I am going through this article on Tree Visitors in Clojure and came across the below example:
(def data [[1 :foo] [2 [3 [4 "abc"]] 5]])
(walk/postwalk #(do (println "visiting:" %) %) data)
What is the outer form of postwalk doing? I can't understand its utility. How and why is postwalk used? Any explanations will be appreciated.
I'm not sure if you're asking what #() means or what the purpose of do(form1 form2) means, so I'll answer both.
#() is a shorthand for declaring an anonymous function. Anonymous functions are useful when you're passing some function into another function.
To illustrate, look at this in the repl
; define an anonymous function
user=> #(+ %1 %2)
#<user$eval68$fn__69 user$eval68$fn__69#9fe84e>
; is equivalent to
user => (fn [a b] (+ a b))
#<user$eval1951$fn__1952 user$eval1951$fn__1952#118bd3c>
; furthermore, you could then assign your anonymous function to a var
(def f #(+ %1 %2))
; is equivalent to
(defn f [a b] (+ a b))
user=> (#(+ %1 %2) 1 2)
3
user=> (f 1 2)
3
The %n refers to the arguments to positional arguments to a function where n means nth argument, starting at 1 As a further shorthand you can use % to refer to the first argument which works well for single arg anonymous functions. This is what you have in your example.
So you example is equivalent to
(def data [[1 :foo] [2 [3 [4 "abc"]] 5]])
(defn f [x] (do (println "visiting:" x) x))
(walk/postwalk f data)
The do here is a special form, which, from the docs:
(do exprs*)
Evaluates the expressions in order and returns the value of the last. If no expressions are supplied, returns nil.
In fact defn already has an implicit do, so my example above doesn't actually need the do...
; your example is equivalent to:
(def data [[1 :foo] [2 [3 [4 "abc"]] 5]])
(defn f [x] (println "visiting:" x) x)
(walk/postwalk f data)
I had the same question today and find this necrotopik. Maybe later is better the newer. Find this on clojure api reference:
postwalk
function
Usage: (postwalk f form)
Performs a depth-first, post-order traversal of form. Calls f on
each sub-form, uses f's return value in place of the original.
Recognizes all Clojure data structures except sorted-map-by.
Consumes seqs as with doall.
Also this example from clojuredocs makes things clearer:
(use 'clojure.walk)
(let [counter (atom -1)]
(postwalk (fn [x]
[(swap! counter inc) x])
{:a 1 :b 2}))
=> [6 {2 [[0 :a] [1 1]], 5 [[3 :b] [4 2]]}]
So, postwalk replaces every subform with result of the function. It is used for updating nested structures with new values. That is why resulting function contains x or % at the end. Adding input to result leads to even more nested stucture.
In the example above it is seen as it walks through the depths of nested map stucture. It is going first on deepest elements of the map, then go up on higher level, then lurk down to the next form, then again goes up and finishes its last move on the whole form.
Related
(defn image-of
"computes the image of the element x under R"
[R x]
(set
(for [r R]
(when (= (first r) x)
(second r)))))
Function idea: Add the second variable in R when it's first is equal to x.
So this function is supposed to compute image of a relation. This is kinda successful. When running a test I get this result:
Input: (image-of #{[1 :a] [2 :b] [1 :c] [3 :a]} 1)
Expected: #{:c :a}
Actual: #{nil :c :a}
So it includes a nil value for some reason. What in the function causes this? I guess I could filter out any nil values but would like to have the solution on a single line.
So the problem was I didn't know exactly how to use when
This solution does it:
(set (for [r R
:when (= (first r) x)]
(second r)))
Let me suggest a different approach.
The natural way to represent a relation in Clojure is as a map from keys to sets (or other collections) of values. A function to convert your collection of pairs to this form is ...
(defn pairs->map [pairs]
(reduce
(fn [acc [key value]]
(assoc acc key (conj (acc key #{}) value)))
{}
pairs))
For example, ...
(pairs->map #{[1 :a] [2 :b] [1 :c] [3 :a]})
=> {2 #{:b}, 1 #{:c :a}, 3 #{:a}}
You can use this map as a function. I you feed it a key, it returns the corresponding value:
({2 #{:b}, 1 #{:c :a}, 3 #{:a}} 1)
=> #{:c :a}
You construct this map once and or all and use it as often as you like. Looking it up as a function is effectively a constant-time operation. But you run through the entire collection of pairs every time you evaluate image-of.
Is it possible to use filter with a predicate with multiple arguments? If so, how would I do it under the context of this code:
;predicate
(defn classInstructor [instructor class]
(str/includes? class instructor))
(defn instructorClasses [instructor classList]
(filter classInstructor classList))
The map function can take a function that applies to several arguments. For example,
=> (map + [1 2 3] [4 5 6])
(5 7 9)
The + gets two arguments, one from each sequence. There is no corresponding version of filter. You could extend the standard filter as follows:
(defn filter
([f coll]
(clojure.core/filter f coll))
([f coll & colls]
(filter #(apply f %) (apply map vector (cons coll colls)))))
For example,
=> (filter (comp odd? +) [1 2 3] [4 6 8])
([1 4] [3 8])
As you can see, we have to present the surviving sequences somehow. I don't find it persuasive or natural to do so. Not worth doing, I think.
I would do it like so, using an anonymous function:
(defn classInstructor [instructor class]
(str/includes? class instructor))
(defn instructorClasses [instructor classList]
(filter #(classInstructor instructor %) classList))
This way, when one calls instructorClasses, the value of instructor is passed through to classInstructor.
Is there a idiomatic / built-in way to flip the argument order that is passed to a function in Clojure?
As I do here with the definition of a helper function:
(defn flip [f & xs]
(apply f (reverse xs)))
(vector 1 2) ; [1 2]
(flip vector 1 2) ; [2 1]
I think it makes sense most times to create a flipped function that you use later, so the variation on your function would be this:
(defn flip [f]
(fn [& xs]
(apply f (reverse xs))))
A flip function does exist in other functional languages, but it's easy enough to do in Clojure as well, and you've already done it!
There are other ways to do it as well.
And here is a discussion about it from the Clojure mailing list.
You can also use anonymous inline function to re-define the order of arguments.
(vector "a" "b") ; ["a" "b"]
(#(vector %2 %1) "a" "b") ; ["b" "a"]
I want to write a function that concatenates vectors or matrices, which can take arbitrary inputs. To combine two vectors I've written the follow code. It also also matrices to be combined such that columns are lengthened.
(defn concats
([x y] (vec (concat x y))))
Where I am stuck is extending the input to n vectors or matrices, and combining matrices to make longer rows.
Ex) (somefunction [[:a :b] [:c :d]] [[1 2] [3 4]] 2]
[[:a :b 1 2] [:c :d 3 4]]
The 2 in the input designates level to concatenate.
If you're not interested in "how it works", here's the solution right up front (note that level is zero-indexed, so what you've called the 1st level I'm calling the 0th level):
(defn into* [to & froms]
(reduce into to froms))
(defn deep-into*
[level & matrices]
(-> (partial partial mapv)
(iterate into*)
(nth level)
(apply matrices)))
The short answer for how it works is this: it iteratively builds up a function that will nest the call to into* at the correct level, and then applies it to the supplied matrices.
Regular old into, given a vector first argument, will concatenate the elements of the second argument onto the end of the vector. The into* function here is just the way I'm doing vector concatting on a variable number of vectors. It uses reduce to iteratively call into on some accumulated vector (which starts as to) and the successive vectors in the list froms. For example:
user> (into* [1 2] [3 4] [5 6])
> [1 2 3 4 5 6]
Now for deep-into*, I had to recognize a pattern. I started by hand-writing different expressions that would satisfy different "levels" of concatenation. For level 0, it's easy (I've extrapolated your example somewhat so that I can make it to level 2):
user> (into* [[[:a :b] [:c :d]]] [[[1 2] [3 4]]])
> [[[:a :b] [:c :d]] [[1 2] [3 4]]]
As for level 1, it's still pretty straightforward. I use mapv, which works just like map except that it returns a vector instead of a lazy sequence:
user> (mapv into* [[[:a :b] [:c :d]]] [[[1 2] [3 4]]])
> [[[:a :b] [:c :d] [1 2] [3 4]]]
Level 2 is a little more involved. This is where I start using partial. The partial function takes a function and a variable number of argument arguments (not a typo), and returns a new function that "assumes" the given arguments. If it helps, (partial f x) is the same as (fn [& args] (apply f x args)). It should be clearer from this example:
user> ((partial + 2) 5)
> 7
user> (map (partial + 2) [5 6 7]) ;why was six afraid of seven?
> (7 8 9)
So knowing that, and also knowing that I'll want to go one level deeper, it makes some sense that level 2 looks like this:
user> (mapv (partial mapv into*) [[[:a :b][:c :d]]] [[[1 2][3 4]]])
> [[[:a :b 1 2] [:c :d 3 4]]]
Here, it's mapping a function that's mapping into* down some collection. Which is kind of like saying: map the level 1 idea of (mapv into* ...) down the matrices. In order to generalize this to a function, you'd have to recognize the pattern here. I'm going to put them all next to each other:
(into* ...) ;level 0
(mapv into* ...) ;level 1
(mapv (partial mapv into*) ...) ;level 2
From here, I remembered that (partial f) is the same as f (think about it: you have a function and you're giving it no additional "assumed" arguments). And by extending that a little, (map f ...) is the same as ((partial map f) ...) So I'll re-write the above, slightly:
(into* ...) ;level 0
((partial mapv into*) ...) ;level 1
((partial mapv (partial mapv into*)) ...) ;level 2
Now an iterative pattern is becoming clearer. We're calling some function on ... (which is just our given matrices), and that function is an iterative build-up of calling (partial mapv ...) on into*, iterating for the number of levels. The (partial mapv ...) part can be functionalized as (partial partial mapv). This is a partial function that returns a partial function of mapving some supplied arguments. This outer partial isn't quite necessary because we know that the ... here will always be one thing. So we could just as easily write it as #(partial mapv %), but I so rarely get a chance to use (partial partial ...) and I think it looks pretty. As for the iteration, I use the pattern (nth (iterate f initial) n). Perhaps another example would make this pattern clear:
user> (nth (iterate inc 6) 5)
> 11
Without the (nth ...) part, it would loop forever, creating an infinite list of incrementing integers greater than or equal to 5. So now, the whole thing abstracted and calculated for level 2:
user> ((nth (iterate (partial partial mapv) into*) 2)
[[[:a :b][:c :d]]] [[[1 2][3 4]]])
> [[[:a :b 1 2] [:c :d 3 4]]]
Then, using the -> macro I can factor out some of these nested parantheses. This macro takes a list of expressions and recursively nests each into the second position of the successive one. It doesn't add any functionality, but can certainly make things more readable:
user> ((-> (partial partial mapv)
(iterate into*)
(nth 2))
[[[:a :b][:c :d]]] [[[1 2][3 4]]])
> [[[:a :b 1 2] [:c :d 3 4]]]
From here, generalizing to a function is pretty trivial--replace the 2 and the matrices with arguments. But because this takes a variable number of matrices, we will have to apply the iteratively-built function. The apply macro takes a function or macro, a variable number of arguments, and finally a collection. Essentially, it prepends the function or macro and the supplied arguments onto the final list, then evaluates the whole thing. For example:
user> (apply + [1 5 10]) ;same as (+ 1 5 10)
> 16
Happily, we can stick the needed apply at the end of the (-> ...). Here's my solution again, for the sake of symmetry:
(defn deep-into*
[level & matrices]
(-> (partial partial mapv)
(iterate into*)
(nth level)
(apply matrices)))
Using the concats function you listed in the question:
user=> (map concats [[:a :b] [:c :d]] [[1 2] [3 4]])
([:a :b 1 2] [:c :d 3 4])
this doesn't take into account the level as you listed, but it handles the input given
Taking arbitrary number of arguments needs a replacement concats function
(defn conc [a b & args]
(if (nil? (first args))
(concat a b)
(recur (concat a b) (first args) (rest args))))
Here are two examples
user=> (map conc [[:a :b] [:c :d]] [[1 2] [3 4]] [["w" "x"] ["y" "z"]])
((:a :b 1 2 "w" "x") (:c :d 3 4 "y" "z"))
user=> (map conc [[:a :b] [:c :d] [:e :f]] [[1 2] [3 4] [5 6]] [["u" "v"] ["w" "x"] ["y" "z"]])
((:a :b 1 2 "u" "v") (:c :d 3 4 "w" "x") (:e :f 5 6 "y" "z"))
Here are two different solutions for a function which will return a vector that's the concatenation of an arbitrary number of input collections:
(defn concats [& colls]
(reduce (fn [result coll]
(into result coll))
[]
colls))
(defn concats [& colls]
(vec (apply concat colls)))
The [& arg-name] notation in the argument lists is how you specify that the function is "variadic" - meaning it can accept a variable number of arguments. The result is that colls (or whatever name you pick) will be a sequence of all the arguments in excess of the positional arguments.
Functions can have multiple arities in Clojure, so you can also do things like this:
(defn concats
([x]
(vec x))
([x y]
(vec (concat x y)))
([x y & colls]
(vec (apply concat (list* x y colls)))))
However, only one of the overloads can be variadic, and its variadic part must come last (i.e. you can't do [& more n], only [n & more].
The Clojure.org page on special forms has more useful information on argument lists in Clojure (in the section on fn).
The function below correctly handles the example input/output you provided. Unfortunately I don't think I understand how you want the levels (and associated numeric input) to work well enough to generalize it as far as you're looking for.
(defn concats [x y]
;; only works with two inputs
(vec (map-indexed (fn [i v] (into v (nth y i)))
x)))
(concats [[:a :b] [:c :d]] [[1 2] [3 4]]) ;=> [[:a :b 1 2] [:c :d 3 4]]
But maybe it will give you some ideas anyway, or if you can add more information (especially examples of how different levels should work) I'll see if I can be more help.
The question doesn't really explain what I want to do but I couldn't think of anything else.
I have an empty map in the outer let function in a piece of code, and an integer array.
I want to iterate through the integer array, perform a simple task, and keep appending the resulting map to the variables in the outer variables.
(let [a {} ;outer variables
b {}]
(doseq [x [1 2 3]]
(let [r (merge a {x (* x x)}) ;I want to append this to a
s (merge b {x (+ x x)})] ;and this to b
(println (str "--a--" r "--b--" s)))))
But as soon as I get out of doseq, my a and b vars are still empty. I get that the scope of a and b doesn't extend outside of doseq for it to persist any changes done from within and that they are immutable.
How do I calculate the values of a and b in such cases, please? I tried to extract the functionality of doseq into another function and calling let with:
(let [a (do-that-function)])
etc but even then I couldn't figure out a way to keep track of all the modifications within doseq loop to then send back as a whole.
Am I approaching this in a wrong way?
Thanks
edit
Really, what I'm trying to do is this:
(let [a (doseq [x [1 2 3]] {x (* x x)})]
(println a))
but doseq returns nil so a is going to be nil :-s
All variables in clojure are immutable. If you need a mutable state you should use atoms or refs.
But in your case you can simply switch from doseq to for:
(let [a (for [x [1 2 3]] {x (* x x)})]
(println a))
Here is an example of solving your problem with atoms:
(let [a (atom {})
b (atom {})]
(doseq [x [1 2 3]]
(swap! a assoc x (* x x))
(swap! b assoc x (+ x x)))
(println "a:" #a)
(println "b:" #b))
But you should avoid using mutable state as far as possible:
(let [l [1 2 3]
a (zipmap l (map * l l))
b (zipmap l (map + l l))]
(println "a:" a)
(println "b:" b))
The trick is to think in terms of flows of data adding to existing data making new data, instead of changing past data. For your specific problem, where a data structure is being built, reduce is typically used:
(reduce (fn [result x] (assoc result x (* x x))) {} [1 2 3])
hehe, I just noticed that "reduce" might seem confusing given that it's building something, but the meaning is that a collection of things is "reduced" to one thing. In this case, we give reduce an empty map to begin with, which binds to result in the fn, and each successive mapping over the collection results in a new result, which we add to again with assoc.
You could also say:
(into {} (map (fn [x] [x (* x x)]) [1 2 3]))
In your question you wanted to make multiple things at once from a single collection. Here's one way to do that:
(reduce (fn [[a b] x] [(assoc a x (* x x)) (assoc b x (+ x x))]) [{} {}] [1 2 3])
Here we used destructuring syntax to refer to our two result structures - just make a picture of the data [with [vectors]]. Note that reduce is still only returning one thing - a vector in this case.
And, we could generalize that:
(defn xfn [n fs]
(reduce
(fn [results x] (map (fn [r f] (assoc r x (f x x))) results fs))
(repeat (count fs) {}) (range n)))
=> (xfn 4 [* + -])
({3 9, 2 4, 1 1, 0 0} {3 6, 2 4, 1 2, 0 0} {3 0, 2 0, 1 0, 0 0})
The result is a list of maps. And if you wanted to take intermediate steps in the building of these results, you could change reduce to reductions. Generally, map for transforming collections, reduce for building a single result from a collection.