Difference between iterate and repeatedly applying a function - clojure

I'm studying the Clojure Koans:
https://github.com/functional-koans/clojure-koans/blob/master/src/koans/10_lazy_sequences.clj
I am stuck on this one:
"Iteration can be used for repetition"
(= (repeat 100 :foo)
(take 100 (iterate ___ :foo)))
I don't know the exact builtin function to fill in the _ blanks with, so I tried writing my own. I wrote it as a separate function as a test.
I intend this one to be: if x is a seq, then just repeat its first element. Otherwise, make it a seq.
(def f (fn [x] (if (seq? x) (cons (first x) x) (cons x '()))))
When I run it explicitly, it looks fine:
user=> (f :abc)
(:abc)
user=> (f (f :abc))
(:abc :abc)
user=> (f (f (f :abc)))
(:abc :abc :abc)
But using iterate adds an extra parenthesis:
user=> (take 1 (iterate f :abc))(:abc)
user=> (take 2 (iterate f :abc))
(:abc (:abc))
user=> (take 3 (iterate f :abc))
(:abc (:abc) (:abc :abc))
What causes this?

(fn [x] x)
solves this particular koan

Re-read the documentation for iterate:
Returns a lazy sequence of x, (f x), (f (f x)) etc.
Use nth instead of take if you want the results of a particular iteration:
user=> (nth (iterate f :abc) 0)
:abc
user=> (nth (iterate f :abc) 1)
(:abc)
user=> (nth (iterate f :abc) 2)
(:abc :abc)
user=> (nth (iterate f :abc) 3)
(:abc :abc :abc)

I've solved it with #(keyword %)
I've tried with #( %) but it doesn't work. Anyone knows why?

Related

Clojure: Implementing the some function

I'm new to clojure and tried to implement the some function (for some specific tests):
(my-some even? [1 2 3 4]) => true
(my-some #{3 4} [1 2 3 4]) => 3
(my-some zero? [1 2 3 4]) => nil
That's what I came up with so far:
(defn my-some [f x]
(loop [[y & t] x]
(if (empty? t) nil
(if (f y)
(f y)
(recur t)))))
I could imagine there are more idiomatic approaches.
Any suggestions?
Firstly, you have a bug: [[y & t] x] destructures x, but the following empty? check on t means you are ignoring the last element in the sequence. You can see this with
(my-some even? [2])
=> nil
You can replace (if (empty? x) nil (else-form)) with when and seq:
(when (seq x) ...)
you can then use first and next to deconstruct the sequence:
(defn my-some [f x]
(when (seq x)
(if (f (first x))
(f (first x))
(recur f (rest x)))))
the call to recur is then back into my-some so you need to pass the predicate f.
you can replace (if x x (else ....)) with (or x (else ...)):
(defn my-some [f x]
(when (seq x)
(or (f (first x)) (recur f (next x)))))
you can compare this with the implementation of some

Make (map f c1 c2) map (count c1) times, even if c2 has less elements

When doing
(map f [0 1 2] [:0 :1])
f will get called twice, with the arguments being
0 :0
1 :1
Is there a simple yet efficient way, i.e. without producing more intermediate sequences etc., to make f get called for every value of the first collection, with the following arguments?
0 :0
1 :1
2 nil
Edit Addressing question by #fl00r in the comments.
The actual use case that triggered this question needed map to always work exactly (count first-coll) times, regardless if the second (or third, or ...) collection was longer.
It's a bit late in the game now and somewhat unfair after having accepted an answer, but if a good answer gets added that only does what I specifically asked for - mapping (count first-coll) times - I would accept that.
You could do:
(map f [0 1 2] (concat [:0 :1] (repeat nil)))
Basically, pad the second coll with an infinite sequence of nils. map stops when it reaches the end of the first collection.
An (eager) loop/recur form that walks to end of longest:
(loop [c1 [0 1 2] c2 [:0 :1] o []]
(if (or (seq c1) (seq c2))
(recur (rest c1) (rest c2) (conj o (f (first c1) (first c2))))
o))
Or you could write a lazy version of map that did something similar.
A general lazy version, as suggested by Alex Miller's answer, is
(defn map-all [f & colls]
(lazy-seq
(when-not (not-any? seq colls)
(cons
(apply f (map first colls))
(apply map-all f (map rest colls))))))
For example,
(map-all vector [0 1 2] [:0 :1])
;([0 :0] [1 :1] [2 nil])
You would probably want to specialise map-all for one and two collections.
just for fun
this could easily be done with common lisp's do macro. We could implement it in clojure and do this (and much more fun things) with it:
(defmacro cl-do [clauses [end-check result] & body]
(let [clauses (map #(if (coll? %) % (list %)) clauses)
bindings (mapcat (juxt first second) clauses)
nexts (map #(nth % 2 (first %)) clauses)]
`(loop [~#bindings]
(if ~end-check
~result
(do
~#body
(recur ~#nexts))))))
and then just use it for mapping (notice it can operate on more than 2 colls):
(defn map-all [f & colls]
(cl-do ((colls colls (map next colls))
(res [] (conj res (apply f (map first colls)))))
((every? empty? colls) res)))
in repl:
user> (map-all vector [1 2 3] [:a :s] '[z x c v])
;;=> [[1 :a z] [2 :s x] [3 nil c] [nil nil v]]

repeatedly apply a function to a datastructure

I would like to apply a function some number of times to a datastructure and was wondering if there is a simpler way.
;; simple map and map-incrementing function
(def a {:a 1})
(defn incmap [x] (update-in x [:a] inc))
;; best I could come up with
(reduce (fn [m _] (incmap m)) a (range 10))
;; was hoping for something like this
(repeatedly-apply incmap a 10)
You are looking for iterate:
(iterate f x)
Returns a lazy sequence of x, (f x), (f (f x)) etc. f must be free of side-effects
You just need to take the nth element:
(nth (iterate incmap a) 9)
Using the threading macro:
(-> (iterate incmap a)
(nth 9))

How do I filter elements from a sequence based on indexes

I have a sequence s and a list of indexes into this sequence indexes. How do I retain only the items given via the indexes?
Simple example:
(filter-by-index '(a b c d e f g) '(0 2 3 4)) ; => (a c d e)
My usecase:
(filter-by-index '(c c# d d# e f f# g g# a a# b) '(0 2 4 5 7 9 11)) ; => (c d e f g a b)
You can use keep-indexed:
(defn filter-by-index [coll idxs]
(keep-indexed #(when ((set idxs) %1) %2)
coll))
Another version using explicit recur and lazy-seq:
(defn filter-by-index [coll idxs]
(lazy-seq
(when-let [idx (first idxs)]
(if (zero? idx)
(cons (first coll)
(filter-by-index (rest coll) (rest (map dec idxs))))
(filter-by-index (drop idx coll)
(map #(- % idx) idxs))))))
make a list of vectors containing the items combined with the indexes,
(def with-indexes (map #(vector %1 %2 ) ['a 'b 'c 'd 'e 'f] (range)))
#'clojure.core/with-indexes
with-indexes
([a 0] [b 1] [c 2] [d 3] [e 4] [f 5])
filter this list
lojure.core=> (def filtered (filter #(#{1 3 5 7} (second % )) with-indexes))
#'clojure.core/filtered
clojure.core=> filtered
([b 1] [d 3] [f 5])
then remove the indexes.
clojure.core=> (map first filtered)
(b d f)
then we thread it together with the "thread last" macro
(defn filter-by-index [coll idxs]
(->> coll
(map #(vector %1 %2)(range))
(filter #(idxs (first %)))
(map second)))
clojure.core=> (filter-by-index ['a 'b 'c 'd 'e 'f 'g] #{2 3 1 6})
(b c d g)
The moral of the story is, break it into small independent parts, test them, then compose them into a working function.
The easiest solution is to use map:
(defn filter-by-index [coll idx]
(map (partial nth coll) idx))
I like Jonas's answer, but neither version will work well for an infinite sequence of indices: the first tries to create an infinite set, and the latter runs into a stack overflow by layering too many unrealized lazy sequences on top of each other. To avoid both problems you have to do slightly more manual work:
(defn filter-by-index [coll idxs]
((fn helper [coll idxs offset]
(lazy-seq
(when-let [idx (first idxs)]
(if (= idx offset)
(cons (first coll)
(helper (rest coll) (rest idxs) (inc offset)))
(helper (rest coll) idxs (inc offset))))))
coll idxs 0))
With this version, both coll and idxs can be infinite and you will still have no problems:
user> (nth (filter-by-index (range) (iterate #(+ 2 %) 0)) 1e6)
2000000
Edit: not trying to single out Jonas's answer: none of the other solutions work for infinite index sequences, which is why I felt a solution that does is needed.
I had a similar use case and came up with another easy solution. This one expects vectors.
I've changed the function name to match other similar clojure functions.
(defn select-indices [coll indices]
(reverse (vals (select-keys coll indices))))
(defn filter-by-index [seq idxs]
(let [idxs (into #{} idxs)]
(reduce (fn [h [char idx]]
(if (contains? idxs idx)
(conj h char) h))
[] (partition 2 (interleave seq (iterate inc 0))))))
(filter-by-index [\a \b \c \d \e \f \g] [0 2 3 4])
=>[\a \c \d \e]
=> (defn filter-by-index [src indexes]
(reduce (fn [a i] (conj a (nth src i))) [] indexes))
=> (filter-by-index '(a b c d e f g) '(0 2 3 4))
[a c d e]
I know this is not what was asked, but after reading these answers, I realized in my own personal use case, what I actually wanted was basically filtering by a mask.
So here was my take. Hopefully this will help someone else.
(defn filter-by-mask [coll mask]
(filter some? (map #(if %1 %2) mask coll)))
(defn make-errors-mask [coll]
(map #(nil? (:error %)) coll))
Usage
(let [v [{} {:error 3} {:ok 2} {:error 4 :yea 7}]
data ["one" "two" "three" "four"]
mask (make-errors-mask v)]
(filter-by-mask data mask))
; ==> ("one" "three")

Piping data through arbitrary functions in Clojure

I know that the -> form can be used to pass the results of one function result to another:
(f1 (f2 (f3 x)))
(-> x f3 f2 f1) ; equivalent to the line above
(taken from the excellent Clojure tutorial at ociweb)
However this form requires that you know the functions you want to use at design time. I'd like to do the same thing, but at run time with a list of arbitrary functions.
I've written this looping function that does it, but I have a feeling there's a better way:
(defn pipe [initialData, functions]
(loop [
frontFunc (first functions)
restFuncs (rest functions)
data initialData ]
(if frontFunc
(recur (first restFuncs) (rest restFuncs) (frontFunc data) )
data )
) )
What's the best way to go about this?
I must admit I'm really new to clojure and I might be missing the point here completely, but can't this just be done using comp and apply?
user> (defn fn1 [x] (+ 2 x))
user> (defn fn2 [x] (/ x 3))
user> (defn fn3 [x] (* 1.2 x))
user> (defn pipe [initial-data my-functions] ((apply comp my-functions) initial-data))
user> (pipe 2 [fn1 fn2 fn3])
2.8
You can do this with a plain old reduce:
(defn pipe [x fs] (reduce (fn [acc f] (f acc)) x fs))
That can be shortened to:
(defn pipe [x fs] (reduce #(%2 %1) x fs))
Used like this:
user> (pipe [1 2 3] [#(conj % 77) rest reverse (partial map inc) vec])
[78 4 3]
If functions is a sequence of functions, you can reduce it using comp to get a composed function. At a REPL:
user> (def functions (list #(* % 5) #(+ % 1) #(/ % 3)))
#'user/my-list
user> ((reduce comp functions) 9)
20
apply also works in this case because comp takes a variable number of arguments:
user> (def functions (list #(* % 5) #(+ % 1) #(/ % 3)))
#'user/my-list
user> ((apply comp functions) 9)
20