When processing each element in a seq I normally use first and rest.
However these will cause a lazy-seq to lose its "laziness" by calling seq on the argument. My solution has been to use (first (take 1 coll)) and (drop 1 coll) in their place when working with lazy-seqs, and while I think drop 1 is just fine, I don't particularly like having to call first and take to get the first element.
Is there a more idiomatic way to do this?
The docstrings for first and rest say that these functions call seq on their arguments to convey the idea that you don't have to call seq yourself when passing in a seqable collection which is not in itself a seq, like, say, a vector or set. For example,
(first [1 2 3])
;= 1
would not work if first didn't call seq on its argument; you'd have to say
(first (seq [1 2 3]))
instead, which would be inconvenient.
Both take and drop also call seq on their arguments, otherwise you couldn't call them on vectors and the like as explained above. In fact this is true of all standard seq collections -- those which do not call seq directly are built upon lower-level components which do.
In no way does this impair the laziness of lazy seqs. The forcing / realization which happens as a result of a first / rest call is the smallest amount possible to obtain the requested result. (How much that is depends on the type of the argument; if it is not in fact lazy, there is no extra realization involved in the first call; if it is partly lazy -- that is, chunked -- there will be some extra realization (up to 32 initial elements will be computed at once); if it's fully lazy, only the first element will be computed.)
Clearly first, when passed a lazy seq, must force the realization of its first element -- that's the whole point. rest is actually somewhat lazy in that it actually doesn't force the realization of the "rest" part of the seq (that's in contrast to next, which is basically equivalent to (seq (rest ...))). The fact that it does force the first element to be realized so that it can skip over it immediately is a conscious design choice which avoids unnecessary layering of lazy seq objects and holding the head of the original seq; you could say something like (lazy-seq (rest xs)) to defer even this initial realization, at the cost of holding on to xs until realized the lazy seq wrapper is realized.
Related
With the introduction of Spec, I try to write test.check generators for all of my functions. This is fine for simple data structures, but tends to become difficult with data structures that have parts that depend on each other. In other words, some state management within the generators is then required.
It would already help enormously to have generator-equivalents of Clojure's loop/recur or reduce, so that a value produced in one iteration can be stored in some aggregated value that is then accessible in a subsequent iteration.
One simple example where this would be required, is to write a generator for splitting up a collection into exactly X partitions, with each partition having between zero and Y elements, and where the elements are then randomly assigned to any of the partitions. (Note that test.chuck's partition function does not allow to specify X or Y).
If you write this generator by looping through the collection, then this would require access to the partitions filled up during previous iterations, to avoid exceeding Y.
Does anybody have any ideas? Partial solutions I have found:
test.check's let and bind allow you to generate a value and then reuse that value later on, but they do not allow iterations.
You can iterate through a collection of previously generated values with a combination of the tuple and bindfunctions, but these iterations do not have access to the values generated during previous iterations.
(defn bind-each [k coll] (apply tcg/tuple (map (fn [x] (tcg/bind (tcg/return x) k)) coll))
You can use atoms (or volatiles) to store & access values generated during previous iterations. This works, but is very un-Clojure, in particular because you need to reset! the atom/volatile before the generator is returned, to avoid that their contents would get reused in the next call of the generator.
Generators are monad-like due to their bind and return functions, which hints at the use of a monad library such as Cats in combination with a State monad. However, the State monad was removed in Cats 2.0 (because it was allegedly not a good fit for Clojure), while other support libraries I am aware of do not have formal Clojurescript support. Furthermore, when implementing a State monad in his own library, Jim Duey — one of Clojure's monad experts — seems to warn that the use of the State monad is not compatible with test.check's shrinking (see the bottom of http://www.clojure.net/2015/09/11/Extending-Generative-Testing/), which significantly reduces the merits of using test.check.
You can accomplish the iteration you're describing by combining gen/let (or equivalently gen/bind) with explicit recursion:
(defn make-foo-generator
[state]
(if (good-enough? state)
(gen/return state)
(gen/let [state' (gen-next-step state)]
(make-foo-generator state'))))
However, it's worth trying to avoid this pattern if possible, because each use of let/bind undermines the shrinking process. Sometimes it's possible to reorganize the generator using gen/fmap. For example, to partition a collection into a sequence of X subsets (which I realize is not exactly what your example was, but I think it could be tweaked to fit), you could do something like this:
(defn partition
[coll subset-count]
(gen/let [idxs (gen/vector (gen/choose 0 (dec subset-count))
(count coll))]
(->> (map vector coll idxs)
(group-by second)
(sort-by key)
(map (fn [[_ pairs]] (map first pairs))))))
When defining an infinite sequence, I noticed that cons is necessary to avoid infinite recursion. However, what I don't understand is why. Here is the code in question:
(defn even-numbers
([] (even-numbers 0))
([n] (cons n (lazy-seq (even-numbers (+ 2 n))))))
(take 10 (even-numbers))
;; (0 2 4 6 8 10 12 14 16 18)
This works great; but since I love to question things, I began to wonder why the cons was needed (other than to include 0). After all, the lazy-seq function creates a lazy-seq. Which means, the rest of the values should not be calculated until called (or chunked). So, I tried it.
(defn even-numbers-v2
([] (even-numbers-v2 0))
([n] (lazy-seq (even-numbers-v2 (+ 2 n)))))
(take 10 (even-numbers-v2))
;; Infinite loooooooooop
So, now I know that cons is necessary, but I'd like to know why cons is necessary to cause lazy evaluation of a supposedly lazy sequence
Lazy seqs are a way to defer computation of actual seq elements, but those elements do need to be computed eventually. That doesn't actually have to involve cons – for example clojure.core/concat uses "chunked conses" when processing chunked operands, and it's ok to wrap any concrete seq type whatsoever in lazy-seq – but some kind of non-lazy return after however many layers of lazy-seq is necessary if any seq processing is to take place. Otherwise there won't even be a first element to get to.
Put yourself in the position of a function that's been handed a lazy seq. The caller has told it, in effect, "here's this thing that's for all intents and purposes a seq, but I don't feel like computing the actual elements until later". Now our function needs some actual elements to operate, so it pokes and prods the seq to try and get it to produce some elements… and then what?
If peeling off some lazy-seq layers eventually produces a Cons cell, a list, a seq over a vector or any other concrete seq-like thing with actual elements, then great, the function can read off an element from that and make progress.
But if the only result of peeling off those layers is that more layers are revealed, and it's lazy-seqs all the way down, well… There are no elements to be found. And since in principle there is no way to determine whether by peeling off sufficiently many layers some elements could eventually be produced (cf. the halting problem), the function consuming an unrealizable lazy seq of this sort has in general no choice but to continue looping forever.
To take another angle, let's consider your even-numbers-v2 function. It takes an argument and returns a lazy-seq object wrapping a further call to itself. Now, the original argument it receives (n) is used to compute the argument to the recursive call ((+ 2 n)), but otherwise isn't placed in any data structure or otherwise conveyed to the caller, so there is no reason why it would occur as an element of the resulting seq. All the caller sees is that the function has produced a lazy seq object and it has no choice but to unwrap that in search for an actual element of the sequence; and of course then the situation repeats itself (not strictly forever in this case, but only because + will eventually complain about arithmetic overflow when dealing with longs).
Can somebody explain me, the difference between 'IndexedSeq' and 'PersistentVector'?
I bumped into this, when updating a vector in my data structure via 'rest'. Here's a REPL excerpt that shows the transformation.
=> (def xs [1 2 3])
...
(type xs)
cljs.core/PersistentVector
=> (def xs2 (rest xs))
...
(type xs2)
cljs.core/IndexedSeq
I'm holding a list in an app-state atom, which needs to be shifted once in a while, so the first item must disappear. Would be really cool, if anybody could give me a hint about which data structure might be preferable here in terms of performance.
Sometimes elements get pushed to the end of the list as well, so I guess it's a LIFO mechanism that I'm creating here.
From your last paragraph, it sounds like you're using this as a stack. Taken together, pop, peek, and conj form a stack interface that can be used with either lists or vectors (working on the front of a list or the end of a vector). I would use those.
If you're just using those functions, I don't think there should be any significant performance differences (all three functions should be constant time).
looking at the superinterfaces here: http://static.javadoc.io/org.clojure/clojure/1.7.0/clojure/lang/IndexedSeq.html
I can guess, it is not the most efficient thing here, since it is just a seq, with no guaranteed constant-time access to the nth member. To ensure the vector semantics you should probably use subvec to remove the first element.
In general, if you don't do random access to elements, in terms of performance it should be enough to use concat to add element to the end (as it produces a lazy sequence, won't consume the whole collection, and should be done in a constant time) and rest to remove the first element (as it is also done in a constant time), to make FIFO stack (which is what you do). (it's not the best variant still, since it may lead to stack owerflow, if you do alot of push without realizing the sequence.
But sure it's better to use vectors. So the combination of conj , first, and subvec should be your choice.
I keep running into situations where I need to filter a collection of maps by some function, and then pull out one value from each of the resulting maps to make my final collection.
I often use this basic structure:
(map :key (filter some-predicate coll))
It occurred to me that this basically accomplishes the same thing as a for loop:
(for [x coll :when (some-predicate x)] (:key x))
Is one way more efficient than the other? I would think the for version would be more efficient since we only go through the collection once.. Is this accurate?
Neither is significantly different.
Both of these return an unrealized lazy sequence where each time an item is read it is computed. The first one does not traverse the list twice, it instead creates one lazy sequence which that produces items that match the filter and is then immediately consumed (still lazily) by the map function. So in this first case you have one lazy sequence consuming items from another lazy sequence lazily. The call to for on the other hand produces a single lazy-seq with a lot of logic in each step.
You can see the code that the for example expands into with:
(pprint (macroexpand-1 '(for [x coll :when (some-predicate x)] (:key x))))
On the whole the performance will be very similar with the second method perhaps producing slightly less garbage so the only way for you to decide between these on the basis of performance will be benchmarking. On the basis of style, I choose the first one because it is shorter, though I might choose to write it with the thread-last macro if there where more stages.
(->> coll
(filter some-predicate)
(take some-limit)
(map :key))
Though this basically comes down to personal style
Every collection in clojure is said to be "sequable" but only list and cons are actually seqs:
user> (seq? {:a 1 :b 2})
false
user> (seq? [1 2 3])
false
All other seq functions first convert a collection to a sequence and only then operate on it.
user> (class (rest {:a 1 :b 2}))
clojure.lang.PersistentArrayMap$Seq
I cannot do things like:
user> (:b (rest {:a 1 :b 2}))
nil
user> (:b (filter #(-> % val (= 1)) {:a 1 :b 1 :c 2}))
nil
and have to coerce back to concrete data type. This looks like bad design to me, but most likely I just don't get it as yet.
So, why clojure collections don't implement ISeq interface directly and all seq functions don't return an object of the same class as the input object?
This has been discussed on the Clojure google group; see for example the thread map semantics from February of this year. I'll take the liberty of reusing some of the points I made in my message to that thread below while adding several new ones.
Before I go on to explain why I think the "separate seq" design is the correct one, I would like to point out that a natural solution for the situations where you'd really want to have an output similar to the input without being explicit about it exists in the form of the function fmap from the contrib library algo.generic. (I don't think it's a good idea to use it by default, however, for the same reasons for which the core library design is a good one.)
Overview
The key observation, I believe, is that the sequence operations like map, filter etc. conceptually divide into three separate concerns:
some way of iterating over their input;
applying a function to each element of the input;
producing an output.
Clearly 2. is unproblematic if we can deal with 1. and 3. So let's have a look at those.
Iteration
For 1., consider that the simplest and most performant way to iterate over a collection typically does not involve allocating intermediate results of the same abstract type as the collection. Mapping a function over a chunked seq over a vector is likely to be much more performant than mapping a function over a seq producing "view vectors" (using subvec) for each call to next; the latter, however, is the best we can do performance-wise for next on Clojure-style vectors (even in the presence of RRB trees, which are great when we need a proper subvector / vector slice operation to implement an interesting algorithm, but make traversals terrifying slow if we used them to implement next).
In Clojure, specialized seq types maintain traversal state and extra functionality such as (1) a node stack for sorted maps and sets (apart from better performance, this has better big-O complexity than traversals using dissoc / disj!), (2) current index + logic for wrapping leaf arrays in chunks for vectors, (3) a traversal "continuation" for hash maps. Traversing a collection through an object like this is simply faster than any attempt at traversing through subvec / dissoc / disj could be.
Suppose, however, that we're willing to accept the performance hit when mapping a function over a vector. Well, let's try filtering now:
(->> some-vector (map f) (filter p?))
There's a problem here -- there's no good way to remove elements from a vector. (Again, RRB trees could help in theory, but in practice all the RRB slicing and concatenating involved in producing "real vector" for filtering operations would absolutely destroy performance.)
Here's a similar problem. Consider this pipeline:
(->> some-sorted-set (filter p?) (map f) (take n))
Here we benefit from laziness (or rather, from the ability to stop filtering and mapping early; there's a point involving reducers to be made here, see below). Clearly take could be reordered with map, but not with filter.
The point is that if it's ok for filter to convert to seq implicitly, then it is also ok for map; and similar arguments can be made for other sequence functions. Once we've made the argument for all -- or nearly all -- of them, it becomes clear that it also makes sense for seq to return specialized seq objects.
Incidentally, filtering or mapping a function over a collection without producing a similar collection as a result is very useful. For example, often we care only about the result of reducing the sequence produced by a pipeline of transformations to some value or about calling a function for side effect at each element. For these scenarios, there is nothing whatsoever to be gained by maintaining the input type and quite a lot to be lost in performance.
Producing an output
As noted above, we do not always want to produce an output of the same type as the input. When we do, however, often the best way to do so is to do the equivalent of pouring a seq over the input into an empty output collection.
In fact, there is absolutely no way to do better for maps and sets. The fundamental reason is that for sets of cardinality greater than 1 there is no way to predict the cardinality of the output of mapping a function over a set, since the function can "glue together" (produce the same outputs for) arbitrary inputs.
Additionally, for sorted maps and sets there is no guarantee that the input set's comparator will be able to deal with outputs from an arbitrary function.
So, if in many cases there is no way to, say, map significantly better than by doing a seq and an into separately, and considering how both seq and into make useful primitives in their own right, Clojure makes the choice of exposing the useful primitives and letting users compose them. This lets us map and into to produce a set from a set, while leaving us the freedom to not go on to the into stage when there is no value to be gained by producing a set (or another collection type, as the case may be).
Not all is seq; or, consider reducers
Some of the problems with using the collection types themselves when mapping, filtering etc. don't apply when using reducers.
The key difference between reducers and seqs is that the intermediate objects produced by clojure.core.reducers/map and friends only produce "descriptor" objects that maintain information on what computations need to be performed in the event that the reducer is actually reduced. Thus, individual stages of the computation can be merged.
This allows us to do things like
(require '[clojure.core.reducers :as r])
(->> some-set (r/map f) (r/filter p?) (into #{}))
Of course we still need to be explicit about our (into #{}), but this is just a way of saying "the reducers pipeline ends here; please produce the result in the form of a set". We could also ask for a different collection type (a vector of results perhaps; note that mapping f over a set may well produce duplicate results and we may in some situations wish to preserve them) or a scalar value ((reduce + 0)).
Summary
The main points are these:
the fastest way to iterate over a collection typically doesn't involve produce intermediate results similar to the input;
seq uses the fastest way to iterate;
the best approach to transforming a set by mapping or filtering involves using a seq-style operation, because we want to iterate very fast while accumulating an output;
thus seq makes a great primitive;
map and filter, in their choice to deal with seqs, depending on the scenario, may avoid performance penalties without upsides, benefit from laziness etc., yet can still be used to produce a collection result with into;
thus they too make great primitives.
Some of these points may not apply to a statically typed language, but of course Clojure is dynamic. Additionally, when we do want to a return that matches input type, we're simply forced to be explicit about it and that, in itself, may be viewed as a good thing.
Sequences are a logical list abstraction. They provide access to a (stable) ordered sequence of values. They are implemented as views over collections (except for lists where the concrete interface matches the logical interface). The sequence (view) is a separate data structure that refers into the collection to provide the logical abstraction.
Sequence functions (map, filter, etc) take a "seqable" thing (something which can produce a sequence), call seq on it to produce the sequence, and then operate on that sequence, returning a new sequence. It is up to you whether you need to or how to re-collect that sequence back into a concrete collection. While vectors and lists are ordered, sets and maps are not and thus sequences over these data structures must compute and retain the order outside the collection.
Specialized functions like mapv, filterv, reduce-kv allow you to stay "in the collection" when you know you want the operation to return a collection at the end instead of sequence.
Seqs are ordered structures, whereas maps and sets are unordered. Two maps that are equal in value may have a different internal ordering. For example:
user=> (seq (array-map :a 1 :b 2))
([:a 1] [:b 2])
user=> (seq (array-map :b 2 :a 1))
([:b 2] [:a 1])
It makes no sense to ask for the rest of a map, because it's not a sequential structure. The same goes for a set.
So what about vectors? They're sequentially ordered, so we could potentially map across a vector, and indeed there is such a function: mapv.
You may well ask: why is this not implicit? If I pass a vector to map, why doesn't it return a vector?
Well, first that would mean making an exception for ordered structures like vectors, and Clojure isn't big on making exceptions.
But more importantly you'd lose one of the most useful properties of seqs: laziness. Chaining together seq functions, such as map and filter is a very common operation, and without laziness this would be much less performant and far more memory-intensive.
The collection classes follow a factory pattern i.e instead of implementing ISeq they implement Sequable i.e you can create a ISeq from the collection but the collection itself is not an ISeq.
Now even if these collections implemented ISeq directly I am not sure how that would solve your problem of having general purpose sequence functions that would return the original object, as that would not make sense at all as these general purpose functions are supposed to work on ISeq, they have no idea about which object gave them this ISeq
Example in java:
interface ISeq {
....
}
class A implements ISeq {
}
class B implements ISeq {
}
static class Helpers {
/*
Filter can only work with ISeq, that's what makes it general purpose.
There is no way it could return A or B objects.
*/
public static ISeq filter(ISeq coll, ...) { }
...
}