher order procedures with foldr so that you only concentrating on what is going to happen with the element in this chain in correspondence with the rest of the process:
(define (listify lst)
(foldr (lambda (e acc)
(cons (list e) ; chain this element wrapped in a list
acc)) ; with the result from the rest of the list
'() ; initiate with an empty list
lst)) ; go through lst
Of course, since we do something with each element in a list and nothing fancy by using map we only need to supply what to do with each element rather telling how to join the chains in the list together as well.
(define (listify lst)
(map list lst)) ; make a new list by applying a list of each element
It's actually a single argument version of zip:
(require srfi/1)
(zip '(1 2 3 4)) ; ==> ((1) (2) (3) (4))
(zip '(1 2 3) '(a b c)) ; ==> ((1 a) (2 b) (3 c))
There you go. As simple as it can get.

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