How to correctly use lists?

Just to address the last part of your question, since that really points out the difference between a list and vector in R:

Why do these two expressions not return the same result? x = list(1, 2, 3, 4); x2 = list(1:4)

A list can contain any other class as each element. So you can have a list where the first element is a character vector, the second is a data frame, etc. In this case, you have created two different lists. x has four vectors, each of length 1. x2 has 1 vector of length 4:

> length(x[[1]])
[1] 1
> length(x2[[1]])
[1] 4

So these are completely different lists.

R lists are very much like a hash map data structure in that each index value can be associated with any object. Here's a simple example of a list that contains 3 different classes (including a function):

> complicated.list <- list("a"=1:4, "b"=1:3, "c"=matrix(1:4, nrow=2), "d"=search)
> lapply(complicated.list, class)
$a
[1] "integer"
$b
[1] "integer"
$c
[1] "matrix"
$d
[1] "function"

Given that the last element is the search function, I can call it like so:

> complicated.list[["d"]]()
[1] ".GlobalEnv" ...

As a final comment on this: it should be noted that a data.frame is really a list (from the data.frame documentation):

A data frame is a list of variables of the same number of rows with unique row names, given class ‘"data.frame"’

That's why columns in a data.frame can have different data types, while columns in a matrix cannot. As an example, here I try to create a matrix with numbers and characters:

> a <- 1:4
> class(a)
[1] "integer"
> b <- c("a","b","c","d")
> d <- cbind(a, b)
> d
 a   b  
[1,] "1" "a"
[2,] "2" "b"
[3,] "3" "c"
[4,] "4" "d"
> class(d[,1])
[1] "character"

Note how I cannot change the data type in the first column to numeric because the second column has characters:

> d[,1] <- as.numeric(d[,1])
> class(d[,1])
[1] "character"

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Regarding your questions, let me address them in order and give some examples:

1) A list is returned if and when the return statement adds one. Consider

 R> retList <- function() return(list(1,2,3,4)); class(retList())
 [1] "list"
 R> notList <- function() return(c(1,2,3,4)); class(notList())
 [1] "numeric"
 R> 

2) Names are simply not set:

R> retList <- function() return(list(1,2,3,4)); names(retList())
NULL
R> 

3) They do not return the same thing. Your example gives

R> x <- list(1,2,3,4)
R> x[1]
[[1]]
[1] 1
R> x[[1]]
[1] 1

where x[1] returns the first element of x -- which is the same as x. Every scalar is a vector of length one. On the other hand x[[1]] returns the first element of the list.

4) Lastly, the two are different between they create, respectively, a list containing four scalars and a list with a single element (that happens to be a vector of four elements).

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Just to take a subset of your questions:

This article on indexing addresses the question of the difference between [] and [[]].

In short [[]] selects a single item from a list and [] returns a list of the selected items. In your example, x = list(1, 2, 3, 4)' item 1 is a single integer but x[[1]] returns a single 1 and x[1] returns a list with only one value.

> x = list(1, 2, 3, 4)
> x[1]
[[1]]
[1] 1

> x[[1]]
[1] 1

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One reason lists work as they do (ordered) is to address the need for an ordered container that can contain any type at any node, which vectors do not do. Lists are re-used for a variety of purposes in R, including forming the base of a data.frame, which is a list of vectors of arbitrary type (but the same length).

Why do these two expressions not return the same result?

x = list(1, 2, 3, 4); x2 = list(1:4)

To add to @Shane's answer, if you wanted to get the same result, try:

x3 = as.list(1:4)

Which coerces the vector 1:4 into a list.

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Just to add one more point to this:

R does have a data structure equivalent to the Python dict in the hash package. You can read about it in this blog post from the Open Data Group. Here's a simple example:

> library(hash)
> h <- hash( keys=c('foo','bar','baz'), values=1:3 )
> h[c('foo','bar')]
<hash> containing 2 key-value pairs.
  bar : 2
  foo : 1

In terms of usability, the hash class is very similar to a list. But the performance is better for large datasets.

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You say:

For another, lists can be returned from functions even though you never passed in a List when you called the function, and even though the function doesn't contain a List constructor, e.g.,

x = strsplit(LETTERS[1:10], "") # passing in an object of type 'character'
class(x)
# => 'list'

And I guess you suggest that this is a problem(?). I'm here to tell you why it's not a problem :-). Your example is a bit simple, in that when you do the string-split, you have a list with elements that are 1 element long, so you know that x[[1]] is the same as unlist(x)[1]. But what if the result of strsplit returned results of different length in each bin. Simply returning a vector (vs. a list) won't do at all.

For instance:

stuff <- c("You, me, and dupree",  "You me, and dupree",
           "He ran away, but not very far, and not very fast")
x <- strsplit(stuff, ",")
xx <- unlist(strsplit(stuff, ","))

In the first case (x : which returns a list), you can tell what the 2nd "part" of the 3rd string was, eg: x[[3]][2]. How could you do the same using xx now that the results have been "unraveled" (unlist-ed)?

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This is a very old question, but I think that a new answer might add some value since, in my opinion, no one directly addressed some of the concerns in the OP.

Despite what the accepted answer suggests, list objects in R are not hash maps. If you want to make a parallel with python, list are more like, you guess, python lists (or tuples actually).

It's better to describe how most R objects are stored internally (the C type of an R object is SEXP). They are made basically of three parts:

an header, which declares the R type of the object, the length and some other meta data;

the data part, which is a standard C heap-allocated array (contiguous block of memory);

the attributes, which are a named linked list of pointers to other R objects (or NULL if the object doesn't have attributes).

From an internal point of view, there is little difference between a list and a numeric vector for instance. The values they store are just different. Let's break two objects into the paradigm we described before:

x <- runif(10)
y <- list(runif(10), runif(3))

For x:

The header will say that the type is numeric (REALSXP in the C-side), the length is 10 and other stuff.

The data part will be an array containing 10 double values.

The attributes are NULL, since the object doesn't have any.

For y:

The header will say that the type is list (VECSXP in the C-side), the length is 2 and other stuff.

The data part will be an array containing 2 pointers to two SEXP types, pointing to the value obtained by runif(10) and runif(3) respectively.

The attributes are NULL, as for x.

So the only difference between a numeric vector and a list is that the numeric data part is made of double values, while for the list the data part is an array of pointers to other R objects.

What happens with names? Well, names are just some of the attributes you can assign to an object. Let's see the object below:

z <- list(a=1:3, b=LETTERS)

The header will say that the type is list (VECSXP in the C-side), the length is 2 and other stuff.

The data part will be an array containing 2 pointers to two SEXP types, pointing to the value obtained by 1:3 and LETTERS respectively.

The attributes are now present and are a names component which is a character R object with value c("a","b").

From the R level, you can retrieve the attributes of an object with the attributes function.

The key-value typical of an hash map in R is just an illusion. When you say:

z[["a"]]

this is what happens:

the [[ subset function is called;

the argument of the function ("a") is of type character, so the method is instructed to search such value from the names attribute (if present) of the object z;

if the names attribute isn't there, NULL is returned;

if present, the "a" value is searched in it. If "a" is not a name of the object, NULL is returned;

if present, the position of the first occurence is determined (1 in the example). So the first element of the list is returned, i.e. the equivalent of z[[1]].

The key-value search is rather indirect and is always positional. Also, useful to keep in mind:

in hash maps the only limit a key must have is that it must be hashable. names in R must be strings (character vectors);

in hash maps you cannot have two identical keys. In R, you can assign names to an object with repeated values. For instance: names(y) <- c("same", "same")

is perfectly valid in R. When you try y[["same"]] the first value is retrieved. You should know why at this point.

In conclusion, the ability to give arbitrary attributes to an object gives you the appearance of something different from an external point of view. But R lists are not hash maps in any way.

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x = list(1, 2, 3, 4)
x2 = list(1:4)
all.equal(x,x2)

is not the same because 1:4 is the same as c(1,2,3,4). If you want them to be the same then:

x = list(c(1,2,3,4))
x2 = list(1:4)
all.equal(x,x2)

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Although this is a pretty old question I must say it is touching exactly the knowledge I was missing during my first steps in R - i.e. how to express data in my hand as an object in R or how to select from existing objects. It is not easy for an R novice to think "in an R box" from the very beginning.

So I myself started to use crutches below which helped me a lot to find out what object to use for what data, and basically to imagine real-world usage.

Though I not giving exact answers to the question the short text below might help the reader who just started with R and is asking similar questions.

Atomic vector ... I called that "sequence" for myself, no direction, just sequence of same types. [ subsets.

Vector ... the sequence with one direction from 2D, [ subsets.

Matrix ... bunch of vectors with the same length forming rows or columns, [ subsets by rows and columns, or by sequence.

Arrays ... layered matrices forming 3D

Dataframe ... a 2D table like in excel, where I can sort, add or remove rows or columns or make arit. operations with them, only after some time I truly recognized that data frame is a clever implementation of list where I can subset using [ by rows and columns, but even using [[.

List ... to help myself I thought about the list as of tree structure where [i] selects and returns whole branches and [[i]] returns item from the branch. And because it is tree like structure, you can even use an index sequence to address every single leaf on a very complex list using its [[index_vector]]. Lists can be simple or very complex and can mix together various types of objects into one.

So for lists you can end up with more ways how to select a leaf depending on situation like in the following example.

l <- list("aaa",5,list(1:3),LETTERS[1:4],matrix(1:9,3,3))
l[[c(5,4)]] # selects 4 from matrix using [[index_vector]] in list
l[[5]][4] # selects 4 from matrix using sequential index in matrix
l[[5]][1,2] # selects 4 from matrix using row and column in matrix

This way of thinking helped me a lot.

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Regarding vectors and the hash/array concept from other languages:

Vectors are the atoms of R. Eg, rpois(1e4,5) (5 random numbers), numeric(55) (length-55 zero vector over doubles), and character(12) (12 empty strings), are all "basic". Either lists or vectors can have names. > n = numeric(10) > n [1] 0 0 0 0 0 0 0 0 0 0 > names(n) NULL > names(n) = LETTERS[1:10] > n A B C D E F G H I J 0 0 0 0 0 0 0 0 0 0 Vectors require everything to be the same data type. Watch this: > i = integer(5) > v = c(n,i) > v A B C D E F G H I J 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 > class(v) [1] "numeric" > i = complex(5) > v = c(n,i) > class(v) [1] "complex" > v A B C D E F G H I J 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i 0+0i Lists can contain varying data types, as seen in other answers and the OP's question itself.

I've seen languages (ruby, javascript) in which "arrays" may contain variable datatypes, but for example in C++ "arrays" must be all the same datatype. I believe this is a speed/efficiency thing: if you have a numeric(1e6) you know its size and the location of every element a priori; if the thing might contain "Flying Purple People Eaters" in some unknown slice, then you have to actually parse stuff to know basic facts about it.

Certain standard R operations also make more sense when the type is guaranteed. For example cumsum(1:9) makes sense whereas cumsum(list(1,2,3,4,5,'a',6,7,8,9)) does not, without the type being guaranteed to be double.

As to your second question:

Lists can be returned from functions even though you never passed in a List when you called the function

Functions return different data types than they're input all the time. plot returns a plot even though it doesn't take a plot as an input. Arg returns a numeric even though it accepted a complex. Etc.

(And as for strsplit: the source code is here.)

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If it helps, I tend to conceive "lists" in R as "records" in other pre-OO languages:

they do not make any assumptions about an overarching type (or rather the type of all possible records of any arity and field names is available).

their fields can be anonymous (then you access them by strict definition order).

The name "record" would clash with the standard meaning of "records" (aka rows) in database parlance, and may be this is why their name suggested itself: as lists (of fields).

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why do these two different operators, [ ], and [[ ]], return the same result?

x = list(1, 2, 3, 4)

[ ] provides sub setting operation. In general sub set of any object will have the same type as the original object. Therefore, x[1] provides a list. Similarly x[1:2] is a subset of original list, therefore it is a list. Ex. x[1:2] [[1]] [1] 1 [[2]] [1] 2 [[ ]] is for extracting an element from the list. x[[1]] is valid and extract the first element from the list. x[[1:2]] is not valid as [[ ]] does not provide sub setting like [ ]. x[[2]] [1] 2 > x[[2:3]] Error in x[[2:3]] : subscript out of bounds

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you can try something like,

set.seed(123)
l <- replicate(20, runif(sample(1:10,1)), simplify = FALSE)

out <- vector("list", length(l))
for (i in seq_along(l)) {
  out[[i]] <- length(unique(l[[i]])) #length(l[[i]])
}
unlist(out)

unlist(lapply(l,length))
unlist(lapply(l, class))
unlist(lapply(l, mean))
unlist(lapply(l, max))

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