This is an introduction to the R language, explaining evaluation, parsing, object oriented programming, computing on the language, and so forth.
The current version of this document is 2.10.0 (2009-10-26) DRAFT.
ISBN 3-900051-13-5
R is a system for statistical computation and graphics. It provides, among other things, a programming language, high level graphics, interfaces to other languages and debugging facilities. This manual details and defines the R language.
The R language is a dialect of S which was designed in the 1980s and has been in widespread use in the statistical community since. Its principal designer, John M. Chambers, was awarded the 1998 ACM Software Systems Award for S.
The language syntax has a superficial similarity with C, but the semantics are of the FPL (functional programming language) variety with stronger affinities with Lisp and APL. In particular, it allows “computing on the language”, which in turn makes it possible to write functions that take expressions as input, something that is often useful for statistical modeling and graphics.
It is possible to get quite far using R interactively, executing simple expressions from the command line. Some users may never need to go beyond that level, others will want to write their own functions either in an ad hoc fashion to systematize repetitive work or with the perspective of writing add-on packages for new functionality.
The purpose of this manual is to document the language per se. That is, the objects that it works on, and the details of the expression evaluation process, which are useful to know when programming R functions. Major subsystems for specific tasks, such as graphics, are only briefly described in this manual and will be documented separately.
Although much of the text will equally apply to S, there are also some substantial differences, and in order not to confuse the issue we shall concentrate on describing R.
The design of the language contains a number of fine points and common pitfalls which may surprise the user. Most of these are due to consistency considerations at a deeper level, as we shall explain. There are also a number of useful shortcuts and idioms, which allow the user to express quite complicated operations succinctly. Many of these become natural once one is familiar with the underlying concepts. In some cases, there are multiple ways of performing a task, but some of the techniques will rely on the language implementation, and others work at a higher level of abstraction. In such cases we shall indicate the preferred usage.
Some familiarity with R is assumed. This is not an introduction to R but rather a programmers' reference manual. Other manuals provide complementary information: in particular Preface provides an introduction to R and System and foreign language interfaces details how to extend R using compiled code.
In every computer language variables provide a means of accessing the data stored in memory. R does not provide direct access to the computer's memory but rather provides a number of specialized data structures we will refer to as objects. These objects are referred to through symbols or variables. In R, however, the symbols are themselves objects and can be manipulated in the same way as any other object. This is different from many other languages and has wide ranging effects.
In this chapter we provide preliminary descriptions of the various data
structures provided in R. More detailed discussions of many of them
will be found in the subsequent chapters. The R specific function
typeof
returns the type of an R object. Note that in the C code
underlying R, all objects are pointers to a structure with typedef
SEXPREC; the different R data types are represented in C by
SEXPTYPE, which determines how the information in the various
parts of the structure is used.
The following table describes the possible values returned by
typeof and what they are.
Users cannot easily get hold of objects of types marked with a `***'.
Function mode gives information about the mode of an object
in the sense of Becker, Chambers & Wilks (1988), and is more compatible
with other implementations of the S language.
Finally, the function storage.mode returns the storage mode
of its argument in the sense of Becker et al. (1988). It is generally
used when calling functions written in another language, such as C or
FORTRAN, to ensure that R objects have the data type expected by the
routine being called. (In the S language, vectors with integer or
real values are both of mode "numeric", so their storage modes
need to be distinguished.)
> x <- 1:3
> typeof(x)
[1] "integer"
> mode(x)
[1] "numeric"
> storage.mode(x)
[1] "integer"
R objects are often coerced to different types during computations. There are also many functions available to perform explicit coercion. When programming in the R language the type of an object generally doesn't affect the computations, however, when dealing with foreign languages or the operating system it is often necessary to ensure that an object is of the correct type.
Vectors can be thought of as contiguous cells containing data. Cells
are accessed through
indexing operations such as
x[5]. More details are given in Indexing.
R has six basic (`atomic') vector types: logical, integer, real, complex, string (or character) and raw. The modes and storage modes for the different vector types are listed in the following table.
typeof mode storage.mode logicallogicallogicalintegernumericintegerdoublenumericdoublecomplexcomplexcomplexcharactercharactercharacterrawrawraw
Single numbers, such as 4.2, and strings, such as "four
point two" are still vectors, of length 1; there are no more basic
types. Vectors with length zero are possible (and useful).
String vectors have mode and storage mode "character". A single
element of a character vector is often referred to as a character
string.
Lists (“generic vectors”) are another kind of data storage. Lists have elements, each of which can contain any type of R object, i.e. the elements of a list do not have to be of the same type. List elements are accessed through three different indexing operations. These are explained in detail in Indexing.
Lists are vectors, and the basic vector types are referred to as atomic vectors where it is necessary to exclude lists.
There are three types of objects that constitute the R language.
They are calls, expressions, and names.
Since R has objects of type "expression" we will try to avoid
the use of the word expression in other contexts. In particular
syntactically correct expressions will be referred to as
statements.
These objects have modes "call", "expression", and
"name", respectively.
They can be created directly from expressions using the quote
mechanism and converted to and from lists by the as.list and
as.call functions.
Components of the
parse tree can be extracted using the standard
indexing operations.
Symbols refer to R
objects. The
name of any R object is usually a
symbol. Symbols can be created through the functions as.name and
quote.
Symbols have mode "name", storage mode "symbol", and type
"symbol". They can be
coerced to and from character strings
using as.character and as.name.
They naturally appear as atoms of parsed expressions, try e.g.
as.list(quote(x + y)).
In R one can have objects of type "expression". An
expression contains one or more statements. A statement is a
syntactically correct collection of
tokens.
Expression objects are special language objects which contain parsed but
unevaluated R statements. The main difference is that an expression
object can contain several such expressions. Another more subtle
difference is that objects of type "expression" are only
evaluated when
explicitly passed to eval, whereas other language objects may get
evaluated in some unexpected cases.
An expression object behaves much like a list and its components should be accessed in the same way as the components of a list.
In R functions are objects and can be manipulated in much the same way as any other object. Functions (or more precisely, function closures) have three basic components: a formal argument list, a body and an environment. The argument list is a comma-separated list of arguments. An argument can be a symbol, or a `symbol = default' construct, or the special argument `...'. The second form of argument is used to specify a default value for an argument. This value will be used if the function is called without any value specified for that argument. The `...' argument is special and can contain any number of arguments. It is generally used if the number of arguments is unknown or in cases where the arguments will be passed on to another function.
The body is a parsed R statement. It is usually a collection of statements in braces but it can be a single statement, a symbol or even a constant.
A function's environment is the environment that was active at the time that the function was created. Any symbols bound in that environment are captured and available to the function. This combination of the code of the function and the bindings in its environment is called a `function closure', a term from functional programming theory. In this document we generally use the term `function', but use `closure' to emphasize the importance of the attached environment.
It is possible to extract and manipulate the three parts of a closure
object using formals, body, and environment
constructs (all three can also be used on the left hand side of
assignments).
The last of these can be used to remove unwanted environment capture.
When a function is called, a new environment (called the evaluation environment) is created, whose enclosure (see Environment objects) is the environment from the function closure. This new environment is initially populated with the unevaluated arguments to the function; as evaluation proceeds, local variables are created within it.
There is also a facility for converting functions to and from list
structures using as.list and as.function.
These have been included to provide compatibility with S and their
use is discouraged.
There is a special object called NULL. It is used whenever there
is a need to indicate or specify that an object is absent. It should not be
confused with a vector or list of zero length.
The NULL object has no type and no modifiable properties. There
is only one NULL object in R, to which all instances refer. To
test for NULL use is.null. You cannot set attributes on
NULL.
These two kinds of object contain the builtin
functions of R, i.e., those that are displayed as .Primitive
in code listings (as well as those accessed via the .Internal
function and hence not user-visible as objects). The difference between
the two lies in the argument handling. Builtin functions have all
their arguments evaluated and passed to the internal function, in
accordance with call-by-value, whereas special functions pass the
unevaluated arguments to the internal function.
From the R language, these objects are just another kind of function,
except that their definition cannot be listed. The typeof
function can distinguish them from interpreted
functions.
Promise objects are part of R's lazy evaluation mechanism. They contain three slots: a value, an expression, and an environment. When a function is called the arguments are matched and then each of the formal arguments is bound to a promise. The expression that was given for that formal argument and a pointer to the environment the function was called from are stored in the promise.
Until that argument is accessed there is no value associated with
the promise. When the argument is accessed, the stored expression is
evaluated in the stored environment, and the result is returned. The
result is also saved by
the promise. The substitute function will extract the content
of the expression slot. This allows the programmer to
access either the value or the expression associated with the promise.
Within the R language, promise objects are almost only seen
implicitly. (In an upcoming release they will never be visible to
R code, as they will always be evaluated when accessed.)
Actual function arguments are of this type.
There is also a delayedAssign function
that will make a promise out of an expression. There is generally no
way in R code to check whether an object is a promise or not, nor is there a
way to use R code to determine the environment of a promise.
The `...' object type is stored as a type of pairlist. The
components of `...' can be accessed in the usual pairlist manner
from C code, but is not easily accessed as an object in interpreted
code. The object can be captured as a list, so for example in
table one sees
args <- list(...)
## ....
for (a in args) {
## ....
If a function has `...' as a formal argument then any actual arguments that do not match a formal argument are matched with `...'.
Environments can be thought of as consisting of two things. A
frame, consisting of a set of symbol-value pairs, and an
enclosure, a pointer to an enclosing environment. When R
looks up the value for a symbol the frame is examined and if a
matching symbol is found its value will be returned. If not, the
enclosing environment is then accessed and the process repeated.
Environments form a tree structure in which the enclosures play the
role of parents. The tree of environments is rooted in an empty
environment, available through emptyenv(), which has no parent.
It is the direct parent of the environment of the base package
(available through the baseenv() function). Formerly
baseenv() had the special value NULL, but as from
version 2.4.0, the use of NULL as an environment is defunct.
Environments are created implicitly by function calls, as described in
Function objects and Lexical environment. In this case the
environment contains the variables local to the function (including the
arguments), and its enclosure is the environment of the currently called
function. Environments may also be created directly by new.env.
The frame content of an environment can be accessed and manipulated by
use of ls, get and assign as well as eval and
evalq.
The parent.env function may be used to access the enclosure of
an environment.
Unlike most other R objects, environments are not copied when passed to functions or used in assignments. Thus, if you assign the same environment to several symbols and change one, the others will change too. In particular, assigning attributes to an environment can lead to surprises.
Pairlist objects are similar to Lisp's dotted-pair lists. They are used
extensively in the internals of R, but are rarely visible in
interpreted code, although they are returned by formals, and can
be created by (e.g.) the pairlist function. A zero-length
pairlist is NULL, as would be expected in Lisp but in contrast to
a zero-length list.
Each such object has three slots, a CAR value, a CDR value and a TAG
value. The TAG value is a text string and CAR and CDR usually
represent, respectively, a list item (head) and the remainder (tail) of
the list with a NULL object as terminator (the CAR/CDR terminology is
traditional Lisp and originally referred to the address and decrement
registers on an early 60's IBM computer).
Pairlists are handled in the R language in exactly the same way as
generic vectors (“lists”). In particular, elements are accessed using
the same [[]] syntax. The use of pairlists is deprecated since
generic vectors are usually more efficient to use. When an internal
pairlist is accessed from R it is generally (including when
subsetted) converted to a generic vector.
In a very few cases pairlists are user-visible: one is .Options.
It is not really possible for an object to be of “Any” type, but it is
nevertheless a valid type value. It gets used in certain (rather rare)
circumstances, e.g. as.vector(x, "any"), indicating that type
coercion should not be done.
All objects except NULL can have one or more attributes attached
to them. Attributes are stored as a pairlist where all elements are
named, but should be thought of as a set of name=value pairs. A listing
of the attributes can be obtained using attributes and set by
attributes<-,
individual components are accessed using attr and attr<-.
Some attributes have special accessor
functions (e.g. levels<-
for factors) and these should be used when available. In addition to
hiding details of implementation they may perform additional operations.
R attempts to intercept calls to attr<- and to
attributes<- that involve the special attributes and enforces
the consistency checks.
Matrices and arrays are simply vectors with the attribute dim and
optionally dimnames attached to the vector.
Attributes are used to implement the class structure used in R. If an
object has a class attribute then that attribute will be examined
during
evaluation. The class structure in R is described in detail
in Object-oriented programming.
A names attribute, when present, labels the individual elements of
a vector or list. When an object is printed the names attribute,
when present, is used to label the elements. The names attribute
can also be used for indexing purposes, for example,
quantile(x)["25%"].
One may get and set the names using names and names<-
constructions.
The latter will perform the necessary consistency checks to ensure that
the names attribute has the proper type and length.
Pairlists and one-dimensional arrays are treated specially. For pairlist
objects, a virtual names attribute is used; the names
attribute is really constructed from the tags of the list components.
For one-dimensional arrays the names attribute really accesses
dimnames[[1]].
The dim attribute is used to implement arrays. The content of
the array is stored in a vector in column-major order and the dim
attribute is a vector of integers specifying the respective extents of
the array. R ensures that the length of the vector is the product of
the lengths of the dimensions. The length of one or more dimensions may
be zero.
A vector is not the same as a one-dimensional array since the latter has
a dim attribute of length one, whereas the former has no
dim attribute.
Arrays may name each dimension separately using the dimnames
attribute which is a list of character vectors. The dimnames
list may itself have names which are then used for extent headings when
printing arrays.
R has an elaborate class system, controlled via the class
attribute. This attribute is a character vector containing the list of
classes that an object inherits from. This forms the basis of the
“generic methods” functionality in R.
This attribute can be accessed and manipulated virtually without
restriction by users. There is no checking that an object actually
contains the components that class methods expect. Thus, altering the
class attribute should be done with caution, and when they are
available specific creation and
coercion functions should be preferred.
The tsp attribute is used to hold parameters of time series,
start, end, and frequency. This construction is mainly used to handle
series with periodic substructure such as monthly or quarterly data.
Whether attributes should be copied when an object is altered is a complex area, but there are some general rules (Becker, Chambers & Wilks, 1988, pp. 144–6).
Scalar functions (those which operate element-by-element on a vector and whose output is similar to the input) should preserve attributes (except perhaps class).
Binary operations normally copy most attributes from the longer argument
(and if they are of the same length from both, preferring the values on
the first). Here `most' means all except the names, dim
and dimnames which are set appropriately by the code for the
operator.
Subsetting (other than by an empty index) generally drops all attributes
except names, dim and dimnames which are reset as
appropriate. On the other hand, subassignment generally preserves
attributes even if the length is changed. Coercion drops all
attributes.
The default method for sorting drops all attributes except names, which are sorted along with the object.
Factors are used to describe items that can have a finite number of
values (gender, social class, etc.). A factor has a levels
attribute and class "factor". Optionally, it may also contain a
contrasts attribute which controls the parametrisation used when
the factor is used in a
modeling functions.
A factor may be purely nominal or may have ordered categories. In the
latter case, it should be defined as such and have a class vector
c("ordered"," factor").
Factors are currently implemented using an integer array to specify the actual levels and a second array of names that are mapped to the integers. Rather unfortunately users often make use of the implementation in order to make some calculations easier. This, however, is an implementation issue and is not guaranteed to hold in all implementations of R.
Data frames are the R structures which most closely mimic the SAS or SPSS data set, i.e. a “cases by variables” matrix of data.
A data frame is a list of vectors, factors, and/or matrices all having
the same length (number of rows in the case of matrices). In addition,
a data frame generally has a names attribute labeling the
variables and a row.names attribute for labeling the cases.
A data frame can contain a list that is the same length as the other components. The list can contain elements of differing lengths thereby providing a data structure for ragged arrays. However, as of this writing such arrays are not generally handled correctly.
When a user types a command at the prompt (or when an expression is read from a file) the first thing that happens to it is that the command is transformed by the parser into an internal representation. The evaluator executes parsed R expressions and returns the value of the expression. All expressions have a value. This is the core of the language.
This chapter describes the basic mechanisms of the evaluator, but avoids discussion of specific functions or groups of functions which are described in separate chapters later on or where the help pages should be sufficient documentation.
Users can construct expressions and invoke the evaluator on them.
Any number typed directly at the prompt is a constant and is evaluated.
> 1
[1] 1
Perhaps unexpectedly, the number returned from the expression 1
is a numeric. In most cases, the difference between an integer and a
numeric value will be unimportant as R will do the right thing when
using the numbers. There are, however, times when we would like to
explicitly create an integer value for a constant. We can do this by
calling the function as.integer or using various other
techniques. But perhaps the simplest approach is to qualify our
constant with the suffix character `L'.
For example, to create the integer value 1, we might use
> 1L
[1]
We can use the `L' suffix to qualify any number with the intent of
making it an explicit integer. So `0x10L' creates the integer value
16 from the hexadecimal representation. The constant 1e3L gives 1000
as an integer rather than a numeric value and is equivalent to 1000L.
(Note that the `L' is treated as qualifying the term 1e3 and not the
3.) If we qualify a value with `L' that is not an integer value,
e.g. 1e-3L, we get a warning and the numeric value is created.
A warning is also created if there is an unnecessary decimal point
in the number, e.g. 1.L.
We get a syntax error when using `L' with complex numbers,
e.g. 12iL gives an error.
Constants are fairly boring and to do more we need symbols.
When a new variable is created it must have a name so it can be referenced and it usually has a value. The name itself is a symbol. When a symbol is evaluated its value is returned. Later we shall explain in detail how to determine the value associated with a symbol.
In this small example y is a symbol and its value is 4. A symbol
is an R object too, but one rarely needs to deal with symbols
directly, except when doing “programming on the language”
(Computing on the language).
> y <- 4
> y
[1] 4
Most of the computations carried out in R involve the evaluation of functions. We will also refer to this as function invocation. Functions are invoked by name with a list of arguments separated by commas.
> mean(1:10)
[1] 5.5
In this example the function mean was called with one argument,
the vector of integers from 1 to 10.
R contains a huge number of functions with different purposes. Most are used for producing a result which is an R object, but others are used for their side effects, e.g., printing and plotting functions.
Function calls can have tagged (or named) arguments, as in
plot(x, y, pch = 3) arguments without tags are known as
positional since the function must distinguish their meaning from
their sequential positions among the arguments of the call, e.g., that
x denotes the abscissa variable and y the ordinate. The
use of tags/names is an obvious convenience for functions with a large
number of optional arguments.
A special type of function calls can appear on the left hand side of the assignment operator as in
> class(x) <- "foo"
What this construction really does is to call the function
class<- with the original object and the right hand side. This
function performs the modification of the object and returns the result
which is then stored back into the original variable. (At least
conceptually, this is what happens. Some additional effort is made to
avoid unnecessary data duplication.)
R allows the use of arithmetic expressions using operators similar to those of the C programming language, for instance
> 1 + 2
[1] 3
Expressions can be grouped using parentheses, mixed with function calls, and assigned to variables in a straightforward manner
> y <- 2 * (a + log(x))
R contains a number of operators. They are listed in the table below.
-Minus, can be unary or binary +Plus, can be unary or binary !Unary not ~Tilde, used for model formulae, can be either unary or binary ?Help :Sequence, binary (in model formulae: interaction) *Multiplication, binary /Division, binary ^Exponentiation, binary %x%Special binary operators, x can be replaced by any valid name %%Modulus, binary %/%Integer divide, binary %*%Matrix product, binary %o%Outer product, binary %x%Kronecker product, binary %in%Matching operator, binary (in model formulae: nesting) <Less than, binary >Greater than, binary ==Equal to, binary >=Greater than or equal to, binary <=Less than or equal to, binary &And, binary, vectorized &&And, binary, not vectorized |Or, binary, vectorized ||Or, binary, not vectorized <-Left assignment, binary ->Right assignment, binary $List subset, binary
Except for the syntax, there is no difference between applying an
operator and calling a function. In fact, x + y can equivalently
be written `+`(x, y). Notice that since `+' is a
non-standard function name, it needs to be quoted.
R deals with entire vectors of data at a time, and most of the
elementary operators and basic mathematical functions like log
are vectorized (as indicated in the table above). This means that
e.g. adding two vectors of the same length will create a vector
containing the element-wise sums, implicitly looping over the vector
index. This applies also to other operators like -, *,
and / as well as to higher dimensional structures. Notice in
particular that multiplying two matrices does not produce the usual
matrix product (the %*% operator exists for that purpose). Some
finer points relating to vectorized operations will be discussed in
Elementary arithmetic operations.
To access individual elements of an atomic vector, one generally uses
the x[i] construction.
> x <- rnorm(5)
> x
[1] -0.12526937 -0.27961154 -1.03718717 -0.08156527 1.37167090
> x[2]
[1] -0.2796115
List components are more commonly accessed using x$a or
x[[i]].
> x <- options()
> x$prompt
[1] "> "
Indexing constructs can also appear on the right hand side of an assignment.
Like the other operators, indexing is really done by functions, and one
could have used `[`(x, 2) instead of x[2].
R's indexing operations contain many advanced features which are further described in Indexing.
Computation in R consists of sequentially evaluating
statements. Statements, such as x<-1:10 or
mean(y), can be separated by either a semi-colon or a new line.
Whenever the
evaluator is presented with a syntactically complete
statement that statement is evaluated and the value returned.
The result of evaluating a statement can be referred to as the value of
the statement1 The value can
always be assigned to a symbol.
Both semicolons and new lines can be used to separate statements. A semicolon always indicates the end of a statement while a new line may indicate the end of a statement. If the current statement is not syntactically complete new lines are simply ignored by the evaluator. If the session is interactive the prompt changes from `>' to `+'.
> x <- 0; x + 5
[1] 5
> y <- 1:10
> 1; 2
[1] 1
[1] 2
Statements can be grouped together using braces `{' and `}'. A group of statements is sometimes called a block. Single statements are evaluated when a new line is typed at the end of the syntactically complete statement. Blocks are not evaluated until a new line is entered after the closing brace. In the remainder of this section, statement refers to either a single statement or a block.
> { x <- 0
+ x + 5
+ }
[1] 5
The if/else statement conditionally evaluates two
statements. There is a condition which is evaluated and if the
value is TRUE then the first statement is evaluated;
otherwise the second statement will be evaluated. The
if/else statement returns, as its value, the value of the
statement that was selected. The formal syntax is
if ( statement1 )
statement2
else
statement3
First, statement1 is evaluated to yield value1. If
value1 is a logical vector with first element TRUE then
statement2 is evaluated. If the first element of value1 is
FALSE then statement3 is evaluated. If value1 is a
numeric vector then statement3 is evaluated when the first element
of value1 is zero and otherwise statement2 is evaluated.
Only the first element of value1 is used. All other elements are
ignored. If value1 has any type other than a logical or a numeric
vector an error is signalled.
If/else statements can be used to avoid numeric problems such as taking the logarithm of a negative number. Because if/else statements are the same as other statements you can assign the value of them. The two examples below are equivalent.
> if( any(x <= 0) ) y <- log(1+x) else y <- log(x)
> y <- if( any(x <= 0) ) log(1+x) else log(x)
The else clause is optional. The statement if(any(x <= 0))
x <- x[x <= 0] is valid. When the if statement is not in a
block the else, if present, must appear on the same line as
statement1. Otherwise the new line at the end of statement1
yields a syntactically complete statement that is evaluated.
If/else statements can be nested.
if ( statement1 )
statement2
else if ( statement3 )
statement4
else if ( statement5 )
statement6
else
statement8
One of the even numbered statements will be evaluated and the resulting
value returned. If the optional else clause is omitted and all
the odd numbered statement's evaluate to FALSE no statement
will be evaluated and NULL is returned.
The odd numbered statements are evaluated, in order, until one
evaluates to TRUE and then the associated even numbered
statement is evaluated. In this example, statement6 will
only be evaluated if statement1 is FALSE and
statement3 is FALSE and statement5 is TRUE.
There is no limit to the number of else if clauses that are
permitted.
R has three statements that provide explicit
looping.2 They are for, while and
repeat. The two built-in constructs, next and
break, provide additional control over the evaluation. Each of
the three statements returns the value of the last statement that was
evaluated. It is possible, although uncommon, to assign the result of
one of these statements to a symbol. R provides other functions for
implicit looping such as tapply, apply, and lapply.
In addition many operations, especially arithmetic ones, are vectorized
so you may not need to use a loop.
There are two statements that can be used to explicitly control looping.
They are break and next.
The break statement causes an exit from the innermost loop that
is currently being executed. The next statement immediately
causes control to return to the start of the loop. The next iteration
of the loop (if there is one) is then executed. No statement below
next in the current loop is evaluated.
The value returned by a loop statement statement is always NULL
and is returned invisibly.
The repeat statement causes repeated evaluation of the body until
a break is specifically requested. This means that you need to be
careful when using repeat because of the danger of an infinite
loop. The syntax of the repeat loop is
repeat statement
When using repeat, statement must be a block statement.
You need to both perform some computation and test whether or not to
break from the loop and usually this requires two statements.
The while statement is very similar to the repeat
statement. The syntax of the while loop is
while ( statement1 ) statement2
where statement1 is evaluated and if its value is TRUE then
statement2 is evaluated. This process continues until
statement1 evaluates to FALSE.
for ( name in vector )
statement1
where vector can be either a vector or a list. For each element in vector the variable name is set to the value of that element and statement1 is evaluated. A side effect is that the variable name still exists after the loop has concluded and it has the value of the last element of vector that the loop was evaluated for.
Technically speaking, switch is just another function, but its
semantics are close to those of control structures of other programming
languages.
The syntax is
switch (statement, list)
where the elements of list may be named. First, statement
is evaluated and the result, value, obtained. If value is a
number between 1 and the length of list then the corresponding
element list is evaluated and the result returned. If value
is too large or too small NULL is returned.
> x <- 3
> switch(x, 2+2, mean(1:10), rnorm(5))
[1] 2.2903605 2.3271663 -0.7060073 1.3622045 -0.2892720
> switch(2, 2+2, mean(1:10), rnorm(5))
[1] 5.5
> switch(6, 2+2, mean(1:10), rnorm(5))
NULL
If value is a character vector then the element of `...' with
a name that exactly matches value is evaluated. If there is no
match NULL is returned.
> y <- "fruit"
> switch(y, fruit = "banana", vegetable = "broccoli", meat = "beef")
[1] "banana"
A common use of switch is to branch according to the character
value of one of the arguments to a function.
> centre <- function(x, type) {
+ switch(type,
+ mean = mean(x),
+ median = median(x),
+ trimmed = mean(x, trim = .1))
+ }
> x <- rcauchy(10)
> centre(x, "mean")
[1] 0.8760325
> centre(x, "median")
[1] 0.5360891
> centre(x, "trimmed")
[1] 0.6086504
switch returns either the value of the statement that was
evaluated or NULL if no statement was evaluated.
To choose from a list of alternatives that already exists switch
may not be the best way to select one for evaluation. It is often
better to use eval and the subset operator, [[, directly
via eval(x[[condition]]).
In this section, we discuss the finer points of the rules that apply to basic operation like addition or multiplication of two vectors or matrices.
If one tries to add two structures with a different number of elements,
then the shortest is recycled to length of longest. That is, if for
instance you add c(1, 2, 3) to a six-element vector then you will
really add c(1, 2, 3, 1, 2, 3). If the length of the longer
vector is not a multiple of the shorter one, a warning is given.
As from R 1.4.0, any arithmetic operation involving a zero-length vector has a zero-length result.
One exception is that when adding vectors to matrices, a warning is not given if the lengths are incompatible.
propagation of names (first one wins, I think - also if it has no names?? —– first one *with names* wins, recycling causes shortest to lose names)
(matrix+matrix, dimensions must match. vector+matrix: first recycle, then check if dims fit, error if not)
Missing values in the statistical sense, that is, variables whose value
is not known, have the value NA. This should not be confused with
the missing property for a function argument that has not been
supplied (see Arguments).
As the elements of an atomic vector must be of the same type there are
multiple types of NA values. There is one case where this is
particularly important to the user. The default type of NA is
logical, unless coerced to some other type, so the appearance of
a missing value may trigger logical rather than numeric indexing (see
Indexing for details).
Numeric and logical calculations with NA generally return
NA. In cases where the result of the operation would be the same
for all possible values the NA could take, the operation may
return this value. In particular, `FALSE & NA' is FALSE,
`TRUE | NA' is TRUE. NA is not equal to any other
value or to itself; testing for NA is done using is.na.
However, an NA value will match another NA value in
match.
Numeric calculations whose result is undefined, such as `0/0',
produce the value NaN. This exists only in the double
type and for real or imaginary components of the complex type. The
function is.nan is provided to check specifically for
NaN, is.na also returns TRUE for NaN.
Coercing NaN to logical or integer type gives an NA of the
appropriate type, but coercion to character gives the string
"NaN". NaN values are incomparable so tests of equality
or collation involving NaN will result in NA. They are
regarded as matching any NaN value (and no other value, not even
NA) by match.
The NA of character type is as from R 1.5.0 distinct from the
string "NA". Programmers who need to specify an explicit string
NA should use `as.character(NA)' rather than "NA", or
set elements to NA using is.na<-.
As from R 2.5.0 there are constants NA_integer_,
NA_real_, NA_complex_ and NA_character_ which will
generate (in the parser) an NA value of the appropriate type,
and will be used in deparsing when it is not otherwise possible to
identify the type of an NA (and the control options ask
for this to be done).
There is no NA value for raw vectors.
R contains several constructs which allow access to individual
elements or subsets through indexing operations. In the case of the
basic vector types one can access the i-th element using x[i],
but there is also indexing of lists, matrices, and multi-dimensional
arrays. There are several forms of indexing in addition to indexing
with a single integer. Indexing can be used both to extract part of an
object and to replace parts of an object (or to add parts).
R has three basic indexing operators, with syntax displayed by the following examples
x[i]
x[i, j]
x[[i]]
x[[i, j]]
x$a
x$"a"
For vectors and matrices the [[ forms are rarely used, although
they have some slight semantic differences from the [ form (e.g.
it drops any names or dimnames attribute, and that partial
matching is used for character indices). When indexing
multi-dimensional structures with a single index, x[[i]] or
x[i] will return the ith sequential element of x.
For lists, one generally uses [[ to select any single element,
whereas [ returns a list of the selected elements.
The [[ form allows only a single element to be selected using
integer or character indices, whereas [ allows indexing by
vectors. Note though that for a list or other recursive object, the
index can be a vector and each element of the vector is applied in
turn to the list, the selected component, the selected component of
that component, and so on. The result is still a single element.
The form using $ applies to recursive objects such as lists and
pairlists. It allows only a literal character string or a symbol as the
index. That is, the index is not computable: for cases where you need
to evaluate an expression to find the index, use x[[expr]]. When
$ is applied to a non-recursive object the result used to be
always NULL: as from R 2.6.0 this is an error.
R allows some powerful constructions using vectors as indices. We
shall discuss indexing of simple vectors first. For simplicity, assume
that the expression is x[i]. Then the following possibilities
exist according to the type of i.
i must have the same sign. If
they are positive, the elements of x with those index numbers are
selected. If i contains negative elements, all elements except
those indicated are selected.
If i is positive and exceeds length(x) then the
corresponding selection is NA. A negative out of bounds value
for i causes an error.
A special case is the zero index, which has null effects: x[0] is
an empty vector and otherwise including zeros among positive or negative
indices has the same effect as if they were omitted.
i should generally have the same
length as x. If it is shorter, then its elements will be
recycled as discussed in Elementary arithmetic operations. If it
is longer, then x is conceptually extended with NAs. The
selected values of x are those for which i is TRUE.
i are matched against the
names attribute of x and the resulting integers are used. For
[[ and $ partial matching is used if exact matching fails,
so x$aa will match x$aabb if x does not a component
named "aa" and "aabb" is the only name which has prefix
"aa". For [[, partial matching can be controlled via the
exact argument which defaults to NA indicating that
partial matching is allowed, but should result in a warning when it
occurs. Setting exact to TRUE prevents partial matching
from occurring, a FALSE value allows it and does not issue any
warnings. Note that [ always requires an exact match. The string
"" is treated specially: it indicates `no name' and matches no
element (not even those without a name). Note that partial matching is
only used when extracting and not when replacing.
x[as.integer(i)].
The factor levels are never used. If so desired, use
x[as.character(i)] or a similar construction.
x[] returns x, but drops
“irrelevant” attributes from the result. Only names and in
multi-dimensional arrays dim and dimnames attributes are
retained.
integer(0).
Indexing with a missing (i.e. NA) value gives an NA
result. This rule applies also to the case of logical indexing,
i.e. the elements of x that have an NA selector in
i get included in the result, but their value will be NA.
Notice however, that there are different modes of NA—the
literal constant is of mode "logical", but it is frequently
automatically coerced to other types. One effect of this is that
x[NA] has the length of x, but x[c(1, NA)] has
length 2. That is because the rules for logical indices apply in the
former case, but those for integer indices in the latter.
Indexing with [ will also carry out the relevant subsetting of
any names attributes.
Subsetting multi-dimensional structures generally follows the same rules
as single-dimensional indexing for each index variable, with the
relevant component of dimnames taking the place of names.
A couple of special rules apply, though:
Normally, a structure is accessed using the number of indices
corresponding to its dimension. It is however also possible to use a
single index in which case the dim and dimnames attributes
are disregarded and the result is effectively that of c(m)[i].
Notice that m[1] is usually very different from m[1, ] or
m[, 1].
It is possible to use a matrix of integers as an index. In this case,
the number of columns of the matrix should match the number of
dimensions of the structure, and the result will be a vector with length
as the number of rows of the matrix. The following example shows how
to extract the elements m[1, 1] and m[2, 2] in one
operation.
> m <- matrix(1:4, 2)
> m
[,1] [,2]
[1,] 1 3
[2,] 2 4
> i <- matrix(c(1, 1, 2, 2), 2, byrow = TRUE)
> i
[,1] [,2]
[1,] 1 1
[2,] 2 2
> m[i]
[1] 1 4
Negative indices are not allowed in indexing matrices. NA and
zero values are allowed: rows in an index matrix containing a zero are
ignored, whereas rows containing an NA produce an NA in
the result.
Both in the case of using a single
index and in matrix indexing, a names attribute is used if
present, as had the structure been one-dimensional.
If an indexing operation causes the result to have one of its extents of
length one, as in selecting a single slice of a three-dimensional matrix
with (say) m[2, , ], the corresponding dimension is generally
dropped from the result. If a single-dimensional structure results, a
vector is obtained. This is occasionally undesirable and can be turned
off by adding the `drop = FALSE' to the indexing operation. Notice
that this is an additional argument to the [ function and doesn't
add to the index count. Hence the correct way of selecting the first
row of a matrix as a 1 by n matrix is m[1, , drop =
FALSE]. Forgetting to disable the dropping feature is a common cause
of failure in general subroutines where an index occasionally, but not
usually has length one. This rule still applies to a one-dimensional
array, where any subsetting will give a vector result unless `drop
= FALSE' is used.
Notice that vectors are distinct from one-dimensional arrays in that the
latter have dim and dimnames attributes (both of length
one). One-dimensional arrays are not easily obtained from subsetting
operations but they can be constructed explicitly and are returned by
table. This is sometimes useful because the elements of the
dimnames list may themselves be named, which is not the case for
the names attribute.
Some operations such as m[FALSE, ] result in structures in which
a dimension has zero extent. R generally tries to handle these
structures sensibly.
The operator [ is a generic function which allows class methods
to be added, and the $ and [[ operators likewise. Thus,
it is possible to have user-defined indexing operations for any
structure. Such a function, say [.foo is called with a set of
arguments of which the first is the structure being indexed and the rest
are the indices. In the case of $, the index argument is of mode
"symbol" even when using the x$"abc" form. It is
important to be aware that class methods do not necessarily behave in
the same way as the basic methods, for example with respect to partial
matching.
The most important example of a class method for [ is that used
for data frames. It is not be described in detail here (see the help
page for [.data.frame, but in broad terms, if two indices are
supplied (even if one is empty) it creates matrix-like indexing for a
structure that is basically a list of vectors of the same length. If a
single index is supplied, it is interpreted as indexing the list of
columns—in that case the drop argument is ignored, with a
warning.
The basic operators $ and [[ can be applied to
environments. Only character indices are allowed and no partial
matching is done.
Assignment to subsets of a structure is a special case of a general mechanism for complex assignment:
x[3:5] <- 13:15
The result of this commands is as if the following had been executed
`*tmp*` <- x
x <- "[<-"(`*tmp*`, 3:5, value=13:15)
rm(`*tmp*`)
Note that the index is first converted to a numeric index and then the
elements are replaced sequentially along the numeric index, as if a
for loop had been used. Any existing variable called
`*tmp*` will be overwritten and deleted, and this variable name
should not be used in code.
The same mechanism can be applied to functions other than [. The
replacement function has the same name with <- pasted on. Its last
argument, which must be called value, is the new value to be
assigned. For example,
names(x) <- c("a","b")
is equivalent to
`*tmp*` <- x
x <- "names<-"(`*tmp*`, value=c("a","b"))
rm(`*tmp*`)
Nesting of complex assignments is evaluated recursively
names(x)[3] <- "Three"
is equivalent to
`*tmp*` <- x
x <- "names<-"(`*tmp*`, value="[<-"(names(`*tmp*`), 3, value="Three"))
rm(`*tmp*`)
Complex assignments in the enclosing environment (using <<-) are
also permitted:
names(x)[3] <<- "Three"
is equivalent to
`*tmp*` <<- get(x, envir=parent.env(), inherits=TRUE)
names(`*tmp*`)[3] <- "Three"
x <<- `*tmp*`
rm(`*tmp*`)
and also to
`*tmp*` <- get(x,envir=parent.env(), inherits=TRUE)
x <<- "names<-"(`*tmp*`, value="[<-"(names(`*tmp*`), 3, value="Three"))
rm(`*tmp*`)
Only the target variable is evaluated in the enclosing environment, so
e<-c(a=1,b=2)
i<-1
local({
e <- c(A=10,B=11)
i <-2
e[i] <<- e[i]+1
})
uses the local value of i on both the LHS and RHS, and the local
value of e on the RHS of the superassignment statement. It sets
e in the outer environment to
a b
1 12
That is, the superassignment is equivalent to the four lines
`*tmp*` <- get(x,envir=parent.env(), inherits=TRUE)
`*tmp*`[i] <- e[i]+1
x <<- `*tmp*`
rm(`*tmp*`)
Similarly
x[is.na(x)] <<- 0
is equivalent to
`*tmp*` <- get(x,envir=parent.env(), inherits=TRUE)
`*tmp*`[is.na(x)] <- 0
x <<- `*tmp*`
rm(`*tmp*`)
and not to
`*tmp*` <- get(x,envir=parent.env(), inherits=TRUE)
`*tmp*`[is.na(`*tmp*`)] <- 0
x <<- `*tmp*`
rm(`*tmp*`)
These two candidate interpretations differ only if there is also a
local variable x. It is a good idea to avoid having a local
variable with the same name as the target variable of a
superassignment. As this case was handled incorrectly in versions
1.9.1 and earlier there must not be a serious need for such code.
Almost every programming language has a set of scoping rules, allowing the same name to be used for different objects. This allows, e.g., a local variable in a function to have the same name as a global object.
R uses a lexical scoping model, similar to languages like Pascal. However, R is a functional programming language and allows dynamic creation and manipulation of functions and language objects, and has additional features reflecting this fact.
The global environment is the root of the user workspace. An assignment operation from the command line will cause the relevant object to belong to the global environment. Its enclosing environment is the next environment on the search path, and so on back to the empty environment that is the enclosure of the base environment.
Every call to a function creates a frame which contains the local variables created in the function, and is evaluated in an environment, which in combination creates a new environment.
Notice the terminology: A frame is a set of variables, an environment is a nesting of frames (or equivalently: the innermost frame plus the enclosing environment).
Environments may be assigned to variables or be contained in other objects. However, notice that they are not standard objects—in particular, they are not copied on assignment.
A closure (mode "function") object will contain the environment
in which it is created as part of its definition (By default. The
environment can be manipulated using environment<-). When the
function is subsequently called, its
evaluation environment is created with the closure's environment as
enclosure. Notice that this is not
necessarily the environment of the caller!
Thus, when a variable is requested inside a function, it is first sought in the evaluation environment, then in the enclosure, the enclosure of the enclosure, etc.; once the global environment or the environment of a package is reached, the search continues up the search path to the environment of the base package. If the variable is not found there, the search will proceed next to the empty environment, and will fail.
Every time a function is invoked a new evaluation frame is created. At any point in time during the computation the currently active environments are accessible through the call stack. Each time a function is invoked a special construct called a context is created internally and is placed on a list of contexts. When a function has finished evaluating its context is removed from the call stack.
Making variables defined higher up the call stack available is called dynamic scope. The binding for a variable is then determined by the most recent (in time) definition of the variable. This contradicts the default scoping rules in R, which use the bindings in the environment in which the function was defined (lexical scope). Some functions, particularly those that use and manipulate model formulas, need to simulate dynamic scope by directly accessing the call stack.
Access to the call stack is provided through a family of functions which have names that start with `sys.'. They are listed briefly below.
sys.callsys.framesys.nframesys.functionsys.parentsys.callssys.framessys.parentssys.on.exitsys.statussys.frames, sys.parents and sys.calls.
parent.frameIn addition to the evaluation environment structure, R has a search path of environments which are searched for variables not found elsewhere. This is used for two things: packages of functions and attached user data.
The first element of the search path is the global environment and the
last is the base package. An Autoloads environment is used for
holding proxy objects that may be loaded on demand. Other environments
are inserted in the path using attach or library.
Packages which have a namespace have a different search path. When a search for an R object is started from an object in such a package, the package itself is searched first, then its imports, then the base namespace and finally the global environment and the rest of the regular search path. The effect is that references to other objects in the same package will be resolved to the package, and objects cannot be masked by objects of the same name in the global environment or in other packages.
While R can be very useful as a data analysis tool most users very quickly find themselves wanting to write their own functions. This is one of the real advantages of R. Users can program it and they can, if they want to, change the system level functions to functions that they find more appropriate.
R also provides facilities that make it easy to document any functions that you have created. See Writing R documentation.
The syntax for writing a function is
function ( arglist ) body
The first component of the function declaration is the keyword
function which indicates to R that you want to create a
function.
An argument list is a comma separated list of formal arguments. A formal argument can be a symbol, a statement of the form `symbol = expression', or the special formal argument `...'.
The body can be any valid R expression. Generally, the body is a group of expressions contained in curly braces (`{' and `}').
Generally
functions are assigned to symbols but they don't need to be.
The value returned by the call to function is a function. If
this is not given a name it is referred to as an
anonymous
function. Anonymous functions are most frequently used as arguments
other functions such as the apply family or outer.
Here is a simple function: echo <- function(x) print(x). So
echo is a function that takes a single argument and when
echo is invoked it prints its argument.
The formal arguments to the function define the variables whose values will be supplied at the time the function is invoked. The names of these arguments can be used within the function body where they obtain the value supplied at the time of function invocation.
Default values for arguments can be specified using the special form `name = expression'. In this case, if the user does not specify a value for the argument when the function is invoked the expression will be associated with the corresponding symbol. When a value is needed the expression is evaluated in the evaluation frame of the function.
Default behaviours can also be specified by using the function
missing. When missing is called with the
name of a formal
argument it returns TRUE if the formal argument was not matched
with any actual argument and has not been subsequently modified in the
body of the function. An argument that is missing will thus
have its default value, if any. The missing function does not
force evaluation of the argument.
The special type of argument `...' can contain any number of supplied arguments. It is used for a variety of purposes. It allows you to write a function that takes an arbitrary number of arguments. It can be used to absorb some arguments into an intermediate function which can then be extracted by functions called subsequently.
Functions are first class objects in R. They can be used anywhere that an R object is required. In particular they can be passed as arguments to functions and returned as values from functions. See Function objects for the details.
When a function is called or invoked a new evaluation frame is created. In this frame the formal arguments are matched with the supplied arguments according to the rules given in Argument matching. The statements in the body of the function are evaluated sequentially in this environment frame.
The enclosing frame of the evaluation frame is the environment frame
associated with the function being invoked. This may be different from
S. While many functions have .GlobalEnv as their environment
this does not have to be true and functions defined in packages with
namespaces (normally) have the package namespace as their environment.
This subsection applies to closures but not to primitive functions. The
latter typically ignore tags and do positional matching, but their help
pages should be consulted for exceptions, which include log,
round, signif, rep and seq.int.
The first thing that occurs in a function evaluation is the matching of formal to the actual or supplied arguments. This is done by a three-pass process:
f <- function(fumble,
fooey) fbody, then f(f = 1, fo = 2) is illegal, even though the
2nd actual argument only matches fooey. f(f = 1, fooey =
2) is legal though since the second argument matches exactly and
is removed from consideration for partial matching. If the formal
arguments contain `...' then partial matching is only applied to
arguments that precede it.
If any arguments remain unmatched an error is declared.
Argument matching is augmented by the functions match.arg,
match.call and match.fun.
Access to the partial matching algorithm used by R is via
pmatch.
One of the most important things to know about the evaluation of arguments to a function is that supplied arguments and default arguments are treated differently. The supplied arguments to a function are evaluated in the evaluation frame of the calling function. The default arguments to a function are evaluated in the evaluation frame of the function.
The semantics of invoking a function in R argument are call-by-value. In general, supplied arguments behave as if they are local variables initialized with the value supplied and the name of the corresponding formal argument. Changing the value of a supplied argument within a function will not affect the value of the variable in the calling frame.
R has a form of lazy evaluation of function arguments. Arguments are
not evaluated until needed. It is important to realize that in some
cases the argument will never be evaluated. Thus, it is bad style to
use arguments to functions to cause side-effects. While in C it is
common to use the form, foo(x = y) to invoke foo with the
value of y and simultaneously to assign the value of y to
x this same style should not be used in R. There is no
guarantee that the argument will ever be evaluated and hence the
assignment may not take place.
It is also worth noting that the effect of foo(x <- y) if the
argument is evaluated is to change the value of x in the calling
environment and not in the
evaluation environment of foo.
It is possible to access the actual (not default) expressions used as
arguments inside the function. The mechanism is implemented via
promises. When a
function is being evaluated the actual expression used as an argument is
stored in the promise together with a pointer to the environment the
function was called from. When (if) the argument is evaluated the
stored expression is evaluated in the environment that the function was
called from. Since only a pointer to the environment is used any
changes made to that environment will be in effect during this
evaluation. The resulting value is then also stored in a separate spot
in the promise. Subsequent evaluations retrieve this stored value (a
second evaluation is not carried out). Access to the unevaluated
expression is also available using substitute.
When a function is called, each formal argument is assigned a promise in the local environment of the call with the expression slot containing the actual argument (if it exists) and the environment slot containing the environment of the caller. If no actual argument for a formal argument is given in the call and there is a default expression, it is similarly assigned to the expression slot of the formal argument, but with the environment set to the local environment.
The process of filling the value slot of a promise by evaluating the contents of the expression slot in the promises environment is called forcing the promise. A promise will only be forced once, the value slot content being used directly later on.
A promise is forced when its value is needed. This usually happens
inside internal
functions, but a promise can also be forced by direct evaluation of the
promise itself. This is occasionally useful when a default expression
depends on the value of another formal argument or other variable in the
local environment. This is seen in the following example where the lone
label ensures that the label is based on the value of x
before it is changed in the next line.
function(x, label = deparse(x)) {
label
x <- x + 1
print(label)
}
The expression slot of a promise can itself involve other promises. This happens whenever an unevaluated argument is passed as an argument to another function. When forcing a promise, other promises in its expression will also be forced recursively as they are evaluated.
Scope or the scoping rules are simply the set of rules used by the evaluator to find a value for a symbol. Every computer language has a set of such rules. In R the rules are fairly simple but there do exist mechanisms for subverting the usual, or default rules.
R adheres to a set of rules that are called lexical scope. This means the variable bindings in effect at the time the expression was created are used to provide values for any unbound symbols in the expression.
Most of the interesting properties of scope are involved with evaluating functions and we concentrate on this issue. A symbol can be either bound or unbound. All of the formal arguments to a function provide bound symbols in the body of the function. Any other symbols in the body of the function are either local variables or unbound variables. A local variable is one that is defined within the function. Because R has no formal definition of variables, they are simply used as needed, it can be difficult to determine whether a variable is local or not. Local variables must first be defined, this is typically done by having them on the left-hand side of an assignment.
During the evaluation process if an unbound symbol is detected then R attempts to find a value for it. The scoping rules determine how this process proceeds. In R the environment of the function is searched first, then its enclosure and so on until the global environment is reached.
The global environment heads a search list of environments that are searched sequentially for a matching symbol. The value of the first match is then used.
When this set of rules is combined with the fact that functions can be returned as values from other functions then some rather nice, but at first glance peculiar, properties obtain.
A simple example:
f <- function() {
y <- 10
g <- function(x) x + y
return(g)
}
h <- f()
h(3)
A rather interesting question is what happens when h is
evaluated. To describe this we need a bit more notation. Within a
function body variables can be bound, local or unbound. The bound
variables are those that match the formal arguments to the function.
The local variables are those that were created or defined within the
function body. The unbound variables are those that are neither local
nor bound. When a function body is evaluated there is no problem
determining values for local variables or for bound variables. Scoping
rules determine how the language will find values for the unbound
variables.
When h(3) is evaluated we see that its body is that of
g. Within that body x is bound to the formal argument
and y is unbound. In a language with
lexical scope x will be associated with the value 3 and
y with the value 10 local to f so h(3) should return the value 13.
In R this is indeed what happens.
In S, because of the different scoping rules one will get an error
indicating that y is not found, unless there is a variable
y in your workspace in which case its value will be used.
Object-oriented programming is a style of programming that has become popular in recent years. Much of the popularity comes from the fact that it makes it easier to write and maintain complicated systems. It does this through several different mechanisms.
Central to any object-oriented language are the concepts of class and of methods. A class is a definition of an object. Typically a class contains several slots that are used to hold class-specific information. An object in the language must be an instance of some class. Programming is based on objects or instances of classes.
Computations are carried out via methods. Methods are basically functions that are specialized to carry out specific calculations on objects, usually of a specific class. This is what makes the language object oriented. In R, generic functions are used to determine the appropriate method. The generic function is responsible for determining the class of its argument(s) and uses that information to select the appropriate method.
Another feature of most object-oriented languages is the concept of inheritance. In most programming problems there are usually many objects that are related to one another. The programming is considerably simplified if some components can be reused.
If a class inherits from another class then generally it gets all the slots in the parent class and can extend it by adding new slots. On method dispatching (via the generic functions) if a method for the class does not exist then a method for the parent is sought.
In this chapter we discuss how this general strategy has been implemented in R and discuss some of the limitations within the current design. One of the advantages that most object systems impart is greater consistency. This is achieved via the rules that are checked by the compiler or interpreter. Unfortunately because of the way that the object system is incorporated into R this advantage does not obtain. Users are cautioned to use the object system in a straightforward manner. While it is possible to perform some rather interesting feats these tend to lead to obfuscated code and may depend on implementation details that will not be carried forward.
The greatest use of object oriented programming in R is through
print methods, summary methods and plot methods.
These methods allow us to have one generic
function call, plot
say, that dispatches on the type of its argument and calls a plotting
function that is specific to the data supplied.
In order to make the concepts clear we will consider the implementation of a small system designed to teach students about probability. In this system the objects are probability functions and the methods we will consider are methods for finding moments and for plotting. Probabilities can always be represented in terms of the cumulative distribution function but can often be represented in other ways. For example as a density, when it exists or as a moment generating function when it exists.
Rather than having a full-fledged
object-oriented system R has a
class system and a mechanism for dispatching based on the class of an
object. The dispatch mechanism for interpreted code relies on four
special objects that are stored in the evaluation frame. These special
objects are .Generic, .Class, .Method and
.Group. There is a separate dispatch mechanism used for internal
functions and types that will be discussed elsewhere.
The class system is facilitated through the class attribute.
This attribute is a list of class names. So to create an object of
class "foo" one simply attaches a class attribute with the string
`"foo"' in it. Thus, virtually anything can be turned in to an
object of class "foo".
The object system makes use of
generic functions via two
dispatching functions, UseMethod and NextMethod. The
typical use of the object system is to begin by calling a generic
function. This is typically a very simple function and consists of a
single line of code. The system function mean is just such a
function,
> mean
function (x, ...)
UseMethod("mean")
When mean is called it can have any number of arguments but its
first argument is special and the class of that first argument is used
to determine which method should be called. The variable .Class
is set to the class attribute of x, .Generic is set to the
string "mean" and a search is made for the correct method to
invoke. The class attributes of any other arguments to mean are
ignored.
Suppose that x had a class attribute that contained "foo"
and "bar", in that order. Then R would first search for a
function called mean.foo and if it did not find one it would then
search for a function mean.bar and if that search was also
unsuccessful then a final search for mean.default would be made.
If the last search is unsuccessful R reports an error. It is a good
idea to always write a default method. Note that the functions
mean.foo etc. are referred to, in this context, as methods.
NextMethod provides another mechanism for dispatching. A
function may have a call to NextMethod anywhere in it. The
determination of which method should then be invoked is based primarily
on the current values of .Class and .Generic. This is
somewhat problematic since the method is really an ordinary function and
users may call it directly. If they do so then there will be no values
for .Generic or .Class.
If a method is invoked directly and it contains a call to
NextMethod then the first argument to NextMethod is used
to determine the
generic function. An error is signalled if this
argument has not been supplied; it is therefore a good idea to always
supply this argument.
In the case that a method is invoked directly the class attribute of the
first argument to the method is used as the value of .Class.
Methods themselves employ NextMethod to provide a form of
inheritance. Commonly a specific method performs a few operations to
set up the data and then it calls the next appropriate method through a
call to NextMethod.
Consider the following simple example. A point in two-dimensional
Euclidean space can be specified by its Cartesian (x-y) or polar
(r-theta) coordinates. Hence, to store information about the location
of the point, we could define two classes, "xypoint" and
"rthetapoint". All the `xypoint' data structures are lists with
an x-component and a y-component. All `rthetapoint' objects are lists
with an r-component and a theta-component.
Now, suppose we want to get the x-position from either type of object.
This can easily be achieved through
generic functions. We define the
generic function xpos as follows.
xpos <- function(x, ...)
UseMethod("xpos")
Now we can define methods:
xpos.xypoint <- function(x) x$x
xpos.rthetapoint <- function(x) x$r * cos(x$theta)
The user simply calls the function xpos with either
representation as the argument. The internal dispatching method finds
the class of the object and calls the appropriate methods.
It is pretty easy to add other representations. One need not write a new generic function only the methods. This makes it easy to add to existing systems since the user is only responsible for dealing with the new representation and not with any of the existing representations.
The bulk of the uses of this methodology are to provided specialized
printing for objects of different types; there are about 40 methods for
print.
The class attribute of an object can have several elements. When a
generic function is called the first inheritance is mainly handled
through NextMethod. NextMethod determines the method
currently being evaluated, finds the next class from th
FIXME: something is missing here
Generic functions should consist of a single statement. They should
usually be of the form foo <- function(x, ...) UseMethod("foo",
x). When UseMethod is called, it determines the appropriate
method and then that method is invoked with the same arguments, in
the same order as the call to the generic, as if the call had been made
directly to the method.
In order to determine the correct method the class attribute of the
first argument to the generic is obtained and used to find the correct
method. The
name of the generic function is combined with the first element of the
class attribute into the form, generic.class and a
function with that name is sought. If the function is found then it is
used. If no such function is found then the second element of the class
attribute is used, and so on until all the elements of the class
attribute have been exhausted. If no method has been found at that
point then the method generic.default is used. If
the first argument to the generic function has no class attribute then
generic.default is used. Since the introduction of
namespaces the methods may not be accessible by their names
(i.e. get("generic.class") may fail), but they will
be accessible by getS3method("generic","class").
Any object can have a class attribute. This attribute can have
any number of elements. Each of these is a string that defines a class.
When a generic function is invoked the class of its first argument is
examined.
UseMethod is a special function and it behaves differently from
other function calls. The syntax of a call to it is
UseMethod(generic, object), where generic is
the name of the generic function, object is the object used to
determine which method should be chosen. UseMethod can only be
called from inside a function. The S definition of UseMethod
contains an additional argument of `...' that can affect the
default values for subsequent methods. R produces a warning if there
are more than two arguments to UseMethod and ignores these
additional arguments.
UseMethod changes the evaluation model in two ways. First, when
it is invoked it determines the next method (function) to be called. It
then invokes that function using the current evaluation
environment;
this process will be described shortly. The second way in which
UseMethod changes the evaluation environment is that it does not
return control to the calling function. This means, that any statements
after a call to UseMethod are guaranteed not to be executed.
When UseMethod is invoked the generic function is the specified
value in the call to UseMethod. The object to dispatch on is
either the supplied second argument or the first argument to the current
function. The class of the argument is determined and the first element
of it is combined with the name of the generic to determine the
appropriate method. So, if the generic had name foo and the
class of the object is "bar", then R will search for a method
named foo.bar. If no such method exists then the inheritance
mechanism described above is used to locate an appropriate method.
Once a method has been determined R invokes it in a special way.
Rather than creating a new evaluation
environment R uses the
environment of the current function call (the call to the generic). Any
assignments or evaluations that were made before the call to
UseMethod will be in effect. The arguments that were used in the
call to the generic are rematched to the formal arguments of the
selected method.
When the method is invoked it is called with arguments that are the same in number and have the same names as in the call to the generic. They are matched to the arguments of the method according to the standard R rules for argument matching. However the object, i.e. the first argument has been evaluated.
The call to UseMethod has the effect of placing some special
objects in the evaluation frame. They are .Class,
.Generic and .Method. These special objects are used to
by R to handle the method dispatch and inheritance. .Class is
the class of the object, .Generic is the name of the generic
function and .Method is the name of the method currently being
invoked. If the method was invoked through one of the internal
interfaces then there may also be an object called .Group. This
will be described in Section Group methods. After the initial
call to UseMethod these special variables, not the object itself,
control the selection of subsequent methods.
The body of the method is then evaluated in the standard fashion. In
particular variable look-up in the body follows the rules for the
method. So if the method has an associated environment then that is
used. In effect we have replaced the call to the generic by a call to
the method. Any local
assignments in the frame of the generic will be
carried forward into the call to the method. Use of this feature
is discouraged. It is important to realize that control will never
return to the generic and hence any expressions after a call to
UseMethod will never be executed.
Any arguments to the generic that were evaluated prior to the call to
UseMethod remain evaluated.
The arguments in the call to the generic are rematched with the arguments for the method using the standard argument matching mechanism. The first argument, i.e. the object, will have been evaluated.
If the first argument to UseMethod is not supplied it is assumed
to be the name of the current function. If two arguments are supplied
to UseMethod then the first is the name of the method and the
second is assumed to be the object that will be dispatched on. It is
evaluated so that the required method can be determined. In this case
the first argument in the call to the generic is not evaluated and is
discarded. There is no way to change the other arguments in the call to
the method these remain as they were in the call to the generic. This
is in contrast to NextMethod where the arguments in the call to
the next method can be altered.
NextMethod is used to provide a simple inheritance mechanism.
Methods invoked as a result of a call to NextMethod behave as if
they had been invoked from the previous method. The arguments to the
inherited method are in the same order and have the same names as the
call to the current method. This means that they are the same as for
the call to the generic. However, the expressions for the arguments are
the names of the corresponding formal arguments of the current method.
Thus the arguments will have values that correspond to their value at
the time NextMethod was invoked.
Unevaluated arguments remain unevaluated. Missing arguments remain missing.
The syntax for a call to NextMethod is NextMethod(generic,
object, ...). If the generic is not supplied the value of
.Generic is used. If the object is not supplied the first
argument in the call to the current method is used. Values in the
`...' argument are used to modify the arguments of the next method.
It is important to realize that the choice of the next method depends on
the current values of .Generic and .Class and not on the
object. So changing the object in a call to NextMethod affects
the arguments received by the next method but does not affect the choice
of the next method.
Methods can be called directly. If they are then there will be no
.Generic, .Class or .Method. In this case the
generic argument of NextMethod must be specified. The
value of .Class is taken to be the class attribute of the object
which is the first argument to the current function. The value of
.Method is the name of the current function. These choices for
default values ensure that the behaviour of a method doesn't change
depending on whether it is called directly or via a call to a generic.
An issue for discussion is the behaviour of the `...' argument to
NextMethod. The White Book describes the behaviour as follows:
- named arguments replace the corresponding arguments in the call to the current method. Unnamed arguments go at the start of the argument list.
What I would like to do is:
-first do the argument matching for NextMethod; -if the object or generic are changed fine -first if a named list element matches an argument (named or not) the list value replaces the argument value. - the first unnamed list element
Values for lookup: Class: comes first from .Class, second from the first argument to the method and last from the object specified in the call to NextMethod
Generic: comes first from .Generic, if nothing then from the first argument to the method and if it's still missing from the call to NextMethod
Method: this should just be the current function name.
For several types of
internal functions R provides a dispatching
mechanism for operators. This means that operators such as == or
< can have their behaviour modified for members of special
classes. The functions and operators have been grouped into three
categories and group methods can be written for each of these
categories. There is currently no mechanism to add groups. It is
possible to write methods specific to any function within a group.
The following table lists the functions for the different Groups.
+, -, *, /, ^, < , >,
<=, >=, !=, ==, %%, %/%,
&, |, !
For operators in the Ops group a special method is invoked if the two operands taken together suggest a single method. Specifically, if both operands correspond to the same method or if one operand corresponds to a method that takes precedence over that of the other operand. If they do not suggest a single method then the default method is used. Either a group method or a class method dominates if the other operand has no corresponding method. A class method dominates a group method.
When the group is Ops the special variable .Method is a string
vector with two elements. The elements of .Method are set to the
name of the method if the corresponding argument is a member of the
class that was used to determine the method. Otherwise the
corresponding element of .Method is set to the zero length
string, "".
Users can easily write their own methods and generic functions. A
generic function is simply a function with a call to UseMethod.
A method is simply a function that has been invoked via method dispatch.
This can be as a result of a call to either UseMethod or
NextMethod.
It is worth remembering that methods can be called directly. That means
that they can be entered without a call to UseMethod having been
made and hence the special variables .Generic, .Class and
.Method will not have been instantiated. In that case the
default rules detailed above will be used to determine these.
The most common use of
generic functions is to provide print and
summary methods for statistical objects, generally the output of
some model fitting process. To do this, each model attaches a class
attribute to its output and then provides a special method that takes
that output and provides a nice readable version of it. The user then
needs only remember that print or summary will provide
nice output for the results of any analysis.
R belongs to a class of programming languages in which subroutines have the ability to modify or construct other subroutines and evaluate the result as an integral part of the language itself. This is similar to Lisp and Scheme and other languages of the “functional programming” variety, but in contrast to FORTRAN and the ALGOL family. The Lisp family takes this feature to the extreme by the “everything is a list” paradigm in which there is no distinction between programs and data.
R presents a friendlier interface to programming than Lisp does, at least to someone used to mathematical formulas and C-like control structures, but the engine is really very Lisp-like. R allows direct access to parsed expressions and functions and allows you to alter and subsequently execute them, or create entirely new functions from scratch.
There is a number of standard applications of this facility, such as
calculation of analytical derivatives of expressions, or the generation
of polynomial functions from a vector of coefficients. However, there
are also uses that are much more fundamental to the workings of the
interpreted part of R. Some of these are essential to the reuse of
functions as components in other functions, as the (admittedly not very
pretty) calls to model.frame that are constructed in several
modeling and plotting routines. Other uses simply allow elegant
interfaces to useful functionality. As an example, consider the
curve function, which allows you to draw the graph of a function
given as an expression like sin(x) or the facilities for plotting
mathematical expressions.
In this chapter, we give an introduction to the set of facilities that are available for computing on the language.
There are three kinds of language objects that are available for
modification, calls, expressions, and functions. At this point, we
shall concentrate on the call objects. These are sometimes referred to
as “unevaluated expressions”, although this terminology is somewhat
confusing. The most direct method of obtaining a call object is to use
quote with an expression argument, e.g.,
> e1 <- quote(2 + 2)
> e2 <- quote(plot(x, y))
The arguments are not evaluated, the result is simply the parsed
argument. The objects e1 and e2 may be evaluated later
using eval, or simply manipulated as data. It is perhaps most
immediately obvious why the e2 object has mode "call",
since it involves a call to the plot function with some
arguments. However, e1 actually has exactly the same structure
as a call to the binary operator + with two arguments, a fact
that gets clearly displayed by the following
> quote("+"(2, 2))
2 + 2
The components of a call object are accessed using a list-like syntax,
and may in fact be converted to and from lists using as.list and
as.call
> e2[[1]]
plot
> e2[[2]]
x
> e2[[3]]
y
When keyword argument matching is used, the keywords can be used as list tags:
> e3 <- quote(plot(x = age, y = weight))
> e3$x
age
> e3$y
weight
All the components of the call object have mode "name" in the
preceding examples. This is true for identifiers in calls, but the
components of a call can also be constants—which can be of any type,
although the first component had better be a function if the call is to
be evaluated successfully—or other call objects, corresponding to
subexpressions. Objects of mode
name can be constructed from character
strings using as.name, so one might modify the e2 object
as follows
> e2[[1]] <- as.name("+")
> e2
x + y
To illustrate the fact that subexpressions are simply components that are themselves calls, consider
> e1[[2]] <- e2
> e1
x + y + 2
All grouping parentheses in input are preserved in parsed expressions.
They are represented as a function call with one argument, so that
4 - (2 - 2) becomes "-"(4, "(" ("-"(2, 2))) in prefix
notation. In evaluations, the `(' operator just returns its
argument.
This is a bit unfortunate, but it is not easy to write a parser/deparser combination that both preserves user input, stores it in minimal form and ensures that parsing a deparsed expression gives the same expression back.
As it happens, R's parser is not perfectly invertible, nor is its deparser, as the following examples show
> deparse(quote(c(1, 2)))
[1] "c(1, 2)"
> deparse(1:2)
[1] "c(1, 2)"
> quote("-"(2, 2))
2 - 2
> quote(2 - 2)
2 - 2
Deparsed expressions should, however, evaluate to an equivalent value to the original expression (up to rounding error).
...internal storage of flow control constructs...note Splus incompatibility...
It is in fact not often that one wants to modify the innards of an
expression like in the previous section. More frequently, one wants to
simply get at an expression in order to deparse it and use it for
labeling plots, for instance. An example of this is seen at the
beginning of plot.default:
xlabel <- if (!missing(x))
deparse(substitute(x))
This causes the variable or expression given as the x argument to
plot to be used for labeling the x-axis later on.
The function used to achieve this is substitute which takes the
expression x and substitutes the expression that was passed
through the formal argument x. Notice that for this to happen,
x must carry information about the expression that creates its
value. This is related to the
lazy evaluation scheme of R
(see Promise objects). A formal argument is really a
promise, an object with three slots, one for the expression that
defines it, one for the environment in which to evaluate that expression,
and one for the value of that expression once evaluated. substitute
will recognize a promise variable and substitute the value of its
expression slot. If substitute is invoked inside a function, the
local variables of the function are also subject to substitution.
The argument to substitute does not have to be a simple
identifier, it can be an expression involving several variables and
substitution will occur for each of these. Also, substitute has
an additional argument which can be an environment or a list in which
the variables are looked up. For example:
> substitute(a + b, list(a = 1, b = quote(x)))
1 + x
Notice that quoting was necessary to substitute the x. This kind
of construction comes in handy in connection with the facilities for
putting math expression in graphs, as the following case shows
> plot(0)
> for (i in 1:4)
+ text(1, 0.2 * i,
+ substitute(x[ix] == y, list(ix = i, y = pnorm(i))))
It is important to realize that the substitutions are purely lexical;
there is no checking that the resulting call objects make sense if they
are evaluated. substitute(x <- x + 1, list(x = 2)) will happily
return 2 <- 2 + 1. However, some parts of R make up their own
rules for what makes sense and what does not and might actually have a
use for such ill-formed expressions. For example, using the “math in
graphs” feature often involves constructions that are syntactically
correct, but which would be meaningless to evaluate, like
`{}>=40*" years"'.
Substitute will not evaluate its first argument. This leads to the
puzzle of how to do substitutions on an object that is contained in a
variable. The solution is to use substitute once more, like this
> expr <- quote(x + y)
> substitute(substitute(e, list(x = 3)), list(e = expr))
substitute(x + y, list(x = 3))
> eval(substitute(substitute(e, list(x = 3)), list(e = expr)))
3 + y
The exact rules for substitutions are as follows: Each
symbol in the
parse tree for the first is matched against the second argument, which
can be a tagged list or an environment frame. If it is a simple local
object, its value is inserted, except if matching against the
global environment. If it is a promise (usually a function argument),
the promise expression is substituted. If the symbol is not matched, it
is left untouched. The special exception for substituting at the top
level is admittedly peculiar. It has been inherited from S and the
rationale is most likely that there is no control over which variables
might be bound at that level so that it would be better to just make
substitute act as quote.
The rule of promise substitution is slightly different from that of
S if the local variable is modified before substitute is
used. R will then use the new value of the variable, whereas S
will unconditionally use the argument expression—unless it was a
constant, which has the curious consequence that f((1)) may be
very different from f(1) in S. The R rule is considerably
cleaner, although it does have consequences in connection with
lazy
evaluation that comes as a surprise to some. Consider
logplot <- function(y, ylab = deparse(substitute(y))) {
y <- log(y)
plot(y, ylab = ylab)
}
This looks straightforward, but one will discover that the y label
becomes an ugly c(...) expression. It happens because the rules
of lazy evaluation causes the evaluation of the ylab expression
to happen after y has been modified. The solution is to
force ylab to be evaluated first, i.e.,
logplot <- function(y, ylab = deparse(substitute(y))) {
ylab
y <- log(y)
plot(y, ylab = ylab)
}
Notice that one should not use eval(ylab) in this situation. If
ylab is a language or expression object, then that would cause
the object to be evaluated as well, which would not at all be desirable
if a math expression like quote(log[e](y)) was being passed.
A variant on substitute is bquote, which is used to replace some subexpressions with their values. The example from above
> plot(0)
> for (i in 1:4)
+ text(1, 0.2 * i,
+ substitute(x[ix] == y, list(ix = i, y = pnorm(i))))
could be written more compactly as
plot(0)
for(i in 1:4)
text(1, 0.2*i, bquote( x[.(i)] == .(pnorm(i)) ))
The expression is quoted except for the contents of .()
subexpressions, which are replaced with their values. There is an
optional argument to compute the values in a different
environment. The syntax for bquote is borrowed from the LISP
backquote macro.
The eval function was introduced earlier in this chapter as a
means of evaluating call objects. However, this is not the full story.
It is also possible to specify the
environment in which the evaluation
is to take place. By default this is the evaluation frame from which
eval is called, but quite frequently it needs to be set to
something else.
Very often, the relevant evaluation frame is that of the parent of the
current frame (cf. ???). In particular, when the object to evaluate
is the result of a substitute operation of the function
arguments, it will contain variables that make sense to the caller only
(notice that there is no reason to expect that the variables of the
caller are in the
lexical scope of the callee). Since evaluation in the
parent frame occurs frequently, an eval.parent function exists as
a shorthand for eval(expr, sys.frame(sys.parent())).
Another case that occurs frequently is evaluation in a list or a data
frame. For instance, this happens in connection with the
model.frame function when a data argument is given.
Generally, the terms of the model formula need to be evaluated in
data, but they may occasionally also contain references to items
in the caller of model.frame. This is sometimes useful in
connection with simulation studies. So for this purpose one needs not
only to evaluate an expression in a list, but also to specify an
enclosure into which the search continues if the variable is not in the
list. Hence, the call has the form
eval(expr, data, sys.frame(sys.parent()))
Notice that evaluation in a given environment may actually change that environment, most obviously in cases involving the assignment operator, such as
eval(quote(total <- 0), environment(robert$balance)) # rob Rob
This is also true when evaluating in lists, but the original list does not change because one is really working on a copy.
Objects of mode "expression" are defined in Expression objects. They are very similar to lists of call objects.
> ex <- expression(2 + 2, 3 + 4)
> ex[[1]]
2 + 2
> ex[[2]]
3 + 4
> eval(ex)
[1] 7
Notice that evaluating an expression object evaluates each call in turn,
but the final value is that of the last call. In this respect it
behaves almost identically to the compound language object
quote({2 + 2; 3 + 4}). However, there is a subtle difference:
Call objects are indistinguishable from subexpressions in a parse tree.
This means that they are automatically evaluated in the same way a
subexpression would be. Expression objects can be recognized during
evaluation and in a sense retain their quotedness. The evaluator will
not evaluate an expression object recursively, only when it is passed
directly to eval function as above. The difference can be seen
like this:
> eval(substitute(mode(x), list(x = quote(2 + 2))))
[1] "numeric"
> eval(substitute(mode(x), list(x = expression(2 + 2))))
[1] "expression"
The deparser represents an expression object by the call that creates it. This is similar to the way it handles numerical vectors and several other objects that do not have a specific external representation. However, it does lead to the following bit of confusion:
> e <- quote(expression(2 + 2))
> e
expression(2 + 2)
> mode(e)
[1] "call"
> ee <- expression(2 + 2)
> ee
expression(2 + 2)
> mode(ee)
[1] "expression"
I.e., e and ee look identical when printed, but one is a
call that generates an expression object and the other is the object
itself.
It is possible for a
function to find out how it has been called by
looking at the result of sys.call as in the following example of
a function that simply returns its own call:
> f <- function(x, y, ...) sys.call()
> f(y = 1, 2, z = 3, 4)
f(y = 1, 2, z = 3, 4)
However, this is not really useful except for debugging because it
requires the function to keep track of argument matching in order to
interpret the call. For instance, it must be able to see that the 2nd
actual argument gets matched to the first formal one (x in the
above example).
More often one requires the call with all actual arguments bound to the
corresponding formals. To this end, the function match.call is
used. Here's a variant of the preceding example, a function that
returns its own call with arguments matched
> f <- function(x, y, ...) match.call()
> f(y = 1, 2, z = 3, 4)
f(x = 2, y = 1, z = 3, 4)
Notice that the second argument now gets matched to x and appears
in the corresponding position in the result.
The primary use of this technique is to call another function with the
same arguments, possibly deleting some and adding others. A typical
application is seen at the start of the lm function:
mf <- cl <- match.call()
mf$singular.ok <- mf$model <- mf$method <- NULL
mf$x <- mf$y <- mf$qr <- mf$contrasts <- NULL
mf$drop.unused.levels <- TRUE
mf[[1]] <- as.name("model.frame")
mf <- eval(mf, sys.frame(sys.parent()))
Notice that the resulting call is
evaluated in the parent frame, in
which one can be certain that the involved expressions make sense. The
call can be treated as a list object where the first element is the name
of the function and the remaining elements are the actual argument
expressions, with the corresponding formal argument names as tags.
Thus, the technique to eliminate undesired arguments is to assign
NULL, as seen in lines 2 and 3, and to add an argument one uses
tagged list
assignment (here to pass drop.unused.levels = TRUE)
as in line 4. To change the name of the function called, assign to the
first element of the list and make sure that the value is a name, either
using the as.name("model.frame") construction here or
quote(model.frame).
The match.call function has an expand.dots argument which
is a switch which if set to FALSE lets all `...' arguments
be collected as a single argument with the tag `...'.
> f <- function(x, y, ...) match.call(expand.dots = FALSE)
> f(y = 1, 2, z = 3, 4)
f(x = 2, y = 1, ... = list(z = 3, 4))
The `...' argument is a list (a pairlist to be precise), not a call
to list like it is in S:
> e1 <- f(y = 1, 2, z = 3, 4)$...
> e1
$z
[1] 3
[[2]]
[1] 4
One reason for using this form of match.call is simply to get rid
of any `...' arguments in order not to be passing unspecified
arguments on to functions that may not know them. Here's an example
paraphrased from plot.formula:
m <- match.call(expand.dots = FALSE)
m$... <- NULL
m[[1]] <- "model.frame"
A more elaborate application is in update.default where a set of
optional extra arguments can add to, replace, or cancel those of the
original call:
extras <- match.call(expand.dots = FALSE)$...
if (length(extras) > 0) {
existing <- !is.na(match(names(extras), names(call)))
for (a in names(extras)[existing]) call[[a]] <- extras[[a]]
if (any(!existing)) {
call <- c(as.list(call), extras[!existing])
call <- as.call(call)
}
}
Notice that care is taken to modify existing arguments individually in
case extras[[a]] == NULL. Concatenation does not work on call
objects without the coercion as shown; this is arguably a bug.
Two further functions exist for the construction of function calls,
namely call and do.call.
The function call allows creation of a call object from the
function name and the list of arguments
> x <- 10.5
> call("round", x)
round(10.5)
As seen, the value of x rather than the
symbol is inserted in the
call, so it is distinctly different from round(x). The form is
used rather rarely, but is occasionally useful where the name of a
function is available as a character variable.
The function do.call is related, but evaluates the call immediately
and takes the arguments from an object of mode "list" containing
all the arguments. A natural use of this is when one wants to apply a
function like cbind to all elements of a list or data frame.
is.na.data.frame <- function (x) {
y <- do.call("cbind", lapply(x, "is.na"))
rownames(y) <- row.names(x)
y
}
Other uses include variations over constructions like do.call("f",
list(...)). However, one should be aware that this involves evaluation
of the arguments before the actual function call, which may defeat
aspects of lazy evaluation and argument substitution in the function
itself. A similar remark applies to the call function.
It is often useful to be able to manipulate the components of a function or closure. R provides a set of interface functions for this purpose.
bodyformalspairlist.
environmentbody<-formals<-environment<-It is also possible to alter the bindings of different variables in the
environment of the function, using code along the lines of evalq(x
<- 5, environment(f)).
It is also possible to convert a
function to a list using
as.list. The result is the concatenation of the list of formal
arguments with the function body. Conversely such a list can be
converted to a function using as.function. This functionality is
mainly included for S compatibility. Notice that environment
information is lost when as.list is used, whereas
as.function has an argument that allows the environment to be
set.
Access to the operating system shell is via the R function
system.
The details will differ by platform (see the on-line help), and about
all that can safely be assumed is that the first argument will be a
string command that will be passed for execution (not necessarily
by a shell) and the second argument will be internal which if
true will collect the output of the command into an R character
vector.
The functions system.time
and proc.time
are available for timing (although the information available may be
limited on non-Unix-like platforms).
Information from the operating system environment can be accessed and manipulated with
Sys.getenvOS environment variables Sys.putenvSys.getlocaleSystem locale Sys.putlocaleSys.localeconvSys.timeCurrent time Sys.timezoneTime zone
A uniform set of file access functions is provided on all platforms:
There are also functions for manipulating file names and paths in a platform-independent way.
basenameFile name without directory dirnameDirectory name file.pathConstruct path to file path.expandExpand ~in Unix path
See System and foreign language interfaces for the details of adding functionality to R via compiled code.
Functions .C and .Fortran provide a standard interface to
compiled code that has been linked into R, either at build time or
via dyn.load. They are primarily intended for compiled C and
FORTRAN code respectively, but the .C function can be used with
other languages which can generate C interfaces, for example C++.
Functions .Call and .External provide interfaces which allow
compiled code (primarily compiled C code) to manipulate R objects.
The .Internal and .Primitive interfaces are used to call
C code compiled into R at build time.
See .Internal and .Primitive.
The exception handling facilities in R are provided through two
mechanisms. Functions such as stop or warning can be
called directly or options such as "warn" can be used to control
the handling of problems.
A call to stop halts the evaluation of the current expression,
prints the message argument and returns execution to top-level.
The function warning takes a single argument that is a character
string. The behaviour of a call to warning depends on the value
of the option "warn". If "warn" is negative warnings are
ignored. If it is zero, they are stored and printed after the top-level
function has completed. If it is one, they are printed as they occur
and if it is 2 (or larger) warnings are turned into errors.
If "warn" is zero (the default), a variable last.warning
is created and the messages associated with each call to warning
are stored, sequentially, in this vector. If there are fewer than 10
warnings they are printed after the function has finished evaluating.
If there are more than 10 then a message indicating how many warnings
occurred is printed. In either case last.warning contains the
vector of messages, and warnings provides a way to access and
print it.
A function can insert a call to on.exit at any point in the body
of a function. The effect of a call to on.exit is to store the
value of the body so that it will be executed when the function exits.
This allows the function to change some system parameters and to ensure
that they are reset to appropriate values when the function is finished.
The on.exit is guaranteed to be executed when the function exits
either directly or as the result of a warning.
An error in the evaluation of the on.exit code causes an
immediate jump to top-level without further processing of the
on.exit code.
on.exit takes a single argument which is an expression to be
evaluated when the function is exited.
There are a number of options variables that can be used to
control how R handles errors and warnings. The are listed in the
table below.
Expressions installed by options("error") are evaluated before
calls to on.exit are carried out.
One can use options(error = expression(q("yes"))) to get R to
quit when an error has been signalled. In this case an error will cause
R to shut down and the global environment will be saved.
Debugging code has always been a bit of an art. R provides several tools that help users find problems in their code. These tools halt execution at particular points in the code and the current state of the computation can be inspected.
Most debugging takes place either through calls to browser or
debug. Both of these functions rely on the same internal
mechanism and both provide the user with a special prompt. Any command
can be typed at the prompt. The evaluation
environment for the command
is the currently active environment. This allows you to examine the
current state of any variables etc.
There are five special commands that R interprets differently. They are,
If there is a local variable with the same name as one of the special
commands listed above then its value can be accessed by using
get. A call to get with the name in quotes will retrieve
the value in the current
environment.
The debugger provides access only to interpreted expressions. If a
function calls a foreign language (such as C) then no access to the
statements in that language is provided. Execution will halt on the
next statement that is evaluated in R. A symbolic debugger such as
gdb can be used to debug compiled code.
A call to the function browser causes R to halt execution at
that point and to provide the user with a special prompt. Arguments to
browser are ignored.
> foo <- function(s) {
+ c <- 3
+ browser()
+ }
> foo(4)
Called from: foo(4)
Browse[1]> s
[1] 4
Browse[1]> get("c")
[1] 3
Browse[1]>
The debugger can be invoked on any function by using the command
debug(fun). Subsequently, each time that function is
evaluated the debugger is invoked. The debugger allows you to control
the evaluation of the statements in the body of the function. Before
each statement is executed the statement is printed out and a special
prompt provided. Any command can be given, those in the table above
have special meaning.
Debugging is turned off by a call to undebug with the function as
an argument.
> debug(mean.default)
> mean(1:10)
debugging in: mean.default(1:10)
debug: {
if (na.rm)
x <- x[!is.na(x)]
trim <- trim[1]
n <- length(c(x, recursive = TRUE))
if (trim > 0) {
if (trim >= 0.5)
return(median(x, na.rm = FALSE))
lo <- floor(n * trim) + 1
hi <- n + 1 - lo
x <- sort(x, partial = unique(c(lo, hi)))[lo:hi]
n <- hi - lo + 1
}
sum(x)/n
}
Browse[1]>
debug: if (na.rm) x <- x[!is.na(x)]
Browse[1]>
debug: trim <- trim[1]
Browse[1]>
debug: n <- length(c(x, recursive = TRUE))
Browse[1]> c
exiting from: mean.default(1:10)
[1] 5.5
Another way of monitoring the behaviour of R is through the
trace mechanism. trace is called with a single argument
that is the name of the function you want to trace. The name does not
need to be quoted but for some functions you will need to quote the name
in order to avoid a syntax error.
When trace has been invoked on a function then every time that
function is evaluated the call to it is printed out. This mechanism is
removed by calling untrace with the function as an argument.
> get("[<-")
.Primitive("[<-")
> trace("[<-")
> x <- 1:10
> x[3] <- 4
trace: "[<-"(*tmp*, 3, value = 4)
When an error has caused a jump to top-level a special variable called
.Traceback is placed into the base environment.
.Traceback is a character vector with one entry for each function
call that was active at the time the error occurred. An examination of
.Traceback can be carried out by a call to traceback.
The parser is what converts the textual representation of R code into an internal form which may then be passed to the R evaluator which causes the specified instructions to be carried out. The internal form is itself an R object and can be saved and otherwise manipulated within the R system.
Parsing in R occurs in three different variants:
The read-eval-print loop forms the basic command line interface to R. Textual input is read until a complete R expression is available. Expressions may be split over several input lines. The primary prompt (by default `> ') indicates that the parser is ready for a new expression, and a continuation prompt (by default `+ ') indicates that the parser expects the remainder of an incomplete expression. The expression is converted to internal form during input and the parsed expression is passed to the evaluator and the result is printed (unless specifically made invisible). If the parser finds itself in a state which is incompatible with the language syntax, a “Syntax Error” is flagged and the parser resets itself and resumes input at the beginning of the next input line.
Text files can be parsed using the parse function. In
particular, this is done during execution of the source
function, which allows commands to be stored in an external file and
executed as if they had been typed at the keyboard. Note, though, that
the entire file is parsed and syntax checked before any evaluation takes
place.
Character strings, or vectors thereof, can be parsed using the
text= argument to parse. The strings are treated exactly
as if they were the lines of an input file.
Parsed expressions are stored in an R object containing the parse
tree. A fuller description of such objects can be found in
Language objects and Expression objects. Briefly, every
elementary R expression is stored in
function call form, as a list
with the first element containing the function name and the remainder
containing the arguments, which may in turn be further R expressions.
The list elements can be named, corresponding to tagged matching of
formal and actual arguments. Note that all R syntax elements
are treated in this way, e.g. the assignment x <- 1 is encoded
as "<-"(x, 1).
Any R object can be converted to an R expression using
deparse. This is frequently used in connection with output of
results, e.g. for labeling plots. Notice that only objects of mode
"expression" can be expected to be unchanged by reparsing the
output of deparsing. For instance, the numeric vector 1:5 will
deparse as "c(1, 2, 3, 4, 5)", which will reparse as a call to
the function c. As far as possible, evaluating the deparsed and
reparsed expression gives the same result as evaluating the original,
but there are a couple of awkward exceptions, mostly involving
expressions that weren't generated from a textual representation in the
first place.
Comments in R are ignored by the parser. Any text from a
# character
to the end of the line is taken to be a comment, unless
the # character is inside a quoted string. For example,
> x <- 1 # This is a comment...
> y <- " #... but this is not."
Tokens are the elementary building blocks of a programming language. They are recognised during lexical analysis which (conceptually, at least) takes place prior to the syntactic analysis performed by the parser itself.
There are five types of constants: integer, logical, numeric, complex and string.
In addition, there are four special constants, NULL, NA,
Inf, and NaN.
NULL is used to indicate the empty object. NA is used for
absent (“Not Available”) data values. Inf denotes infinity and
NaN is not-a-number in the IEEE floating point calculus
(results of the operations respectively 1/0 and 0/0, for
instance).
Logical constants are either TRUE or FALSE.
Numeric constants follow a similar syntax to that of the C language. They consist of an integer part consisting of zero or more digits, followed optionally by `.' and a fractional part of zero or more digits optionally followed by an exponent part consisting of an `E' or an `e', an optional sign and a string of zero or more digits. Either the fractional or the decimal part can be empty, but not both at once.
Valid numeric constants: 1 10 0.1 .2 1e-7 1.2e+7 2e 3e+
The two latter examples are hardly useful in practice, but they are accepted and treated as `2' and `3', respectively.
Numeric constants can also be hexadecimal, starting with `0x' or `0x' followed by zero or more digits, `a-f' or `A-F'.
There is now a separate class of integer constants. They are created
by using the qualifier L at the end of the number. For
example, 123L gives an integer value rather than a numeric
value. The suffix L can be used to qualify any non-complex
number with the intent of creating an integer. So it can be used with
numbers given by hexadecimal or scientific notation. However, if the
value is not a valid integer, a warning is emitted and the numeric
value created. The following shows examples of valid integer
constants, values which will generate a warning and give numeric
constants and syntax errors.
Valid integer constants: 1L, 0x10L, 1000000L, 1e6L Valid numeric constants: 1.1L, 1e-3L Syntax error: 12iL
A warning is emitted for values that contain an unnecessary
decimal point, e.g. 1.L.
Note also that a preceding sign (+ or -) is treated as a
unary operator, not as part of the constant.
Complex constants have the form of a decimal numeric constant followed by `i'. Notice that only purely imaginary numbers are actual constants, other complex numbers are parsed a unary or binary operations on numeric and imaginary numbers.
Valid complex constants: 2i 4.1i 1e-2i
String constants are delimited by a pair of single (`'') or double (`"') quotes and can contain all other printable characters. Quotes and other special characters within strings are specified using escape sequences:
\'\"\n\r\t\b\a\f\v\\\nnn0 ... 8 are accepted.
\xnn0 ... 9 A ... F a ... f).
\unnnn \u{nnnn}\Unnnnnnnn \U{nnnnnnnn}A single quote may also be embedded directly in a double-quote delimited string and vice versa.
As from R 2.8.0, a `nul' (\0) is not allowed in a character
string, so using \0 in a string constant terminates the constant
(usually with a warning): further characters up to the closing quote are
scanned but ignored.
Identifiers consist of a sequence of letters, digits, the period (`.') and the underscore. They must not start with a digit nor underscore, nor with a period followed by a digit.
The definition of a letter depends on the current locale: the precise
set of characters allowed is given by the C expression (isalnum(c)
|| c == '.' || c == '_') and will include accented letters in many
Western European locales.
Notice that identifiers starting with a period are not by default listed
by the ls function and that `...' and `..1',
`..2', etc. are special.
Notice also that objects can have names that are not identifiers. These
are generally accessed via get and assign, although they
can also be represented by text strings in some limited circumstances
when there is no ambiguity (e.g. "x" <- 1). As get and
assign are not restricted to names that are identifiers they do
not recognise subscripting operators or assignment functions. The
following pairs are not equivalent
x$a<-1assign("x$a",1)x[[1]]get("x[[1]]")names(x)<-nmassign("names(x)",nm)
The following identifiers have a special meaning and cannot be used for object names
if else repeat while function for in next break
TRUE FALSE NULL Inf NaN
NA NA_integer_ NA_real_ NA_complex_ NA_character_
... ..1 ..2 etc.
R allows user-defined infix operators. These have the form of a string of characters delimited by the `%' character. The string can contain any printable character except `%'. The escape sequences for strings do not apply here.
Note that the following operators are predefined
%% %*% %/% %in% %o% %x%
Although not strictly tokens, stretches of whitespace characters
(spaces, tabs and formfeeds, on Windows and UTF-8 locales other Unicode
whitespace characters3) serve to delimit tokens in case of
ambiguity, (compare x<-5 and x < -5).
Newlines have a function which is a combination of token separator and expression terminator. If an expression can terminate at the end of the line the parser will assume it does so, otherwise the newline is treated as whitespace. Semicolons (`;') may be used to separate elementary expressions on the same line.
Special rules apply to the else keyword: inside a compound
expression, a newline before else is discarded, whereas at the
outermost level, the newline terminates the if construction and a
subsequent else causes a syntax error. This somewhat anomalous
behaviour occurs because R should be usable in interactive mode and
then it must decide whether the input expression is complete,
incomplete, or invalid as soon as the user presses <RET>.
The comma (`,') is used to separate function arguments and multiple indices.
R uses the following operator tokens
+ - * / %% ^arithmetic > >= < <= == !=relational ! & |logical ~model formulae -> <-assignment $list indexing :sequence
(Several of the operators have different meaning inside model formulas)
Ordinary parentheses—`(' and `)'—are used for explicit grouping within expressions and to delimit the argument lists for function definitions and function calls.
Braces—`{' and `}'—delimit blocks of expressions in function definitions, conditional expressions, and iterative constructs.
Indexing of arrays and vectors performed using the single and double brackets, `[]' and `[[]]'. Also, indexing tagged lists may be done using the `$' operator.
An R program consists of a sequence of R expressions. An expression can be a simple expression consisting of only a constant or an identifier, or it can be a compound expression constructed from other parts (which may themselves be expressions).
The following sections detail the various syntactical constructs that are available.
A function call takes the form of a function reference followed by a comma-separated list of arguments within a set of parentheses.
function_reference ( arg1, arg2, ...... , argn )
The function reference can be either
Each argument can be tagged (tag=expr), or just be a
simple expression. It can also be empty or it can be one of the special
tokens `...', `..2', etc.
A tag can be an identifier or a text string.
Examples:
f(x)
g(tag = value, , 5)
"odd name"("strange tag" = 5, y)
(function(x) x^2)(5)
The order of precedence (highest first) of the operators are
::
$ @
^
- + (unary)
:
%xyz%
* /
+ - (binary)
> >= < <= == !=
!
& &&
| ||
~ (unary and binary)
-> ->>
= (as assignment)
<- <<-
The exponentiation operator `^' and the
left assignment operators
`<- - = <<-' group right to left, all other operators group left to
right. That is, 2 ^ 2 ^ 3 is 2 ^ 8, not 4 ^ 3,
whereas 1 - 1 - 1 is -1, not 1.
Notice that the operators %% and %/% for integer
remainder and divide have higher precedence than multiply and divide.
Although it is not strictly an operator, it also needs mentioning that the `=' sign is used for tagging arguments in function calls and for assigning default values in function definitions.
The `$' sign is in some sense an operator, but does not allow arbitrary right hand sides and is discussed under Index constructions. It has higher precedence than any of the other operators.
The parsed form of a unary or binary operation is completely equivalent to a function call with the operator as the function name and the operands as the function arguments.
Parentheses are recorded as equivalent to a unary operator, with name
"(", even in cases where the parentheses could be inferred from
operator precedence (e.g., a * (b + c)).
Notice that the
assignment symbols are operators just like the arithmetic, relational,
and logical ones. Any expressions is allowed also on the target side of
an assignment, as far as the parser is concerned (2 + 2 <- 5 is a
valid expression as far as the parser is concerned. The evaluator will
object, though). Similar comments apply to the model formula operator.
R has three indexing constructs, two of which are syntactically similar although with somewhat different semantics:
object [ arg1, ...... , argn ]
object [[ arg1, ...... , argn ]]
The object can formally be any valid expression, but it is
understood to denote or evaluate to a subsettable object. The arguments
generally evaluate to numerical or character indices, but other kinds of
arguments are possible (notably drop = FALSE).
Internally, these index constructs are stored as function calls with
function name "[" respectively "[[".
The third index construction is
object $ tag
Here, object is as above, whereas tag is an identifier or a
text string. Internally, it is stored as a function call with name
"$"
A compound expression is of the form
{ expr1 ; expr2 ; ...... ; exprn }
The semicolons may be replaced by newlines. Internally, this is stored
as a function call with "{" as the function name and the
expressions as arguments.
R contains the following control structures as special syntactic constructs
if ( cond ) expr
if ( cond ) expr1 else expr2
while ( cond ) expr
repeat expr
for ( var in list ) expr
The expressions in these constructs will typically be compound expressions.
Within the loop constructs (while, repeat, for),
one may use break (to terminate the loop) and next (to
skip to the next iteration).
Internally, the constructs are stored as function calls:
"if"(cond, expr)
"if"(cond, expr1, expr2)
"while"(cond, expr)
"repeat"(expr)
"for"(var, list, expr)
"break"()
"next"()
A function definition is of the form
function ( arglist ) body
The function body is an expression, often a compound expression. The arglist is a comma-separated list of items each of which can be an identifier, or of the form `identifier = default', or the special token `...'. The default can be any valid expression.
Notice that function arguments unlike list tags, etc., cannot have “strange names” given as text strings.
Internally, a function definition is stored as a function call with
function name function and two arguments, the arglist and
the body. The arglist is stored as a tagged pairlist where
the tags are the argument names and the values are the default
expressions.
The parser currently only supports one directive, #line.
This is similar to the C-preprocessor directive of the same name. The
syntax is
#line nn [ "filename" ]
where nn is an integer line number, and the optional filename (in required double quotes) names the source file.
Unlike the C directive, #line must appear as the first five characters
on a line. As in C, nn and "filename" entries may be separated
from it by whitespace. And unlike C, any following text on the line will be
treated as a comment and ignored.
This directive tells the parser that the following line should be assumed to be line nn of file filename. (If the filename is not given, it is assumed to be the same as for the previous directive.) This is not typically used by users, but may be used by preprocessors so that diagnostic messages refer to the original file.
#: Comments$: Index constructions$: Indexing.C: Foreign language interfaces.Call: Foreign language interfaces.External: Foreign language interfaces.Fortran: Foreign language interfaces.Internal: .Internal and .Primitive.Primitive: .Internal and .Primitive[: Index constructions[: Indexing[[: Index constructions[[: Indexingas.call: Language objectsas.character: Symbol objectsas.function: Function objectsas.list: Language objectsas.name: Symbol objectsassign: Identifiersattr: Attributesattr<-: Attributesattributes: Attributesattributes<-: Attributesbaseenv: Environment objectsbasename: Operating system accessbody: Manipulation of functionsbody: Function objectsbody<-: Manipulation of functionsbreak: Loopingbrowser: browserdebug: debug/undebugdirname: Operating system accessdo.call: Manipulation of function callsemptyenv: Environment objectsenvironment: Manipulation of functionsenvironment: Function objectsenvironment<-: Manipulation of functionseval: More on evaluationfile.access: Operating system accessfile.append: Operating system accessfile.choose: Operating system accessfile.copy: Operating system accessfile.create: Operating system accessfile.exists: Operating system accessfile.info: Operating system accessfile.path: Operating system accessfile.remove: Operating system accessfile.rename: Operating system accessfile.show: Operating system accessfor: forformals: Manipulation of functionsformals: Function objectsformals<-: Manipulation of functionsget: Identifiersis.na: NA handlingis.nan: NA handlingmatch.arg: Argument matchingmatch.call: Manipulation of function callsmatch.call: Argument matchingmatch.fun: Argument matchingmissing: NA handlingmode: ObjectsNA: Indexing by vectorsNA: NA handlingnames: Namesnames<-: NamesNaN: NA handlingnew.env: Environment objectsnext: LoopingNextMethod: NextMethodNULL: NULL objecton.exit: on.exitpairlist: Pairlist objectspath.expand: Operating system accessproc.time: Operating system accessquote: Language objectsrepeat: repeatstop: stopstorage.mode: Objectssubstitute: Substitutionsswitch: switchSys.getenv: Operating system accessSys.getlocale: Operating system accessSys.localeconv: Operating system accessSys.putenv: Operating system accessSys.putlocale: Operating system accessSys.time: Operating system accessSys.timezone: Operating system accesssystem: Operating system accesssystem.time: Operating system accesstrace: trace/untracetraceback: tracebacktypeof: Objectsundebug: debug/undebugunlink: Operating system accessuntrace: trace/untraceUseMethod: UseMethodwarning: warningwarnings: warningwhile: whileRichard A. Becker, John M. Chambers and Allan R. Wilks (1988), The New S Language. Chapman & Hall, New York. This book is often called the “Blue Book”.
[1] Evaluation always takes place in an environment. See Scope of variables for more details.
[2] Looping is the repeated evaluation of a statement or block of statements.
[3] such as U+A0, non-breaking space,
and U+3000, ideographic space.