(scm_make_complex): Discouraged by moving to discouraged.h and

[bpt/guile.git] / doc / ref / api-data.texi

@c -*-texinfo-*-
@c This is part of the GNU Guile Reference Manual.
@c Copyright (C)  1996, 1997, 2000, 2001, 2002, 2003, 2004
@c   Free Software Foundation, Inc.
@c See the file guile.texi for copying conditions.

@page
@node Simple Data Types
@section Simple Generic Data Types

This chapter describes those of Guile's simple data types which are
primarily used for their role as items of generic data.  By
@dfn{simple} we mean data types that are not primarily used as
containers to hold other data --- i.e.@: pairs, lists, vectors and so on.
For the documentation of such @dfn{compound} data types, see
@ref{Compound Data Types}.

@c One of the great strengths of Scheme is that there is no straightforward
@c distinction between ``data'' and ``functionality''.  For example,
@c Guile's support for dynamic linking could be described:

@c @itemize @bullet
@c @item
@c either in a ``data-centric'' way, as the behaviour and properties of the
@c ``dynamically linked object'' data type, and the operations that may be
@c applied to instances of this type

@c @item
@c or in a ``functionality-centric'' way, as the set of procedures that
@c constitute Guile's support for dynamic linking, in the context of the
@c module system.
@c @end itemize

@c The contents of this chapter are, therefore, a matter of judgment.  By
@c @dfn{generic}, we mean to select those data types whose typical use as
@c @emph{data} in a wide variety of programming contexts is more important
@c than their use in the implementation of a particular piece of
@c @emph{functionality}.  The last section of this chapter provides
@c references for all the data types that are documented not here but in a
@c ``functionality-centric'' way elsewhere in the manual.

@menu
* Booleans::                    True/false values.
* Numbers::                     Numerical data types.
* Characters::                  New character names.
* Strings::                     Special things about strings.
* Regular Expressions::         Pattern matching and substitution.
* Symbols::                     Symbols.
* Keywords::                    Self-quoting, customizable display keywords.
* Other Types::                 "Functionality-centric" data types.
@end menu


@node Booleans
@subsection Booleans
@tpindex Booleans

The two boolean values are @code{#t} for true and @code{#f} for false.

Boolean values are returned by predicate procedures, such as the general
equality predicates @code{eq?}, @code{eqv?} and @code{equal?}
(@pxref{Equality}) and numerical and string comparison operators like
@code{string=?} (@pxref{String Comparison}) and @code{<=}
(@pxref{Comparison}).

@lisp
(<= 3 8)
@result{} #t

(<= 3 -3)
@result{} #f

(equal? "house" "houses")
@result{} #f

(eq? #f #f)
@result{}
#t
@end lisp

In test condition contexts like @code{if} and @code{cond} (@pxref{if
cond case}), where a group of subexpressions will be evaluated only if a
@var{condition} expression evaluates to ``true'', ``true'' means any
value at all except @code{#f}.

@lisp
(if #t "yes" "no")
@result{} "yes"

(if 0 "yes" "no")
@result{} "yes"

(if #f "yes" "no")
@result{} "no"
@end lisp

A result of this asymmetry is that typical Scheme source code more often
uses @code{#f} explicitly than @code{#t}: @code{#f} is necessary to
represent an @code{if} or @code{cond} false value, whereas @code{#t} is
not necessary to represent an @code{if} or @code{cond} true value.

It is important to note that @code{#f} is @strong{not} equivalent to any
other Scheme value.  In particular, @code{#f} is not the same as the
number 0 (like in C and C++), and not the same as the ``empty list''
(like in some Lisp dialects).

In C, the two Scheme boolean values are available as the two constants
@code{SCM_BOOL_T} for @code{#t} and @code{SCM_BOOL_F} for @code{#f}.
Care must be taken with the false value @code{SCM_BOOL_F}: it is not
false when used in C conditionals.  In order to test for it, use
@code{scm_is_false} or @code{scm_is_true}.

@rnindex not
@deffn {Scheme Procedure} not x
@deffnx {C Function} scm_not (x)
Return @code{#t} if @var{x} is @code{#f}, else return @code{#f}.
@end deffn

@rnindex boolean?
@deffn {Scheme Procedure} boolean? obj
@deffnx {C Function} scm_boolean_p (obj)
Return @code{#t} if @var{obj} is either @code{#t} or @code{#f}, else
return @code{#f}.
@end deffn

@deftypevr {C Macro} SCM SCM_BOOL_T
The @code{SCM} representation of the Scheme object @code{#t}.
@end deftypevr

@deftypevr {C Macro} SCM SCM_BOOL_F
The @code{SCM} representation of the Scheme object @code{#f}.
@end deftypevr

@deftypefn {C Function} int scm_is_true (SCM obj)
Return @code{0} if @var{obj} is @code{#f}, else return @code{1}.
@end deftypefn

@deftypefn {C Function} int scm_is_false (SCM obj)
Return @code{1} if @var{obj} is @code{#f}, else return @code{0}.
@end deftypefn

@deftypefn {C Function} int scm_is_bool (SCM obj)
Return @code{1} if @var{obj} is either @code{#t} or @code{#f}, else
return @code{0}.
@end deftypefn

@deftypefn {C Function} SCM scm_from_bool (int val)
Return @code{#f} if @var{val} is @code{0}, else return @code{#t}.
@end deftypefn

@deftypefn {C Function} int scm_to_bool (SCM val)
Return @code{1} if @var{val} is @code{SCM_BOOL_T}, return @code{0}
when @var{val} is @code{SCM_BOOL_F}, else signal a `wrong type' error.

You should probably use @code{scm_is_true} instead of this function
when you just want to test a @code{SCM} value for trueness.
@end deftypefn

@node Numbers
@subsection Numerical data types
@tpindex Numbers

Guile supports a rich ``tower'' of numerical types --- integer,
rational, real and complex --- and provides an extensive set of
mathematical and scientific functions for operating on numerical
data.  This section of the manual documents those types and functions.

You may also find it illuminating to read R5RS's presentation of numbers
in Scheme, which is particularly clear and accessible: see
@ref{Numbers,,,r5rs,R5RS}.

@menu
* Numerical Tower::             Scheme's numerical "tower".
* Integers::                    Whole numbers.
* Reals and Rationals::         Real and rational numbers.
* Complex Numbers::             Complex numbers.
* Exactness::                   Exactness and inexactness.
* Number Syntax::               Read syntax for numerical data.
* Integer Operations::          Operations on integer values.
* Comparison::                  Comparison predicates.
* Conversion::                  Converting numbers to and from strings.
* Complex::                     Complex number operations.
* Arithmetic::                  Arithmetic functions.
* Scientific::                  Scientific functions.
* Primitive Numerics::          Primitive numeric functions.
* Bitwise Operations::          Logical AND, OR, NOT, and so on.
* Random::                      Random number generation.
@end menu


@node Numerical Tower
@subsubsection Scheme's Numerical ``Tower''
@rnindex number?

Scheme's numerical ``tower'' consists of the following categories of
numbers:

@table @dfn
@item integers
Whole numbers, positive or negative; e.g.@: --5, 0, 18.

@item rationals
The set of numbers that can be expressed as @math{@var{p}/@var{q}}
where @var{p} and @var{q} are integers; e.g.@: @math{9/16} works, but
pi (an irrational number) doesn't. These include integers
(@math{@var{n}/1}).

@item real numbers
The set of numbers that describes all possible positions along a
one-dimensional line. This includes rationals as well as irrational
numbers.

@item complex numbers
The set of numbers that describes all possible positions in a two
dimensional space. This includes real as well as imaginary numbers
(@math{@var{a}+@var{b}i}, where @var{a} is the @dfn{real part},
@var{b} is the @dfn{imaginary part}, and @math{i} is the square root of
@minus{}1.)
@end table

It is called a tower because each category ``sits on'' the one that
follows it, in the sense that every integer is also a rational, every
rational is also real, and every real number is also a complex number
(but with zero imaginary part).

In addition to the classification into integers, rationals, reals and
complex numbers, Scheme also distinguishes between whether a number is
represented exactly or not.  For example, the result of
@m{2\sin(\pi/4),sin(pi/4)} is exactly @m{\sqrt{2},2^(1/2)} but Guile
can neither represent @m{\pi/4,pi/4} nor @m{\sqrt{2},2^(1/2)} exactly.
Instead, it stores an inexact approximation, using the C type
@code{double}.

Guile can represent exact rationals of any magnitude, inexact
rationals that fit into a C @code{double}, and inexact complex numbers
with @code{double} real and imaginary parts.

The @code{number?} predicate may be applied to any Scheme value to
discover whether the value is any of the supported numerical types.

@deffn {Scheme Procedure} number? obj
@deffnx {C Function} scm_number_p (obj)
Return @code{#t} if @var{obj} is any kind of number, else @code{#f}.
@end deffn

For example:

@lisp
(number? 3)
@result{} #t

(number? "hello there!")
@result{} #f

(define pi 3.141592654)
(number? pi)
@result{} #t
@end lisp

The next few subsections document each of Guile's numerical data types
in detail.

@node Integers
@subsubsection Integers

@tpindex Integer numbers

@rnindex integer?

Integers are whole numbers, that is numbers with no fractional part,
such as 2, 83, and @minus{}3789.

Integers in Guile can be arbitrarily big, as shown by the following
example.

@lisp
(define (factorial n)
  (let loop ((n n) (product 1))
    (if (= n 0)
        product
        (loop (- n 1) (* product n)))))

(factorial 3)
@result{} 6

(factorial 20)
@result{} 2432902008176640000

(- (factorial 45))
@result{} -119622220865480194561963161495657715064383733760000000000
@end lisp

Readers whose background is in programming languages where integers are
limited by the need to fit into just 4 or 8 bytes of memory may find
this surprising, or suspect that Guile's representation of integers is
inefficient.  In fact, Guile achieves a near optimal balance of
convenience and efficiency by using the host computer's native
representation of integers where possible, and a more general
representation where the required number does not fit in the native
form.  Conversion between these two representations is automatic and
completely invisible to the Scheme level programmer.

The infinities @samp{+inf.0} and @samp{-inf.0} are considered to be
inexact integers.  They are explained in detail in the next section,
together with reals and rationals.

C has a host of different integer types, and Guile offers a host of
functions to convert between them and the @code{SCM} representation.
For example, a C @code{int} can be handled with @code{scm_to_int} and
@code{scm_from_int}.  Guile also defines a few C integer types of its
own, to help with differences between systems.

C integer types that are not covered can be handled with the generic
@code{scm_to_signed_integer} and @code{scm_from_signed_integer} for
signed types, or with @code{scm_to_unsigned_integer} and
@code{scm_from_unsigned_integer} for unsigned types.

Scheme integers can be exact and inexact.  For example, a number
written as @code{3.0} with an explicit decimal-point is inexact, but
it is also an integer.  The functions @code{integer?} and
@code{scm_is_integer} report true for such a number, but the functions
@code{scm_is_signed_integer} and @code{scm_is_unsigned_integer} only
allow exact integers and thus report false.  Likewise, the conversion
functions like @code{scm_to_signed_integer} only accept exact
integers.

The motivation for this behavior is that the inexactness of a number
should not be lost silently.  If you want to allow inexact integers,
you can explicitely insert a call to @code{inexact->exact} or to its C
equivalent @code{scm_inexact_to_exact}.  (Only inexact integers will
be converted by this call into exact integers; inexact non-integers
will become exact fractions.)

@deffn {Scheme Procedure} integer? x
@deffnx {C Function} scm_integer_p (x)
Return @code{#t} if @var{x} is an exactor inexact integer number, else
@code{#f}.

@lisp
(integer? 487)
@result{} #t

(integer? 3.0)
@result{} #t

(integer? -3.4)
@result{} #f

(integer? +inf.0)
@result{} #t
@end lisp
@end deffn

@deftypefn {C Function} int scm_is_integer (SCM x)
This is equivalent to @code{scm_is_true (scm_integer_p (x))}.
@end deftypefn

@defvr  {C Type} scm_t_int8
@defvrx {C Type} scm_t_uint8
@defvrx {C Type} scm_t_int16
@defvrx {C Type} scm_t_uint16
@defvrx {C Type} scm_t_int32
@defvrx {C Type} scm_t_uint32
@defvrx {C Type} scm_t_int64
@defvrx {C Type} scm_t_uint64
@defvrx {C Type} scm_t_intmax
@defvrx {C Type} scm_t_uintmax
The C types are equivalent to the corresponding ISO C types but are
defined on all platforms, with the exception of @code{scm_t_int64} and
@code{scm_t_uint64}, which are only defined when a 64-bit type is
available.  For example, @code{scm_t_int8} is equivalent to
@code{int8_t}.

You can regard these definitions as a stop-gap measure until all
platforms provide these types.  If you know that all the platforms
that you are interested in already provide these types, it is better
to use them directly instead of the types provided by Guile.
@end defvr

@deftypefn  {C Function} int scm_is_signed_integer (SCM x, scm_t_intmax min, scm_t_intmax max)
@deftypefnx {C Function} int scm_is_unsigned_integer (SCM x, scm_t_uintmax min, scm_t_uintmax max)
Return @code{1} when @var{x} represents an exact integer that is
between @var{min} and @var{max}, inclusive.

These functions can be used to check whether a @code{SCM} value will
fit into a given range, such as the range of a given C integer type.
If you just want to convert a @code{SCM} value to a given C integer
type, use one of the conversion functions directly.
@end deftypefn

@deftypefn  {C Function} scm_t_intmax scm_to_signed_integer (SCM x, scm_t_intmax min, scm_t_intmax max)
@deftypefnx {C Function} scm_t_uintmax scm_to_unsigned_integer (SCM x, scm_t_uintmax min, scm_t_uintmax max)
When @var{x} represents an exact integer that is between @var{min} and
@var{max} inclusive, return that integer.  Else signal an error,
either a `wrong-type' error when @var{x} is not an exact integer, or
an `out-of-range' error when it doesn't fit the given range.
@end deftypefn

@deftypefn  {C Function} SCM scm_from_signed_integer (scm_t_intmax x)
@deftypefnx {C Function} SCM scm_from_unsigned_integer (scm_t_uintmax x)
Return the @code{SCM} value that represents the integer @var{x}.  This
function will always succeed and will always return an exact number.
@end deftypefn

@deftypefn  {C Function} char scm_to_char (SCM x)
@deftypefnx {C Function} {signed char} scm_to_schar (SCM x)
@deftypefnx {C Function} {unsigned char} scm_to_uchar (SCM x)
@deftypefnx {C Function} short scm_to_short (SCM x)
@deftypefnx {C Function} {unsigned short} scm_to_ushort (SCM x)
@deftypefnx {C Function} int scm_to_int (SCM x)
@deftypefnx {C Function} {unsigned int} scm_to_uint (SCM x)
@deftypefnx {C Function} long scm_to_long (SCM x)
@deftypefnx {C Function} {unsigned long} scm_to_ulong (SCM x)
@deftypefnx {C Function} {long long} scm_to_long_long (SCM x)
@deftypefnx {C Function} {unsigned long long} scm_to_ulong_long (SCM x)
@deftypefnx {C Function} size_t scm_to_size_t (SCM x)
@deftypefnx {C Function} ssize_t scm_to_ssize_t (SCM x)
@deftypefnx {C Function} scm_t_int8 scm_to_int8 (SCM x)
@deftypefnx {C Function} scm_t_uint8 scm_to_uint8 (SCM x)
@deftypefnx {C Function} scm_t_int16 scm_to_int16 (SCM x)
@deftypefnx {C Function} scm_t_uint16 scm_to_uint16 (SCM x)
@deftypefnx {C Function} scm_t_int32 scm_to_int32 (SCM x)
@deftypefnx {C Function} scm_t_uint32 scm_to_uint32 (SCM x)
@deftypefnx {C Function} scm_t_int64 scm_to_int64 (SCM x)
@deftypefnx {C Function} scm_t_uint64 scm_to_uint64 (SCM x)
@deftypefnx {C Function} scm_t_intmax scm_to_intmax (SCM x)
@deftypefnx {C Function} scm_t_uintmax scm_to_uintmax (SCM x)
When @var{x} represents an exact integer that fits into the indicated
C type, return that integer.  Else signal an error, either a
`wrong-type' error when @var{x} is not an exact integer, or an
`out-of-range' error when it doesn't fit the given range.

The functions @code{scm_to_long_long}, @code{scm_to_ulong_long},
@code{scm_to_int64}, and @code{scm_to_uint64} are only available when
the corresponding types are.
@end deftypefn

@deftypefn  {C Function} SCM scm_from_char (char x)
@deftypefnx {C Function} SCM scm_from_schar (signed char x)
@deftypefnx {C Function} SCM scm_from_uchar (unsigned char x)
@deftypefnx {C Function} SCM scm_from_short (short x)
@deftypefnx {C Function} SCM scm_from_ushort (unsigned short x)
@deftypefnx {C Function} SCM scm_from_int (int  x)
@deftypefnx {C Function} SCM scm_from_uint (unsigned int x)
@deftypefnx {C Function} SCM scm_from_long (long x)
@deftypefnx {C Function} SCM scm_from_ulong (unsigned long x)
@deftypefnx {C Function} SCM scm_from_long_long (long long x)
@deftypefnx {C Function} SCM scm_from_ulong_long (unsigned long long x)
@deftypefnx {C Function} SCM scm_from_size_t (size_t x)
@deftypefnx {C Function} SCM scm_from_ssize_t (ssize_t x)
@deftypefnx {C Function} SCM scm_from_int8 (scm_t_int8 x)
@deftypefnx {C Function} SCM scm_from_uint8 (scm_t_uint8 x)
@deftypefnx {C Function} SCM scm_from_int16 (scm_t_int16 x)
@deftypefnx {C Function} SCM scm_from_uint16 (scm_t_uint16 x)
@deftypefnx {C Function} SCM scm_from_int32 (scm_t_int32 x)
@deftypefnx {C Function} SCM scm_from_uint32 (scm_t_uint32 x)
@deftypefnx {C Function} SCM scm_from_int64 (scm_t_int64 x)
@deftypefnx {C Function} SCM scm_from_uint64 (scm_t_uint64 x)
@deftypefnx {C Function} SCM scm_from_intmax (scm_t_intmax x)
@deftypefnx {C Function} SCM scm_from_uintmax (scm_t_uintmax x)
Return the @code{SCM} value that represents the integer @var{x}.
These functions will always succeed and will always return an exact
number.
@end deftypefn

@node Reals and Rationals
@subsubsection Real and Rational Numbers
@tpindex Real numbers
@tpindex Rational numbers

@rnindex real?
@rnindex rational?

Mathematically, the real numbers are the set of numbers that describe
all possible points along a continuous, infinite, one-dimensional line.
The rational numbers are the set of all numbers that can be written as
fractions @var{p}/@var{q}, where @var{p} and @var{q} are integers.
All rational numbers are also real, but there are real numbers that
are not rational, for example the square root of 2, and pi.

Guile can represent both exact and inexact rational numbers, but it
can not represent irrational numbers.  Exact rationals are represented
by storing the numerator and denominator as two exact integers.
Inexact rationals are stored as floating point numbers using the C
type @code{double}.

Exact rationals are written as a fraction of integers.  There must be
no whitespace around the slash:

@lisp
1/2
-22/7
@end lisp

Even though the actual encoding of inexact rationals is in binary, it
may be helpful to think of it as a decimal number with a limited
number of significant figures and a decimal point somewhere, since
this corresponds to the standard notation for non-whole numbers.  For
example:

@lisp
0.34
-0.00000142857931198
-5648394822220000000000.0
4.0
@end lisp

The limited precision of Guile's encoding means that any ``real'' number
in Guile can be written in a rational form, by multiplying and then dividing
by sufficient powers of 10 (or in fact, 2).  For example,
@samp{-0.00000142857931198} is the same as @minus{}142857931198 divided by
100000000000000000.  In Guile's current incarnation, therefore, the
@code{rational?} and @code{real?} predicates are equivalent.


Dividing by an exact zero leads to a error message, as one might
expect.  However, dividing by an inexact zero does not produce an
error.  Instead, the result of the division is either plus or minus
infinity, depending on the sign of the divided number.

The infinities are written @samp{+inf.0} and @samp{-inf.0},
respectivly.  This syntax is also recognized by @code{read} as an
extension to the usual Scheme syntax.

Dividing zero by zero yields something that is not a number at all:
@samp{+nan.0}.  This is the special `not a number' value.

On platforms that follow @acronym{IEEE} 754 for their floating point
arithmetic, the @samp{+inf.0}, @samp{-inf.0}, and @samp{+nan.0} values
are implemented using the corresponding @acronym{IEEE} 754 values.
They behave in arithmetic operations like @acronym{IEEE} 754 describes
it, i.e., @code{(= +nan.0 +nan.0)} @result{} @code{#f}.

The infinities are inexact integers and are considered to be both even
and odd.  While @samp{+nan.0} is not @code{=} to itself, it is
@code{eqv?} to itself.

To test for the special values, use the functions @code{inf?} and
@code{nan?}.

@deffn {Scheme Procedure} real? obj
@deffnx {C Function} scm_real_p (obj)
Return @code{#t} if @var{obj} is a real number, else @code{#f}.  Note
that the sets of integer and rational values form subsets of the set
of real numbers, so the predicate will also be fulfilled if @var{obj}
is an integer number or a rational number.
@end deffn

@deffn {Scheme Procedure} rational? x
@deffnx {C Function} scm_rational_p (x)
Return @code{#t} if @var{x} is a rational number, @code{#f} otherwise.
Note that the set of integer values forms a subset of the set of
rational numbers, i. e. the predicate will also be fulfilled if
@var{x} is an integer number.

Since Guile can not represent irrational numbers, every number
satisfying @code{real?} also satisfies @code{rational?} in Guile.
@end deffn

@deffn {Scheme Procedure} rationalize x eps
@deffnx {C Function} scm_rationalize (x, eps)
Returns the @emph{simplest} rational number differing
from @var{x} by no more than @var{eps}.  

As required by @acronym{R5RS}, @code{rationalize} only returns an
exact result when both its arguments are exact.  Thus, you might need
to use @code{inexact->exact} on the arguments.

@lisp
(rationalize (inexact->exact 1.2) 1/100)
@result{} 6/5
@end lisp

@end deffn

@deffn  {Scheme Procedure} inf? x
@deffnx {C Function} scm_inf_p (x)
Return @code{#t} if @var{x} is either @samp{+inf.0} or @samp{-inf.0},
@code{#f} otherwise.
@end deffn

@deffn {Scheme Procedure} nan? x
@deffnx {C Function} scm_nan_p (x)
Return @code{#t} if @var{x} is @samp{+nan.0}, @code{#f} otherwise.
@end deffn

@deffn {Scheme Procedure} numerator x
@deffnx {C Function} scm_numerator (x)
Return the numerator of the rational number @var{x}.
@end deffn

@deffn {Scheme Procedure} denominator x
@deffnx {C Function} scm_denominator (x)
Return the denominator of the rational number @var{x}.
@end deffn

@deftypefn  {C Function} int scm_is_real (SCM val)
@deftypefnx {C Function} int scm_is_rational (SCM val)
Equivalent to @code{scm_is_true (scm_real_p (val))} and
@code{scm_is_true (scm_rational_p (val))}, respectively.
@end deftypefn

@deftypefn {C Function} double scm_to_double (SCM val)
Returns the number closest to @var{val} that is representable as a
@code{double}.  Returns infinity for a @var{val} that is too large in
magnitude.  The argument @var{val} must be a real number.
@end deftypefn

@deftypefn {C Function} SCM scm_from_double (double val)
Return the @code{SCM} value that representats @var{val}.  The returned
value is inexact according to the predicate @code{inexact?}, but it
will be exactly equal to @var{val}.
@end deftypefn

@node Complex Numbers
@subsubsection Complex Numbers
@tpindex Complex numbers

@rnindex complex?

Complex numbers are the set of numbers that describe all possible points
in a two-dimensional space.  The two coordinates of a particular point
in this space are known as the @dfn{real} and @dfn{imaginary} parts of
the complex number that describes that point.

In Guile, complex numbers are written in rectangular form as the sum of
their real and imaginary parts, using the symbol @code{i} to indicate
the imaginary part.

@lisp
3+4i
@result{}
3.0+4.0i

(* 3-8i 2.3+0.3i)
@result{}
9.3-17.5i
@end lisp

Guile represents a complex number with a non-zero imaginary part as a
pair of inexact rationals, so the real and imaginary parts of a
complex number have the same properties of inexactness and limited
precision as single inexact rational numbers.  Guile can not represent
exact complex numbers with non-zero imaginary parts.

@deffn {Scheme Procedure} complex? x
@deffnx {C Function} scm_number_p (x)
Return @code{#t} if @var{x} is a complex number, @code{#f}
otherwise.  Note that the sets of real, rational and integer
values form subsets of the set of complex numbers, i. e. the
predicate will also be fulfilled if @var{x} is a real,
rational or integer number.
@end deffn


@node Exactness
@subsubsection Exact and Inexact Numbers
@tpindex Exact numbers
@tpindex Inexact numbers

@rnindex exact?
@rnindex inexact?
@rnindex exact->inexact
@rnindex inexact->exact

R5RS requires that a calculation involving inexact numbers always
produces an inexact result.  To meet this requirement, Guile
distinguishes between an exact integer value such as @samp{5} and the
corresponding inexact real value which, to the limited precision
available, has no fractional part, and is printed as @samp{5.0}.  Guile
will only convert the latter value to the former when forced to do so by
an invocation of the @code{inexact->exact} procedure.

@deffn {Scheme Procedure} exact? z
@deffnx {C Function} scm_exact_p (z)
Return @code{#t} if the number @var{z} is exact, @code{#f}
otherwise.

@lisp
(exact? 2)
@result{} #t

(exact? 0.5)
@result{} #f

(exact? (/ 2))
@result{} #t
@end lisp

@end deffn

@deffn {Scheme Procedure} inexact? z
@deffnx {C Function} scm_inexact_p (z)
Return @code{#t} if the number @var{z} is inexact, @code{#f}
else.
@end deffn

@deffn {Scheme Procedure} inexact->exact z
@deffnx {C Function} scm_inexact_to_exact (z)
Return an exact number that is numerically closest to @var{z}, when
there is one.  For inexact rationals, Guile returns the exact rational
that is numerically equal to the inexact rational.  Inexact complex
numbers with a non-zero imaginary part can not be made exact.

@lisp
(inexact->exact 0.5)
@result{} 1/2
@end lisp

The following happens because 12/10 is not exactly representable as a
@code{double} (on most platforms).  However, when reading a decimal
number that has been marked exact with the ``#e'' prefix, Guile is
able to represent it correctly.

@lisp
(inexact->exact 1.2)  
@result{} 5404319552844595/4503599627370496

#e1.2
@result{} 6/5
@end lisp

@end deffn

@c begin (texi-doc-string "guile" "exact->inexact")
@deffn {Scheme Procedure} exact->inexact z
@deffnx {C Function} scm_exact_to_inexact (z)
Convert the number @var{z} to its inexact representation.
@end deffn


@node Number Syntax
@subsubsection Read Syntax for Numerical Data

The read syntax for integers is a string of digits, optionally
preceded by a minus or plus character, a code indicating the
base in which the integer is encoded, and a code indicating whether
the number is exact or inexact.  The supported base codes are:

@table @code
@item #b
@itemx #B
the integer is written in binary (base 2)

@item #o
@itemx #O
the integer is written in octal (base 8)

@item #d
@itemx #D
the integer is written in decimal (base 10)

@item #x
@itemx #X
the integer is written in hexadecimal (base 16)
@end table

If the base code is omitted, the integer is assumed to be decimal.  The
following examples show how these base codes are used.

@lisp
-13
@result{} -13

#d-13
@result{} -13

#x-13
@result{} -19

#b+1101
@result{} 13

#o377
@result{} 255
@end lisp

The codes for indicating exactness (which can, incidentally, be applied
to all numerical values) are:

@table @code
@item #e
@itemx #E
the number is exact

@item #i
@itemx #I
the number is inexact.
@end table

If the exactness indicator is omitted, the number is exact unless it
contains a radix point.  Since Guile can not represent exact complex
numbers, an error is signalled when asking for them.

@lisp
(exact? 1.2)
@result{} #f

(exact? #e1.2)
@result{} #t

(exact? #e+1i)
ERROR: Wrong type argument
@end lisp

Guile also understands the syntax @samp{+inf.0} and @samp{-inf.0} for
plus and minus infinity, respectively.  The value must be written
exactly as shown, that is, they always must have a sign and exactly
one zero digit after the decimal point.  It also understands
@samp{+nan.0} and @samp{-nan.0} for the special `not-a-number' value.
The sign is ignored for `not-a-number' and the value is always printed
as @samp{+nan.0}.

@node Integer Operations
@subsubsection Operations on Integer Values
@rnindex odd?
@rnindex even?
@rnindex quotient
@rnindex remainder
@rnindex modulo
@rnindex gcd
@rnindex lcm

@deffn {Scheme Procedure} odd? n
@deffnx {C Function} scm_odd_p (n)
Return @code{#t} if @var{n} is an odd number, @code{#f}
otherwise.
@end deffn

@deffn {Scheme Procedure} even? n
@deffnx {C Function} scm_even_p (n)
Return @code{#t} if @var{n} is an even number, @code{#f}
otherwise.
@end deffn

@c begin (texi-doc-string "guile" "quotient")
@c begin (texi-doc-string "guile" "remainder")
@deffn {Scheme Procedure} quotient n d
@deffnx {Scheme Procedure} remainder n d
@deffnx {C Function} scm_quotient (n, d)
@deffnx {C Function} scm_remainder (n, d)
Return the quotient or remainder from @var{n} divided by @var{d}.  The
quotient is rounded towards zero, and the remainder will have the same
sign as @var{n}.  In all cases quotient and remainder satisfy
@math{@var{n} = @var{q}*@var{d} + @var{r}}.

@lisp
(remainder 13 4) @result{} 1
(remainder -13 4) @result{} -1
@end lisp
@end deffn

@c begin (texi-doc-string "guile" "modulo")
@deffn {Scheme Procedure} modulo n d
@deffnx {C Function} scm_modulo (n, d)
Return the remainder from @var{n} divided by @var{d}, with the same
sign as @var{d}.

@lisp
(modulo 13 4) @result{} 1
(modulo -13 4) @result{} 3
(modulo 13 -4) @result{} -3
(modulo -13 -4) @result{} -1
@end lisp
@end deffn

@c begin (texi-doc-string "guile" "gcd")
@deffn {Scheme Procedure} gcd
@deffnx {C Function} scm_gcd (x, y)
Return the greatest common divisor of all arguments.
If called without arguments, 0 is returned.

The C function @code{scm_gcd} always takes two arguments, while the
Scheme function can take an arbitrary number.
@end deffn

@c begin (texi-doc-string "guile" "lcm")
@deffn {Scheme Procedure} lcm
@deffnx {C Function} scm_lcm (x, y)
Return the least common multiple of the arguments.
If called without arguments, 1 is returned.

The C function @code{scm_lcm} always takes two arguments, while the
Scheme function can take an arbitrary number.
@end deffn


@node Comparison
@subsubsection Comparison Predicates
@rnindex zero?
@rnindex positive?
@rnindex negative?

The C comparison functions below always takes two arguments, while the
Scheme functions can take an arbitrary number.  Also keep in mind that
the C functions return one of the Scheme boolean values
@code{SCM_BOOL_T} or @code{SCM_BOOL_F} which are both true as far as C
is concerned.  Thus, always write @code{scm_is_true (scm_num_eq_p (x,
y))} when testing the two Scheme numbers @code{x} and @code{y} for
equality, for example.

@c begin (texi-doc-string "guile" "=")
@deffn {Scheme Procedure} =
@deffnx {C Function} scm_num_eq_p (x, y)
Return @code{#t} if all parameters are numerically equal.
@end deffn

@c begin (texi-doc-string "guile" "<")
@deffn {Scheme Procedure} <
@deffnx {C Function} scm_less_p (x, y)
Return @code{#t} if the list of parameters is monotonically
increasing.
@end deffn

@c begin (texi-doc-string "guile" ">")
@deffn {Scheme Procedure} >
@deffnx {C Function} scm_gr_p (x, y)
Return @code{#t} if the list of parameters is monotonically
decreasing.
@end deffn

@c begin (texi-doc-string "guile" "<=")
@deffn {Scheme Procedure} <=
@deffnx {C Function} scm_leq_p (x, y)
Return @code{#t} if the list of parameters is monotonically
non-decreasing.
@end deffn

@c begin (texi-doc-string "guile" ">=")
@deffn {Scheme Procedure} >=
@deffnx {C Function} scm_geq_p (x, y)
Return @code{#t} if the list of parameters is monotonically
non-increasing.
@end deffn

@c begin (texi-doc-string "guile" "zero?")
@deffn {Scheme Procedure} zero? z
@deffnx {C Function} scm_zero_p (z)
Return @code{#t} if @var{z} is an exact or inexact number equal to
zero.
@end deffn

@c begin (texi-doc-string "guile" "positive?")
@deffn {Scheme Procedure} positive? x
@deffnx {C Function} scm_positive_p (x)
Return @code{#t} if @var{x} is an exact or inexact number greater than
zero.
@end deffn

@c begin (texi-doc-string "guile" "negative?")
@deffn {Scheme Procedure} negative? x
@deffnx {C Function} scm_negative_p (x)
Return @code{#t} if @var{x} is an exact or inexact number less than
zero.
@end deffn


@node Conversion
@subsubsection Converting Numbers To and From Strings
@rnindex number->string
@rnindex string->number

@deffn {Scheme Procedure} number->string n [radix]
@deffnx {C Function} scm_number_to_string (n, radix)
Return a string holding the external representation of the
number @var{n} in the given @var{radix}.  If @var{n} is
inexact, a radix of 10 will be used.
@end deffn

@deffn {Scheme Procedure} string->number string [radix]
@deffnx {C Function} scm_string_to_number (string, radix)
Return a number of the maximally precise representation
expressed by the given @var{string}. @var{radix} must be an
exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}
is a default radix that may be overridden by an explicit radix
prefix in @var{string} (e.g. "#o177"). If @var{radix} is not
supplied, then the default radix is 10. If string is not a
syntactically valid notation for a number, then
@code{string->number} returns @code{#f}.
@end deffn


@node Complex
@subsubsection Complex Number Operations
@rnindex make-rectangular
@rnindex make-polar
@rnindex real-part
@rnindex imag-part
@rnindex magnitude
@rnindex angle

@deffn {Scheme Procedure} make-rectangular real imaginary
@deffnx {C Function} scm_make_rectangular (real, imaginary)
Return a complex number constructed of the given @var{real} and
@var{imaginary} parts.
@end deffn

@deffn {Scheme Procedure} make-polar x y
@deffnx {C Function} scm_make_polar (x, y)
Return the complex number @var{x} * e^(i * @var{y}).
@end deffn

@c begin (texi-doc-string "guile" "real-part")
@deffn {Scheme Procedure} real-part z
@deffnx {C Function} scm_real_part (z)
Return the real part of the number @var{z}.
@end deffn

@c begin (texi-doc-string "guile" "imag-part")
@deffn {Scheme Procedure} imag-part z
@deffnx {C Function} scm_imag_part (z)
Return the imaginary part of the number @var{z}.
@end deffn

@c begin (texi-doc-string "guile" "magnitude")
@deffn {Scheme Procedure} magnitude z
@deffnx {C Function} scm_magnitude (z)
Return the magnitude of the number @var{z}. This is the same as
@code{abs} for real arguments, but also allows complex numbers.
@end deffn

@c begin (texi-doc-string "guile" "angle")
@deffn {Scheme Procedure} angle z
@deffnx {C Function} scm_angle (z)
Return the angle of the complex number @var{z}.
@end deffn


@node Arithmetic
@subsubsection Arithmetic Functions
@rnindex max
@rnindex min
@rnindex +
@rnindex *
@rnindex -
@rnindex /
@rnindex abs
@rnindex floor
@rnindex ceiling
@rnindex truncate
@rnindex round

The C arithmetic functions below always takes two arguments, while the
Scheme functions can take an arbitrary number.  When you need to
invoke them with just one argument, for example to compute the
equivalent od @code{(- x)}, pass @code{SCM_UNDEFINED} as the second
one: @code{scm_difference (x, SCM_UNDEFINED)}.

@c begin (texi-doc-string "guile" "+")
@deffn {Scheme Procedure} + z1 @dots{}
@deffnx {C Function} scm_sum (z1, z2)
Return the sum of all parameter values.  Return 0 if called without any
parameters.
@end deffn

@c begin (texi-doc-string "guile" "-")
@deffn {Scheme Procedure} - z1 z2 @dots{}
@deffnx {C Function} scm_difference (z1, z2)
If called with one argument @var{z1}, -@var{z1} is returned. Otherwise
the sum of all but the first argument are subtracted from the first
argument.
@end deffn

@c begin (texi-doc-string "guile" "*")
@deffn {Scheme Procedure} * z1 @dots{}
@deffnx {C Function} scm_product (z1, z2)
Return the product of all arguments.  If called without arguments, 1 is
returned.
@end deffn

@c begin (texi-doc-string "guile" "/")
@deffn {Scheme Procedure} / z1 z2 @dots{}
@deffnx {C Function} scm_divide (z1, z2)
Divide the first argument by the product of the remaining arguments.  If
called with one argument @var{z1}, 1/@var{z1} is returned.
@end deffn

@c begin (texi-doc-string "guile" "abs")
@deffn {Scheme Procedure} abs x
@deffnx {C Function} scm_abs (x)
Return the absolute value of @var{x}.

@var{x} must be a number with zero imaginary part.  To calculate the
magnitude of a complex number, use @code{magnitude} instead.
@end deffn

@c begin (texi-doc-string "guile" "max")
@deffn {Scheme Procedure} max x1 x2 @dots{}
@deffnx {C Function} scm_max (x1, x2)
Return the maximum of all parameter values.
@end deffn

@c begin (texi-doc-string "guile" "min")
@deffn {Scheme Procedure} min x1 x2 @dots{}
@deffnx {C Function} scm_min (x1, x2)
Return the minimum of all parameter values.
@end deffn

@c begin (texi-doc-string "guile" "truncate")
@deffn {Scheme Procedure} truncate
@deffnx {C Function} scm_truncate_number (x)
Round the inexact number @var{x} towards zero.
@end deffn

@c begin (texi-doc-string "guile" "round")
@deffn {Scheme Procedure} round x
@deffnx {C Function} scm_round_number (x)
Round the inexact number @var{x} to the nearest integer.  When exactly
halfway between two integers, round to the even one.
@end deffn

@c begin (texi-doc-string "guile" "floor")
@deffn {Scheme Procedure} floor x
@deffnx {C Function} scm_floor (x)
Round the number @var{x} towards minus infinity.
@end deffn

@c begin (texi-doc-string "guile" "ceiling")
@deffn {Scheme Procedure} ceiling x
@deffnx {C Function} scm_ceiling (x)
Round the number @var{x} towards infinity.
@end deffn


@node Scientific
@subsubsection Scientific Functions

The following procedures accept any kind of number as arguments,
including complex numbers.

@rnindex sqrt
@c begin (texi-doc-string "guile" "sqrt")
@deffn {Scheme Procedure} sqrt z
Return the square root of @var{z}.
@end deffn

@rnindex expt
@c begin (texi-doc-string "guile" "expt")
@deffn {Scheme Procedure} expt z1 z2
Return @var{z1} raised to the power of @var{z2}.
@end deffn

@rnindex sin
@c begin (texi-doc-string "guile" "sin")
@deffn {Scheme Procedure} sin z
Return the sine of @var{z}.
@end deffn

@rnindex cos
@c begin (texi-doc-string "guile" "cos")
@deffn {Scheme Procedure} cos z
Return the cosine of @var{z}.
@end deffn

@rnindex tan
@c begin (texi-doc-string "guile" "tan")
@deffn {Scheme Procedure} tan z
Return the tangent of @var{z}.
@end deffn

@rnindex asin
@c begin (texi-doc-string "guile" "asin")
@deffn {Scheme Procedure} asin z
Return the arcsine of @var{z}.
@end deffn

@rnindex acos
@c begin (texi-doc-string "guile" "acos")
@deffn {Scheme Procedure} acos z
Return the arccosine of @var{z}.
@end deffn

@rnindex atan
@c begin (texi-doc-string "guile" "atan")
@deffn {Scheme Procedure} atan z
@deffnx {Scheme Procedure} atan y x
Return the arctangent of @var{z}, or of @math{@var{y}/@var{x}}.
@end deffn

@rnindex exp
@c begin (texi-doc-string "guile" "exp")
@deffn {Scheme Procedure} exp z
Return e to the power of @var{z}, where e is the base of natural
logarithms (2.71828@dots{}).
@end deffn

@rnindex log
@c begin (texi-doc-string "guile" "log")
@deffn {Scheme Procedure} log z
Return the natural logarithm of @var{z}.
@end deffn

@c begin (texi-doc-string "guile" "log10")
@deffn {Scheme Procedure} log10 z
Return the base 10 logarithm of @var{z}.
@end deffn

@c begin (texi-doc-string "guile" "sinh")
@deffn {Scheme Procedure} sinh z
Return the hyperbolic sine of @var{z}.
@end deffn

@c begin (texi-doc-string "guile" "cosh")
@deffn {Scheme Procedure} cosh z
Return the hyperbolic cosine of @var{z}.
@end deffn

@c begin (texi-doc-string "guile" "tanh")
@deffn {Scheme Procedure} tanh z
Return the hyperbolic tangent of @var{z}.
@end deffn

@c begin (texi-doc-string "guile" "asinh")
@deffn {Scheme Procedure} asinh z
Return the hyperbolic arcsine of @var{z}.
@end deffn

@c begin (texi-doc-string "guile" "acosh")
@deffn {Scheme Procedure} acosh z
Return the hyperbolic arccosine of @var{z}.
@end deffn

@c begin (texi-doc-string "guile" "atanh")
@deffn {Scheme Procedure} atanh z
Return the hyperbolic arctangent of @var{z}.
@end deffn


@node Primitive Numerics
@subsubsection Primitive Numeric Functions

Many of Guile's numeric procedures which accept any kind of numbers as
arguments, including complex numbers, are implemented as Scheme
procedures that use the following real number-based primitives.  These
primitives signal an error if they are called with complex arguments.

@c begin (texi-doc-string "guile" "$abs")
@deffn {Scheme Procedure} $abs x
Return the absolute value of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$sqrt")
@deffn {Scheme Procedure} $sqrt x
Return the square root of @var{x}.
@end deffn

@deffn {Scheme Procedure} $expt x y
@deffnx {C Function} scm_sys_expt (x, y)
Return @var{x} raised to the power of @var{y}. This
procedure does not accept complex arguments.
@end deffn

@c begin (texi-doc-string "guile" "$sin")
@deffn {Scheme Procedure} $sin x
Return the sine of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$cos")
@deffn {Scheme Procedure} $cos x
Return the cosine of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$tan")
@deffn {Scheme Procedure} $tan x
Return the tangent of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$asin")
@deffn {Scheme Procedure} $asin x
Return the arcsine of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$acos")
@deffn {Scheme Procedure} $acos x
Return the arccosine of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$atan")
@deffn {Scheme Procedure} $atan x
Return the arctangent of @var{x} in the range @minus{}@math{PI/2} to
@math{PI/2}.
@end deffn

@deffn {Scheme Procedure} $atan2 x y
@deffnx {C Function} scm_sys_atan2 (x, y)
Return the arc tangent of the two arguments @var{x} and
@var{y}. This is similar to calculating the arc tangent of
@var{x} / @var{y}, except that the signs of both arguments
are used to determine the quadrant of the result. This
procedure does not accept complex arguments.
@end deffn

@c begin (texi-doc-string "guile" "$exp")
@deffn {Scheme Procedure} $exp x
Return e to the power of @var{x}, where e is the base of natural
logarithms (2.71828@dots{}).
@end deffn

@c begin (texi-doc-string "guile" "$log")
@deffn {Scheme Procedure} $log x
Return the natural logarithm of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$sinh")
@deffn {Scheme Procedure} $sinh x
Return the hyperbolic sine of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$cosh")
@deffn {Scheme Procedure} $cosh x
Return the hyperbolic cosine of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$tanh")
@deffn {Scheme Procedure} $tanh x
Return the hyperbolic tangent of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$asinh")
@deffn {Scheme Procedure} $asinh x
Return the hyperbolic arcsine of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$acosh")
@deffn {Scheme Procedure} $acosh x
Return the hyperbolic arccosine of @var{x}.
@end deffn

@c begin (texi-doc-string "guile" "$atanh")
@deffn {Scheme Procedure} $atanh x
Return the hyperbolic arctangent of @var{x}.
@end deffn

C functions for the above are provided by the standard mathematics
library.  Naturally these expect and return @code{double} arguments
(@pxref{Mathematics,,, libc, GNU C Library Reference Manual}).

@multitable {xx} {Scheme Procedure} {C Function}
@item @tab Scheme Procedure @tab C Function

@item @tab @code{$abs}      @tab @code{fabs}
@item @tab @code{$sqrt}     @tab @code{sqrt}
@item @tab @code{$sin}      @tab @code{sin}
@item @tab @code{$cos}      @tab @code{cos}
@item @tab @code{$tan}      @tab @code{tan}
@item @tab @code{$asin}     @tab @code{asin}
@item @tab @code{$acos}     @tab @code{acos}
@item @tab @code{$atan}     @tab @code{atan}
@item @tab @code{$atan2}    @tab @code{atan2}
@item @tab @code{$exp}      @tab @code{exp}
@item @tab @code{$expt}     @tab @code{pow}
@item @tab @code{$log}      @tab @code{log}
@item @tab @code{$sinh}     @tab @code{sinh}
@item @tab @code{$cosh}     @tab @code{cosh}
@item @tab @code{$tanh}     @tab @code{tanh}
@item @tab @code{$asinh}    @tab @code{asinh}
@item @tab @code{$acosh}    @tab @code{acosh}
@item @tab @code{$atanh}    @tab @code{atanh}
@end multitable

@code{asinh}, @code{acosh} and @code{atanh} are C99 standard but might
not be available on older systems.  Guile provides the following
equivalents (on all systems).

@deftypefn {C Function} double scm_asinh (double x)
@deftypefnx {C Function} double scm_acosh (double x)
@deftypefnx {C Function} double scm_atanh (double x)
Return the hyperbolic arcsine, arccosine or arctangent of @var{x}
respectively.
@end deftypefn


@node Bitwise Operations
@subsubsection Bitwise Operations

For the following bitwise functions, negative numbers are treated as
infinite precision twos-complements.  For instance @math{-6} is bits
@math{@dots{}111010}, with infinitely many ones on the left.  It can
be seen that adding 6 (binary 110) to such a bit pattern gives all
zeros.

@deffn {Scheme Procedure} logand n1 n2 @dots{}
@deffnx {C Function} scm_logand (n1, n2)
Return the bitwise @sc{and} of the integer arguments.

@lisp
(logand) @result{} -1
(logand 7) @result{} 7
(logand #b111 #b011 #b001) @result{} 1
@end lisp
@end deffn

@deffn {Scheme Procedure} logior n1 n2 @dots{}
@deffnx {C Function} scm_logior (n1, n2)
Return the bitwise @sc{or} of the integer arguments.

@lisp
(logior) @result{} 0
(logior 7) @result{} 7
(logior #b000 #b001 #b011) @result{} 3
@end lisp
@end deffn

@deffn {Scheme Procedure} logxor n1 n2 @dots{}
@deffnx {C Function} scm_loxor (n1, n2)
Return the bitwise @sc{xor} of the integer arguments.  A bit is
set in the result if it is set in an odd number of arguments.

@lisp
(logxor) @result{} 0
(logxor 7) @result{} 7
(logxor #b000 #b001 #b011) @result{} 2
(logxor #b000 #b001 #b011 #b011) @result{} 1
@end lisp
@end deffn

@deffn {Scheme Procedure} lognot n
@deffnx {C Function} scm_lognot (n)
Return the integer which is the ones-complement of the integer
argument, ie.@: each 0 bit is changed to 1 and each 1 bit to 0.

@lisp
(number->string (lognot #b10000000) 2)
   @result{} "-10000001"
(number->string (lognot #b0) 2)
   @result{} "-1"
@end lisp
@end deffn

@deffn {Scheme Procedure} logtest j k
@deffnx {C Function} scm_logtest (j, k)
@lisp
(logtest j k) @equiv{} (not (zero? (logand j k)))

(logtest #b0100 #b1011) @result{} #f
(logtest #b0100 #b0111) @result{} #t
@end lisp
@end deffn

@deffn {Scheme Procedure} logbit? index j
@deffnx {C Function} scm_logbit_p (index, j)
@lisp
(logbit? index j) @equiv{} (logtest (integer-expt 2 index) j)

(logbit? 0 #b1101) @result{} #t
(logbit? 1 #b1101) @result{} #f
(logbit? 2 #b1101) @result{} #t
(logbit? 3 #b1101) @result{} #t
(logbit? 4 #b1101) @result{} #f
@end lisp
@end deffn

@deffn {Scheme Procedure} ash n cnt
@deffnx {C Function} scm_ash (n, cnt)
Return @var{n} shifted left by @var{cnt} bits, or shifted right if
@var{cnt} is negative.  This is an ``arithmetic'' shift.

This is effectively a multiplication by @m{2^{cnt}, 2^@var{cnt}}, and
when @var{cnt} is negative it's a division, rounded towards negative
infinity.  (Note that this is not the same rounding as @code{quotient}
does.)

With @var{n} viewed as an infinite precision twos complement,
@code{ash} means a left shift introducing zero bits, or a right shift
dropping bits.

@lisp
(number->string (ash #b1 3) 2)     @result{} "1000"
(number->string (ash #b1010 -1) 2) @result{} "101"

;; -23 is bits ...11101001, -6 is bits ...111010
(ash -23 -2) @result{} -6
@end lisp
@end deffn

@deffn {Scheme Procedure} logcount n
@deffnx {C Function} scm_logcount (n)
Return the number of bits in integer @var{n}.  If integer is
positive, the 1-bits in its binary representation are counted.
If negative, the 0-bits in its two's-complement binary
representation are counted.  If 0, 0 is returned.

@lisp
(logcount #b10101010)
   @result{} 4
(logcount 0)
   @result{} 0
(logcount -2)
   @result{} 1
@end lisp
@end deffn

@deffn {Scheme Procedure} integer-length n
@deffnx {C Function} scm_integer_length (n)
Return the number of bits necessary to represent @var{n}.

For positive @var{n} this is how many bits to the most significant one
bit.  For negative @var{n} it's how many bits to the most significant
zero bit in twos complement form.

@lisp
(integer-length #b10101010) @result{} 8
(integer-length #b1111)     @result{} 4
(integer-length 0)          @result{} 0
(integer-length -1)         @result{} 0
(integer-length -256)       @result{} 8
(integer-length -257)       @result{} 9
@end lisp
@end deffn

@deffn {Scheme Procedure} integer-expt n k
@deffnx {C Function} scm_integer_expt (n, k)
Return @var{n} raised to the non-negative integer exponent
@var{k}.

@lisp
(integer-expt 2 5)
   @result{} 32
(integer-expt -3 3)
   @result{} -27
@end lisp
@end deffn

@deffn {Scheme Procedure} bit-extract n start end
@deffnx {C Function} scm_bit_extract (n, start, end)
Return the integer composed of the @var{start} (inclusive)
through @var{end} (exclusive) bits of @var{n}.  The
@var{start}th bit becomes the 0-th bit in the result.

@lisp
(number->string (bit-extract #b1101101010 0 4) 2)
   @result{} "1010"
(number->string (bit-extract #b1101101010 4 9) 2)
   @result{} "10110"
@end lisp
@end deffn


@node Random
@subsubsection Random Number Generation

Pseudo-random numbers are generated from a random state object, which
can be created with @code{seed->random-state}.  The @var{state}
parameter to the various functions below is optional, it defaults to
the state object in the @code{*random-state*} variable.

@deffn {Scheme Procedure} copy-random-state [state]
@deffnx {C Function} scm_copy_random_state (state)
Return a copy of the random state @var{state}.
@end deffn

@deffn {Scheme Procedure} random n [state]
@deffnx {C Function} scm_random (n, state)
Return a number in [0, @var{n}).

Accepts a positive integer or real n and returns a
number of the same type between zero (inclusive) and
@var{n} (exclusive). The values returned have a uniform
distribution.
@end deffn

@deffn {Scheme Procedure} random:exp [state]
@deffnx {C Function} scm_random_exp (state)
Return an inexact real in an exponential distribution with mean
1.  For an exponential distribution with mean @var{u} use @code{(*
@var{u} (random:exp))}.
@end deffn

@deffn {Scheme Procedure} random:hollow-sphere! vect [state]
@deffnx {C Function} scm_random_hollow_sphere_x (vect, state)
Fills @var{vect} with inexact real random numbers the sum of whose
squares is equal to 1.0.  Thinking of @var{vect} as coordinates in
space of dimension @var{n} @math{=} @code{(vector-length @var{vect})},
the coordinates are uniformly distributed over the surface of the unit
n-sphere.
@end deffn

@deffn {Scheme Procedure} random:normal [state]
@deffnx {C Function} scm_random_normal (state)
Return an inexact real in a normal distribution.  The distribution
used has mean 0 and standard deviation 1.  For a normal distribution
with mean @var{m} and standard deviation @var{d} use @code{(+ @var{m}
(* @var{d} (random:normal)))}.
@end deffn

@deffn {Scheme Procedure} random:normal-vector! vect [state]
@deffnx {C Function} scm_random_normal_vector_x (vect, state)
Fills @var{vect} with inexact real random numbers that are
independent and standard normally distributed
(i.e., with mean 0 and variance 1).
@end deffn

@deffn {Scheme Procedure} random:solid-sphere! vect [state]
@deffnx {C Function} scm_random_solid_sphere_x (vect, state)
Fills @var{vect} with inexact real random numbers the sum of whose
squares is less than 1.0.  Thinking of @var{vect} as coordinates in
space of dimension @var{n} @math{=} @code{(vector-length @var{vect})},
the coordinates are uniformly distributed within the unit
@var{n}-sphere.  The sum of the squares of the numbers is returned.
@c FIXME: What does this mean, particularly the n-sphere part?
@end deffn

@deffn {Scheme Procedure} random:uniform [state]
@deffnx {C Function} scm_random_uniform (state)
Return a uniformly distributed inexact real random number in
[0,1).
@end deffn

@deffn {Scheme Procedure} seed->random-state seed
@deffnx {C Function} scm_seed_to_random_state (seed)
Return a new random state using @var{seed}.
@end deffn

@defvar *random-state*
The global random state used by the above functions when the
@var{state} parameter is not given.
@end defvar


@node Characters
@subsection Characters
@tpindex Characters

@noindent
[@strong{FIXME}: how do you specify regular (non-control) characters?]

Most of the ``control characters'' (those below codepoint 32) in the
@acronym{ASCII} character set, as well as the space, may be referred
to by name: for example, @code{#\tab}, @code{#\esc}, @code{#\stx}, and
so on.  The following table describes the @acronym{ASCII} names for
each character.

@multitable @columnfractions .25 .25 .25 .25
@item 0 = @code{#\nul}
 @tab 1 = @code{#\soh}
 @tab 2 = @code{#\stx}
 @tab 3 = @code{#\etx}
@item 4 = @code{#\eot}
 @tab 5 = @code{#\enq}
 @tab 6 = @code{#\ack}
 @tab 7 = @code{#\bel}
@item 8 = @code{#\bs}
 @tab 9 = @code{#\ht}
 @tab 10 = @code{#\nl}
 @tab 11 = @code{#\vt}
@item 12 = @code{#\np}
 @tab 13 = @code{#\cr}
 @tab 14 = @code{#\so}
 @tab 15 = @code{#\si}
@item 16 = @code{#\dle}
 @tab 17 = @code{#\dc1}
 @tab 18 = @code{#\dc2}
 @tab 19 = @code{#\dc3}
@item 20 = @code{#\dc4}
 @tab 21 = @code{#\nak}
 @tab 22 = @code{#\syn}
 @tab 23 = @code{#\etb}
@item 24 = @code{#\can}
 @tab 25 = @code{#\em}
 @tab 26 = @code{#\sub}
 @tab 27 = @code{#\esc}
@item 28 = @code{#\fs}
 @tab 29 = @code{#\gs}
 @tab 30 = @code{#\rs}
 @tab 31 = @code{#\us}
@item 32 = @code{#\sp}
@end multitable

The ``delete'' character (octal 177) may be referred to with the name
@code{#\del}.

Several characters have more than one name:

@multitable {@code{#\backspace}} {Original}
@item Alias @tab Original
@item @code{#\space} @tab @code{#\sp}
@item @code{#\newline} @tab @code{#\nl}
@item @code{#\tab} @tab @code{#\ht}
@item @code{#\backspace} @tab @code{#\bs}
@item @code{#\return} @tab @code{#\cr}
@item @code{#\page} @tab @code{#\np}
@item @code{#\null} @tab @code{#\nul}
@end multitable

@rnindex char?
@deffn {Scheme Procedure} char? x
@deffnx {C Function} scm_char_p (x)
Return @code{#t} iff @var{x} is a character, else @code{#f}.
@end deffn

@rnindex char=?
@deffn {Scheme Procedure} char=? x y
Return @code{#t} iff @var{x} is the same character as @var{y}, else @code{#f}.
@end deffn

@rnindex char<?
@deffn {Scheme Procedure} char<? x y
Return @code{#t} iff @var{x} is less than @var{y} in the @acronym{ASCII} sequence,
else @code{#f}.
@end deffn

@rnindex char<=?
@deffn {Scheme Procedure} char<=? x y
Return @code{#t} iff @var{x} is less than or equal to @var{y} in the
@acronym{ASCII} sequence, else @code{#f}.
@end deffn

@rnindex char>?
@deffn {Scheme Procedure} char>? x y
Return @code{#t} iff @var{x} is greater than @var{y} in the @acronym{ASCII}
sequence, else @code{#f}.
@end deffn

@rnindex char>=?
@deffn {Scheme Procedure} char>=? x y
Return @code{#t} iff @var{x} is greater than or equal to @var{y} in the
@acronym{ASCII} sequence, else @code{#f}.
@end deffn

@rnindex char-ci=?
@deffn {Scheme Procedure} char-ci=? x y
Return @code{#t} iff @var{x} is the same character as @var{y} ignoring
case, else @code{#f}.
@end deffn

@rnindex char-ci<?
@deffn {Scheme Procedure} char-ci<? x y
Return @code{#t} iff @var{x} is less than @var{y} in the @acronym{ASCII} sequence
ignoring case, else @code{#f}.
@end deffn

@rnindex char-ci<=?
@deffn {Scheme Procedure} char-ci<=? x y
Return @code{#t} iff @var{x} is less than or equal to @var{y} in the
@acronym{ASCII} sequence ignoring case, else @code{#f}.
@end deffn

@rnindex char-ci>?
@deffn {Scheme Procedure} char-ci>? x y
Return @code{#t} iff @var{x} is greater than @var{y} in the @acronym{ASCII}
sequence ignoring case, else @code{#f}.
@end deffn

@rnindex char-ci>=?
@deffn {Scheme Procedure} char-ci>=? x y
Return @code{#t} iff @var{x} is greater than or equal to @var{y} in the
@acronym{ASCII} sequence ignoring case, else @code{#f}.
@end deffn

@rnindex char-alphabetic?
@deffn {Scheme Procedure} char-alphabetic? chr
@deffnx {C Function} scm_char_alphabetic_p (chr)
Return @code{#t} iff @var{chr} is alphabetic, else @code{#f}.
Alphabetic means the same thing as the @code{isalpha} C library function.
@end deffn

@rnindex char-numeric?
@deffn {Scheme Procedure} char-numeric? chr
@deffnx {C Function} scm_char_numeric_p (chr)
Return @code{#t} iff @var{chr} is numeric, else @code{#f}.
Numeric means the same thing as the @code{isdigit} C library function.
@end deffn

@rnindex char-whitespace?
@deffn {Scheme Procedure} char-whitespace? chr
@deffnx {C Function} scm_char_whitespace_p (chr)
Return @code{#t} iff @var{chr} is whitespace, else @code{#f}.
Whitespace means the same thing as the @code{isspace} C library function.
@end deffn

@rnindex char-upper-case?
@deffn {Scheme Procedure} char-upper-case? chr
@deffnx {C Function} scm_char_upper_case_p (chr)
Return @code{#t} iff @var{chr} is uppercase, else @code{#f}.
Uppercase means the same thing as the @code{isupper} C library function.
@end deffn

@rnindex char-lower-case?
@deffn {Scheme Procedure} char-lower-case? chr
@deffnx {C Function} scm_char_lower_case_p (chr)
Return @code{#t} iff @var{chr} is lowercase, else @code{#f}.
Lowercase means the same thing as the @code{islower} C library function.
@end deffn

@deffn {Scheme Procedure} char-is-both? chr
@deffnx {C Function} scm_char_is_both_p (chr)
Return @code{#t} iff @var{chr} is either uppercase or lowercase, else
@code{#f}.  Uppercase and lowercase are as defined by the
@code{isupper} and @code{islower} C library functions.
@end deffn

@rnindex char->integer
@deffn {Scheme Procedure} char->integer chr
@deffnx {C Function} scm_char_to_integer (chr)
Return the number corresponding to ordinal position of @var{chr} in the
@acronym{ASCII} sequence.
@end deffn

@rnindex integer->char
@deffn {Scheme Procedure} integer->char n
@deffnx {C Function} scm_integer_to_char (n)
Return the character at position @var{n} in the @acronym{ASCII} sequence.
@end deffn

@rnindex char-upcase
@deffn {Scheme Procedure} char-upcase chr
@deffnx {C Function} scm_char_upcase (chr)
Return the uppercase character version of @var{chr}.
@end deffn

@rnindex char-downcase
@deffn {Scheme Procedure} char-downcase chr
@deffnx {C Function} scm_char_downcase (chr)
Return the lowercase character version of @var{chr}.
@end deffn

@xref{Classification of Characters,,,libc,GNU C Library Reference
Manual}, for information about the @code{is*} Standard C functions
mentioned above.


@node Strings
@subsection Strings
@tpindex Strings

Strings are fixed-length sequences of characters.  They can be created
by calling constructor procedures, but they can also literally get
entered at the @acronym{REPL} or in Scheme source files.

@c Guile provides a rich set of string processing procedures, because text
@c handling is very important when Guile is used as a scripting language.

Strings always carry the information about how many characters they are
composed of with them, so there is no special end-of-string character,
like in C.  That means that Scheme strings can contain any character,
even the @samp{NUL} character @samp{\0}.  But note: Since most operating
system calls dealing with strings (such as for file operations) expect
strings to be zero-terminated, they might do unexpected things when
called with string containing unusual characters.

@menu
* String Syntax::               Read syntax for strings.
* String Predicates::           Testing strings for certain properties.
* String Constructors::         Creating new string objects.
* List/String Conversion::      Converting from/to lists of characters.
* String Selection::            Select portions from strings.
* String Modification::         Modify parts or whole strings.
* String Comparison::           Lexicographic ordering predicates.
* String Searching::            Searching in strings.
* Alphabetic Case Mapping::     Convert the alphabetic case of strings.
* Appending Strings::           Appending strings to form a new string.
@end menu

@node String Syntax
@subsubsection String Read Syntax

@c  In the following @code is used to get a good font in TeX etc, but
@c  is omitted for Info format, so as not to risk any confusion over
@c  whether surrounding ` ' quotes are part of the escape or are
@c  special in a string (they're not).

The read syntax for strings is an arbitrarily long sequence of
characters enclosed in double quotes (@nicode{"}). @footnote{Actually,
the current implementation restricts strings to a length of
@math{2^24}, or 16,777,216, characters.  Sorry.}

Backslash is an escape character and can be used to insert the
following special characters.  @nicode{\"} and @nicode{\\} are R5RS
standard, the rest are Guile extensions, notice they follow C string
syntax.

@table @asis
@item @nicode{\\}
Backslash character.

@item @nicode{\"}
Double quote character (an unescaped @nicode{"} is otherwise the end
of the string).

@item @nicode{\0}
NUL character (ASCII 0).

@item @nicode{\a}
Bell character (ASCII 7).

@item @nicode{\f}
Formfeed character (ASCII 12).

@item @nicode{\n}
Newline character (ASCII 10).

@item @nicode{\r}
Carriage return character (ASCII 13).

@item @nicode{\t}
Tab character (ASCII 9).

@item @nicode{\v}
Vertical tab character (ASCII 11).

@item @nicode{\xHH}
Character code given by two hexadecimal digits.  For example
@nicode{\x7f} for an ASCII DEL (127).
@end table

@noindent
The following are examples of string literals:

@lisp
"foo"
"bar plonk"
"Hello World"
"\"Hi\", he said."
@end lisp


@node String Predicates
@subsubsection String Predicates

The following procedures can be used to check whether a given string
fulfills some specified property.

@rnindex string?
@deffn {Scheme Procedure} string? obj
@deffnx {C Function} scm_string_p (obj)
Return @code{#t} if @var{obj} is a string, else @code{#f}.
@end deffn

@deffn {Scheme Procedure} string-null? str
@deffnx {C Function} scm_string_null_p (str)
Return @code{#t} if @var{str}'s length is zero, and
@code{#f} otherwise.
@lisp
(string-null? "")  @result{} #t
y                    @result{} "foo"
(string-null? y)     @result{} #f
@end lisp
@end deffn

@node String Constructors
@subsubsection String Constructors

The string constructor procedures create new string objects, possibly
initializing them with some specified character data.

@c FIXME::martin: list->string belongs into `List/String Conversion'

@rnindex string
@rnindex list->string
@deffn {Scheme Procedure} string . chrs
@deffnx {Scheme Procedure} list->string chrs
@deffnx {C Function} scm_string (chrs)
Return a newly allocated string composed of the arguments,
@var{chrs}.
@end deffn

@rnindex make-string
@deffn {Scheme Procedure} make-string k [chr]
@deffnx {C Function} scm_make_string (k, chr)
Return a newly allocated string of
length @var{k}.  If @var{chr} is given, then all elements of
the string are initialized to @var{chr}, otherwise the contents
of the @var{string} are unspecified.
@end deffn

@node List/String Conversion
@subsubsection List/String conversion

When processing strings, it is often convenient to first convert them
into a list representation by using the procedure @code{string->list},
work with the resulting list, and then convert it back into a string.
These procedures are useful for similar tasks.

@rnindex string->list
@deffn {Scheme Procedure} string->list str
@deffnx {C Function} scm_string_to_list (str)
Return a newly allocated list of the characters that make up
the given string @var{str}. @code{string->list} and
@code{list->string} are inverses as far as @samp{equal?} is
concerned.
@end deffn

@deffn {Scheme Procedure} string-split str chr
@deffnx {C Function} scm_string_split (str, chr)
Split the string @var{str} into the a list of the substrings delimited
by appearances of the character @var{chr}.  Note that an empty substring
between separator characters will result in an empty string in the
result list.

@lisp
(string-split "root:x:0:0:root:/root:/bin/bash" #\:)
@result{}
("root" "x" "0" "0" "root" "/root" "/bin/bash")

(string-split "::" #\:)
@result{}
("" "" "")

(string-split "" #\:)
@result{}
("")
@end lisp
@end deffn


@node String Selection
@subsubsection String Selection

Portions of strings can be extracted by these procedures.
@code{string-ref} delivers individual characters whereas
@code{substring} can be used to extract substrings from longer strings.

@rnindex string-length
@deffn {Scheme Procedure} string-length string
@deffnx {C Function} scm_string_length (string)
Return the number of characters in @var{string}.
@end deffn

@rnindex string-ref
@deffn {Scheme Procedure} string-ref str k
@deffnx {C Function} scm_string_ref (str, k)
Return character @var{k} of @var{str} using zero-origin
indexing. @var{k} must be a valid index of @var{str}.
@end deffn

@rnindex string-copy
@deffn {Scheme Procedure} string-copy str
@deffnx {C Function} scm_string_copy (str)
Return a newly allocated copy of the given @var{string}.
@end deffn

@rnindex substring
@deffn {Scheme Procedure} substring str start [end]
@deffnx {C Function} scm_substring (str, start, end)
Return a newly allocated string formed from the characters
of @var{str} beginning with index @var{start} (inclusive) and
ending with index @var{end} (exclusive).
@var{str} must be a string, @var{start} and @var{end} must be
exact integers satisfying:

0 <= @var{start} <= @var{end} <= @code{(string-length @var{str})}.
@end deffn

@node String Modification
@subsubsection String Modification

These procedures are for modifying strings in-place.  This means that the
result of the operation is not a new string; instead, the original string's
memory representation is modified.

@rnindex string-set!
@deffn {Scheme Procedure} string-set! str k chr
@deffnx {C Function} scm_string_set_x (str, k, chr)
Store @var{chr} in element @var{k} of @var{str} and return
an unspecified value. @var{k} must be a valid index of
@var{str}.
@end deffn

@rnindex string-fill!
@deffn {Scheme Procedure} string-fill! str chr
@deffnx {C Function} scm_string_fill_x (str, chr)
Store @var{char} in every element of the given @var{string} and
return an unspecified value.
@end deffn

@deffn {Scheme Procedure} substring-fill! str start end fill
@deffnx {C Function} scm_substring_fill_x (str, start, end, fill)
Change every character in @var{str} between @var{start} and
@var{end} to @var{fill}.

@lisp
(define y "abcdefg")
(substring-fill! y 1 3 #\r)
y
@result{} "arrdefg"
@end lisp
@end deffn

@deffn {Scheme Procedure} substring-move! str1 start1 end1 str2 start2
@deffnx {C Function} scm_substring_move_x (str1, start1, end1, str2, start2)
Copy the substring of @var{str1} bounded by @var{start1} and @var{end1}
into @var{str2} beginning at position @var{start2}.
@var{str1} and @var{str2} can be the same string.
@end deffn


@node String Comparison
@subsubsection String Comparison

The procedures in this section are similar to the character ordering
predicates (@pxref{Characters}), but are defined on character sequences.
They all return @code{#t} on success and @code{#f} on failure.  The
predicates ending in @code{-ci} ignore the character case when comparing
strings.


@rnindex string=?
@deffn {Scheme Procedure} string=? s1 s2
Lexicographic equality predicate; return @code{#t} if the two
strings are the same length and contain the same characters in
the same positions, otherwise return @code{#f}.

The procedure @code{string-ci=?} treats upper and lower case
letters as though they were the same character, but
@code{string=?} treats upper and lower case as distinct
characters.
@end deffn

@rnindex string<?
@deffn {Scheme Procedure} string<? s1 s2
Lexicographic ordering predicate; return @code{#t} if @var{s1}
is lexicographically less than @var{s2}.
@end deffn

@rnindex string<=?
@deffn {Scheme Procedure} string<=? s1 s2
Lexicographic ordering predicate; return @code{#t} if @var{s1}
is lexicographically less than or equal to @var{s2}.
@end deffn

@rnindex string>?
@deffn {Scheme Procedure} string>? s1 s2
Lexicographic ordering predicate; return @code{#t} if @var{s1}
is lexicographically greater than @var{s2}.
@end deffn

@rnindex string>=?
@deffn {Scheme Procedure} string>=? s1 s2
Lexicographic ordering predicate; return @code{#t} if @var{s1}
is lexicographically greater than or equal to @var{s2}.
@end deffn

@rnindex string-ci=?
@deffn {Scheme Procedure} string-ci=? s1 s2
Case-insensitive string equality predicate; return @code{#t} if
the two strings are the same length and their component
characters match (ignoring case) at each position; otherwise
return @code{#f}.
@end deffn

@rnindex string-ci<
@deffn {Scheme Procedure} string-ci<? s1 s2
Case insensitive lexicographic ordering predicate; return
@code{#t} if @var{s1} is lexicographically less than @var{s2}
regardless of case.
@end deffn

@rnindex string<=?
@deffn {Scheme Procedure} string-ci<=? s1 s2
Case insensitive lexicographic ordering predicate; return
@code{#t} if @var{s1} is lexicographically less than or equal
to @var{s2} regardless of case.
@end deffn

@rnindex string-ci>?
@deffn {Scheme Procedure} string-ci>? s1 s2
Case insensitive lexicographic ordering predicate; return
@code{#t} if @var{s1} is lexicographically greater than
@var{s2} regardless of case.
@end deffn

@rnindex string-ci>=?
@deffn {Scheme Procedure} string-ci>=? s1 s2
Case insensitive lexicographic ordering predicate; return
@code{#t} if @var{s1} is lexicographically greater than or
equal to @var{s2} regardless of case.
@end deffn


@node String Searching
@subsubsection String Searching

When searching for the index of a character in a string, these
procedures can be used.

@deffn {Scheme Procedure} string-index str chr [frm [to]]
@deffnx {C Function} scm_string_index (str, chr, frm, to)
Return the index of the first occurrence of @var{chr} in
@var{str}.  The optional integer arguments @var{frm} and
@var{to} limit the search to a portion of the string.  This
procedure essentially implements the @code{index} or
@code{strchr} functions from the C library.

@lisp
(string-index "weiner" #\e)
@result{} 1

(string-index "weiner" #\e 2)
@result{} 4

(string-index "weiner" #\e 2 4)
@result{} #f
@end lisp
@end deffn

@deffn {Scheme Procedure} string-rindex str chr [frm [to]]
@deffnx {C Function} scm_string_rindex (str, chr, frm, to)
Like @code{string-index}, but search from the right of the
string rather than from the left.  This procedure essentially
implements the @code{rindex} or @code{strrchr} functions from
the C library.

@lisp
(string-rindex "weiner" #\e)
@result{} 4

(string-rindex "weiner" #\e 2 4)
@result{} #f

(string-rindex "weiner" #\e 2 5)
@result{} 4
@end lisp
@end deffn

@node Alphabetic Case Mapping
@subsubsection Alphabetic Case Mapping

These are procedures for mapping strings to their upper- or lower-case
equivalents, respectively, or for capitalizing strings.

@deffn {Scheme Procedure} string-upcase str
@deffnx {C Function} scm_string_upcase (str)
Return a freshly allocated string containing the characters of
@var{str} in upper case.
@end deffn

@deffn {Scheme Procedure} string-upcase! str
@deffnx {C Function} scm_string_upcase_x (str)
Destructively upcase every character in @var{str} and return
@var{str}.
@lisp
y                  @result{} "arrdefg"
(string-upcase! y) @result{} "ARRDEFG"
y                  @result{} "ARRDEFG"
@end lisp
@end deffn

@deffn {Scheme Procedure} string-downcase str
@deffnx {C Function} scm_string_downcase (str)
Return a freshly allocation string containing the characters in
@var{str} in lower case.
@end deffn

@deffn {Scheme Procedure} string-downcase! str
@deffnx {C Function} scm_string_downcase_x (str)
Destructively downcase every character in @var{str} and return
@var{str}.
@lisp
y                     @result{} "ARRDEFG"
(string-downcase! y)  @result{} "arrdefg"
y                     @result{} "arrdefg"
@end lisp
@end deffn

@deffn {Scheme Procedure} string-capitalize str
@deffnx {C Function} scm_string_capitalize (str)
Return a freshly allocated string with the characters in
@var{str}, where the first character of every word is
capitalized.
@end deffn

@deffn {Scheme Procedure} string-capitalize! str
@deffnx {C Function} scm_string_capitalize_x (str)
Upcase the first character of every word in @var{str}
destructively and return @var{str}.

@lisp
y                      @result{} "hello world"
(string-capitalize! y) @result{} "Hello World"
y                      @result{} "Hello World"
@end lisp
@end deffn


@node Appending Strings
@subsubsection Appending Strings

The procedure @code{string-append} appends several strings together to
form a longer result string.

@rnindex string-append
@deffn {Scheme Procedure} string-append . args
@deffnx {C Function} scm_string_append (args)
Return a newly allocated string whose characters form the
concatenation of the given strings, @var{args}.

@example
(let ((h "hello "))
  (string-append h "world"))
@result{} "hello world"
@end example
@end deffn


@node Regular Expressions
@subsection Regular Expressions
@tpindex Regular expressions

@cindex regular expressions
@cindex regex
@cindex emacs regexp

A @dfn{regular expression} (or @dfn{regexp}) is a pattern that
describes a whole class of strings.  A full description of regular
expressions and their syntax is beyond the scope of this manual;
an introduction can be found in the Emacs manual (@pxref{Regexps,
, Syntax of Regular Expressions, emacs, The GNU Emacs Manual}), or
in many general Unix reference books.

If your system does not include a POSIX regular expression library,
and you have not linked Guile with a third-party regexp library such
as Rx, these functions will not be available.  You can tell whether
your Guile installation includes regular expression support by
checking whether @code{(provided? 'regex)} returns true.

The following regexp and string matching features are provided by the
@code{(ice-9 regex)} module.  Before using the described functions,
you should load this module by executing @code{(use-modules (ice-9
regex))}.

@menu
* Regexp Functions::            Functions that create and match regexps.
* Match Structures::            Finding what was matched by a regexp.
* Backslash Escapes::           Removing the special meaning of regexp
                                meta-characters.
@end menu


@node Regexp Functions
@subsubsection Regexp Functions

By default, Guile supports POSIX extended regular expressions.
That means that the characters @samp{(}, @samp{)}, @samp{+} and
@samp{?} are special, and must be escaped if you wish to match the
literal characters.

This regular expression interface was modeled after that
implemented by SCSH, the Scheme Shell.  It is intended to be
upwardly compatible with SCSH regular expressions.

@deffn {Scheme Procedure} string-match pattern str [start]
Compile the string @var{pattern} into a regular expression and compare
it with @var{str}.  The optional numeric argument @var{start} specifies
the position of @var{str} at which to begin matching.

@code{string-match} returns a @dfn{match structure} which
describes what, if anything, was matched by the regular
expression.  @xref{Match Structures}.  If @var{str} does not match
@var{pattern} at all, @code{string-match} returns @code{#f}.
@end deffn

Two examples of a match follow.  In the first example, the pattern
matches the four digits in the match string.  In the second, the pattern
matches nothing.

@example
(string-match "[0-9][0-9][0-9][0-9]" "blah2002")
@result{} #("blah2002" (4 . 8))

(string-match "[A-Za-z]" "123456")
@result{} #f
@end example

Each time @code{string-match} is called, it must compile its
@var{pattern} argument into a regular expression structure.  This
operation is expensive, which makes @code{string-match} inefficient if
the same regular expression is used several times (for example, in a
loop).  For better performance, you can compile a regular expression in
advance and then match strings against the compiled regexp.

@deffn {Scheme Procedure} make-regexp pat flag@dots{}
@deffnx {C Function} scm_make_regexp (pat, flaglst)
Compile the regular expression described by @var{pat}, and
return the compiled regexp structure.  If @var{pat} does not
describe a legal regular expression, @code{make-regexp} throws
a @code{regular-expression-syntax} error.

The @var{flag} arguments change the behavior of the compiled
regular expression.  The following values may be supplied:

@defvar regexp/icase
Consider uppercase and lowercase letters to be the same when
matching.
@end defvar

@defvar regexp/newline
If a newline appears in the target string, then permit the
@samp{^} and @samp{$} operators to match immediately after or
immediately before the newline, respectively.  Also, the
@samp{.} and @samp{[^...]} operators will never match a newline
character.  The intent of this flag is to treat the target
string as a buffer containing many lines of text, and the
regular expression as a pattern that may match a single one of
those lines.
@end defvar

@defvar regexp/basic
Compile a basic (``obsolete'') regexp instead of the extended
(``modern'') regexps that are the default.  Basic regexps do
not consider @samp{|}, @samp{+} or @samp{?} to be special
characters, and require the @samp{@{...@}} and @samp{(...)}
metacharacters to be backslash-escaped (@pxref{Backslash
Escapes}).  There are several other differences between basic
and extended regular expressions, but these are the most
significant.
@end defvar

@defvar regexp/extended
Compile an extended regular expression rather than a basic
regexp.  This is the default behavior; this flag will not
usually be needed.  If a call to @code{make-regexp} includes
both @code{regexp/basic} and @code{regexp/extended} flags, the
one which comes last will override the earlier one.
@end defvar
@end deffn

@deffn {Scheme Procedure} regexp-exec rx str [start [flags]]
@deffnx {C Function} scm_regexp_exec (rx, str, start, flags)
Match the compiled regular expression @var{rx} against
@code{str}.  If the optional integer @var{start} argument is
provided, begin matching from that position in the string.
Return a match structure describing the results of the match,
or @code{#f} if no match could be found.

The @var{flags} arguments change the matching behavior.
The following flags may be supplied:

@defvar regexp/notbol
Operator @samp{^} always fails (unless @code{regexp/newline}
is used).  Use this when the beginning of the string should
not be considered the beginning of a line.
@end defvar

@defvar regexp/noteol
Operator @samp{$} always fails (unless @code{regexp/newline}
is used).  Use this when the end of the string should not be
considered the end of a line.
@end defvar
@end deffn

@lisp
;; Regexp to match uppercase letters
(define r (make-regexp "[A-Z]*"))

;; Regexp to match letters, ignoring case
(define ri (make-regexp "[A-Z]*" regexp/icase))

;; Search for bob using regexp r
(match:substring (regexp-exec r "bob"))
@result{} ""                  ; no match

;; Search for bob using regexp ri
(match:substring (regexp-exec ri "Bob"))
@result{} "Bob"               ; matched case insensitive
@end lisp

@deffn {Scheme Procedure} regexp? obj
@deffnx {C Function} scm_regexp_p (obj)
Return @code{#t} if @var{obj} is a compiled regular expression,
or @code{#f} otherwise.
@end deffn

Regular expressions are commonly used to find patterns in one string and
replace them with the contents of another string.

@c begin (scm-doc-string "regex.scm" "regexp-substitute")
@deffn {Scheme Procedure} regexp-substitute port match [item@dots{}]
Write to the output port @var{port} selected contents of the match
structure @var{match}.  Each @var{item} specifies what should be
written, and may be one of the following arguments:

@itemize @bullet
@item
A string.  String arguments are written out verbatim.

@item
An integer.  The submatch with that number is written.

@item
The symbol @samp{pre}.  The portion of the matched string preceding
the regexp match is written.

@item
The symbol @samp{post}.  The portion of the matched string following
the regexp match is written.
@end itemize

The @var{port} argument may be @code{#f}, in which case nothing is
written; instead, @code{regexp-substitute} constructs a string from the
specified @var{item}s and returns that.
@end deffn

The following example takes a regular expression that matches a standard
@sc{yyyymmdd}-format date such as @code{"20020828"}.  The
@code{regexp-substitute} call returns a string computed from the
information in the match structure, consisting of the fields and text
from the original string reordered and reformatted.

@lisp
(define date-regex "([0-9][0-9][0-9][0-9])([0-9][0-9])([0-9][0-9])")
(define s "Date 20020429 12am.")
(define sm (string-match date-regex s))
(regexp-substitute #f sm 'pre 2 "-" 3 "-" 1 'post " (" 0 ")")
@result{} "Date 04-29-2002 12am. (20020429)"
@end lisp

@c begin (scm-doc-string "regex.scm" "regexp-substitute")
@deffn {Scheme Procedure} regexp-substitute/global port regexp target [item@dots{}]
Similar to @code{regexp-substitute}, but can be used to perform global
substitutions on @var{str}.  Instead of taking a match structure as an
argument, @code{regexp-substitute/global} takes two string arguments: a
@var{regexp} string describing a regular expression, and a @var{target}
string which should be matched against this regular expression.

Each @var{item} behaves as in @code{regexp-substitute}, with the
following exceptions:

@itemize @bullet
@item
A function may be supplied.  When this function is called, it will be
passed one argument: a match structure for a given regular expression
match.  It should return a string to be written out to @var{port}.

@item
The @samp{post} symbol causes @code{regexp-substitute/global} to recurse
on the unmatched portion of @var{str}.  This @emph{must} be supplied in
order to perform global search-and-replace on @var{str}; if it is not
present among the @var{item}s, then @code{regexp-substitute/global} will
return after processing a single match.
@end itemize
@end deffn

The example above for @code{regexp-substitute} could be rewritten as
follows to remove the @code{string-match} stage:

@lisp
(define date-regex "([0-9][0-9][0-9][0-9])([0-9][0-9])([0-9][0-9])")
(define s "Date 20020429 12am.")
(regexp-substitute/global #f date-regex s
  'pre 2 "-" 3 "-" 1 'post " (" 0 ")")
@result{} "Date 04-29-2002 12am. (20020429)"
@end lisp


@node Match Structures
@subsubsection Match Structures

@cindex match structures

A @dfn{match structure} is the object returned by @code{string-match} and
@code{regexp-exec}.  It describes which portion of a string, if any,
matched the given regular expression.  Match structures include: a
reference to the string that was checked for matches; the starting and
ending positions of the regexp match; and, if the regexp included any
parenthesized subexpressions, the starting and ending positions of each
submatch.

In each of the regexp match functions described below, the @code{match}
argument must be a match structure returned by a previous call to
@code{string-match} or @code{regexp-exec}.  Most of these functions
return some information about the original target string that was
matched against a regular expression; we will call that string
@var{target} for easy reference.

@c begin (scm-doc-string "regex.scm" "regexp-match?")
@deffn {Scheme Procedure} regexp-match? obj
Return @code{#t} if @var{obj} is a match structure returned by a
previous call to @code{regexp-exec}, or @code{#f} otherwise.
@end deffn

@c begin (scm-doc-string "regex.scm" "match:substring")
@deffn {Scheme Procedure} match:substring match [n]
Return the portion of @var{target} matched by subexpression number
@var{n}.  Submatch 0 (the default) represents the entire regexp match.
If the regular expression as a whole matched, but the subexpression
number @var{n} did not match, return @code{#f}.
@end deffn

@lisp
(define s (string-match "[0-9][0-9][0-9][0-9]" "blah2002foo"))
(match:substring s)
@result{} "2002"

;; match starting at offset 6 in the string
(match:substring
  (string-match "[0-9][0-9][0-9][0-9]" "blah987654" 6))
@result{} "7654"
@end lisp

@c begin (scm-doc-string "regex.scm" "match:start")
@deffn {Scheme Procedure} match:start match [n]
Return the starting position of submatch number @var{n}.
@end deffn

In the following example, the result is 4, since the match starts at
character index 4:

@lisp
(define s (string-match "[0-9][0-9][0-9][0-9]" "blah2002foo"))
(match:start s)
@result{} 4
@end lisp

@c begin (scm-doc-string "regex.scm" "match:end")
@deffn {Scheme Procedure} match:end match [n]
Return the ending position of submatch number @var{n}.
@end deffn

In the following example, the result is 8, since the match runs between
characters 4 and 8 (i.e. the ``2002'').

@lisp
(define s (string-match "[0-9][0-9][0-9][0-9]" "blah2002foo"))
(match:end s)
@result{} 8
@end lisp

@c begin (scm-doc-string "regex.scm" "match:prefix")
@deffn {Scheme Procedure} match:prefix match
Return the unmatched portion of @var{target} preceding the regexp match.

@lisp
(define s (string-match "[0-9][0-9][0-9][0-9]" "blah2002foo"))
(match:prefix s)
@result{} "blah"
@end lisp
@end deffn

@c begin (scm-doc-string "regex.scm" "match:suffix")
@deffn {Scheme Procedure} match:suffix match
Return the unmatched portion of @var{target} following the regexp match.
@end deffn

@lisp
(define s (string-match "[0-9][0-9][0-9][0-9]" "blah2002foo"))
(match:suffix s)
@result{} "foo"
@end lisp

@c begin (scm-doc-string "regex.scm" "match:count")
@deffn {Scheme Procedure} match:count match
Return the number of parenthesized subexpressions from @var{match}.
Note that the entire regular expression match itself counts as a
subexpression, and failed submatches are included in the count.
@end deffn

@c begin (scm-doc-string "regex.scm" "match:string")
@deffn {Scheme Procedure} match:string match
Return the original @var{target} string.
@end deffn

@lisp
(define s (string-match "[0-9][0-9][0-9][0-9]" "blah2002foo"))
(match:string s)
@result{} "blah2002foo"
@end lisp


@node Backslash Escapes
@subsubsection Backslash Escapes

Sometimes you will want a regexp to match characters like @samp{*} or
@samp{$} exactly.  For example, to check whether a particular string
represents a menu entry from an Info node, it would be useful to match
it against a regexp like @samp{^* [^:]*::}.  However, this won't work;
because the asterisk is a metacharacter, it won't match the @samp{*} at
the beginning of the string.  In this case, we want to make the first
asterisk un-magic.

You can do this by preceding the metacharacter with a backslash
character @samp{\}.  (This is also called @dfn{quoting} the
metacharacter, and is known as a @dfn{backslash escape}.)  When Guile
sees a backslash in a regular expression, it considers the following
glyph to be an ordinary character, no matter what special meaning it
would ordinarily have.  Therefore, we can make the above example work by
changing the regexp to @samp{^\* [^:]*::}.  The @samp{\*} sequence tells
the regular expression engine to match only a single asterisk in the
target string.

Since the backslash is itself a metacharacter, you may force a regexp to
match a backslash in the target string by preceding the backslash with
itself.  For example, to find variable references in a @TeX{} program,
you might want to find occurrences of the string @samp{\let\} followed
by any number of alphabetic characters.  The regular expression
@samp{\\let\\[A-Za-z]*} would do this: the double backslashes in the
regexp each match a single backslash in the target string.

@c begin (scm-doc-string "regex.scm" "regexp-quote")
@deffn {Scheme Procedure} regexp-quote str
Quote each special character found in @var{str} with a backslash, and
return the resulting string.
@end deffn

@strong{Very important:} Using backslash escapes in Guile source code
(as in Emacs Lisp or C) can be tricky, because the backslash character
has special meaning for the Guile reader.  For example, if Guile
encounters the character sequence @samp{\n} in the middle of a string
while processing Scheme code, it replaces those characters with a
newline character.  Similarly, the character sequence @samp{\t} is
replaced by a horizontal tab.  Several of these @dfn{escape sequences}
are processed by the Guile reader before your code is executed.
Unrecognized escape sequences are ignored: if the characters @samp{\*}
appear in a string, they will be translated to the single character
@samp{*}.

This translation is obviously undesirable for regular expressions, since
we want to be able to include backslashes in a string in order to
escape regexp metacharacters.  Therefore, to make sure that a backslash
is preserved in a string in your Guile program, you must use @emph{two}
consecutive backslashes:

@lisp
(define Info-menu-entry-pattern (make-regexp "^\\* [^:]*"))
@end lisp

The string in this example is preprocessed by the Guile reader before
any code is executed.  The resulting argument to @code{make-regexp} is
the string @samp{^\* [^:]*}, which is what we really want.

This also means that in order to write a regular expression that matches
a single backslash character, the regular expression string in the
source code must include @emph{four} backslashes.  Each consecutive pair
of backslashes gets translated by the Guile reader to a single
backslash, and the resulting double-backslash is interpreted by the
regexp engine as matching a single backslash character.  Hence:

@lisp
(define tex-variable-pattern (make-regexp "\\\\let\\\\=[A-Za-z]*"))
@end lisp

The reason for the unwieldiness of this syntax is historical.  Both
regular expression pattern matchers and Unix string processing systems
have traditionally used backslashes with the special meanings
described above.  The POSIX regular expression specification and ANSI C
standard both require these semantics.  Attempting to abandon either
convention would cause other kinds of compatibility problems, possibly
more severe ones.  Therefore, without extending the Scheme reader to
support strings with different quoting conventions (an ungainly and
confusing extension when implemented in other languages), we must adhere
to this cumbersome escape syntax.


@node Symbols
@subsection Symbols
@tpindex Symbols

Symbols in Scheme are widely used in three ways: as items of discrete
data, as lookup keys for alists and hash tables, and to denote variable
references.

A @dfn{symbol} is similar to a string in that it is defined by a
sequence of characters.  The sequence of characters is known as the
symbol's @dfn{name}.  In the usual case --- that is, where the symbol's
name doesn't include any characters that could be confused with other
elements of Scheme syntax --- a symbol is written in a Scheme program by
writing the sequence of characters that make up the name, @emph{without}
any quotation marks or other special syntax.  For example, the symbol
whose name is ``multiply-by-2'' is written, simply:

@lisp
multiply-by-2
@end lisp

Notice how this differs from a @emph{string} with contents
``multiply-by-2'', which is written with double quotation marks, like
this:

@lisp
"multiply-by-2"
@end lisp

Looking beyond how they are written, symbols are different from strings
in two important respects.

The first important difference is uniqueness.  If the same-looking
string is read twice from two different places in a program, the result
is two @emph{different} string objects whose contents just happen to be
the same.  If, on the other hand, the same-looking symbol is read twice
from two different places in a program, the result is the @emph{same}
symbol object both times.

Given two read symbols, you can use @code{eq?} to test whether they are
the same (that is, have the same name).  @code{eq?} is the most
efficient comparison operator in Scheme, and comparing two symbols like
this is as fast as comparing, for example, two numbers.  Given two
strings, on the other hand, you must use @code{equal?} or
@code{string=?}, which are much slower comparison operators, to
determine whether the strings have the same contents.

@lisp
(define sym1 (quote hello))
(define sym2 (quote hello))
(eq? sym1 sym2) @result{} #t

(define str1 "hello")
(define str2 "hello")
(eq? str1 str2) @result{} #f
(equal? str1 str2) @result{} #t
@end lisp

The second important difference is that symbols, unlike strings, are not
self-evaluating.  This is why we need the @code{(quote @dots{})}s in the
example above: @code{(quote hello)} evaluates to the symbol named
"hello" itself, whereas an unquoted @code{hello} is @emph{read} as the
symbol named "hello" and evaluated as a variable reference @dots{} about
which more below (@pxref{Symbol Variables}).

@menu
* Symbol Data::                 Symbols as discrete data.
* Symbol Keys::                 Symbols as lookup keys.
* Symbol Variables::            Symbols as denoting variables.
* Symbol Primitives::           Operations related to symbols.
* Symbol Props::                Function slots and property lists.
* Symbol Read Syntax::          Extended read syntax for symbols.
* Symbol Uninterned::           Uninterned symbols.
@end menu


@node Symbol Data
@subsubsection Symbols as Discrete Data

Numbers and symbols are similar to the extent that they both lend
themselves to @code{eq?} comparison.  But symbols are more descriptive
than numbers, because a symbol's name can be used directly to describe
the concept for which that symbol stands.

For example, imagine that you need to represent some colours in a
computer program.  Using numbers, you would have to choose arbitrarily
some mapping between numbers and colours, and then take care to use that
mapping consistently:

@lisp
;; 1=red, 2=green, 3=purple

(if (eq? (colour-of car) 1)
    ...)
@end lisp

@noindent
You can make the mapping more explicit and the code more readable by
defining constants:

@lisp
(define red 1)
(define green 2)
(define purple 3)

(if (eq? (colour-of car) red)
    ...)
@end lisp

@noindent
But the simplest and clearest approach is not to use numbers at all, but
symbols whose names specify the colours that they refer to:

@lisp
(if (eq? (colour-of car) 'red)
    ...)
@end lisp

The descriptive advantages of symbols over numbers increase as the set
of concepts that you want to describe grows.  Suppose that a car object
can have other properties as well, such as whether it has or uses:

@itemize @bullet
@item
automatic or manual transmission
@item
leaded or unleaded fuel
@item
power steering (or not).
@end itemize

@noindent
Then a car's combined property set could be naturally represented and
manipulated as a list of symbols:

@lisp
(properties-of car1)
@result{}
(red manual unleaded power-steering)

(if (memq 'power-steering (properties-of car1))
    (display "Unfit people can drive this car.\n")
    (display "You'll need strong arms to drive this car!\n"))
@print{}
Unfit people can drive this car.
@end lisp

Remember, the fundamental property of symbols that we are relying on
here is that an occurrence of @code{'red} in one part of a program is an
@emph{indistinguishable} symbol from an occurrence of @code{'red} in
another part of a program; this means that symbols can usefully be
compared using @code{eq?}.  At the same time, symbols have naturally
descriptive names.  This combination of efficiency and descriptive power
makes them ideal for use as discrete data.


@node Symbol Keys
@subsubsection Symbols as Lookup Keys

Given their efficiency and descriptive power, it is natural to use
symbols as the keys in an association list or hash table.

To illustrate this, consider a more structured representation of the car
properties example from the preceding subsection.  Rather than
mixing all the properties up together in a flat list, we could use an
association list like this:

@lisp
(define car1-properties '((colour . red)
                          (transmission . manual)
                          (fuel . unleaded)
                          (steering . power-assisted)))
@end lisp

Notice how this structure is more explicit and extensible than the flat
list.  For example it makes clear that @code{manual} refers to the
transmission rather than, say, the windows or the locking of the car.
It also allows further properties to use the same symbols among their
possible values without becoming ambiguous:

@lisp
(define car1-properties '((colour . red)
                          (transmission . manual)
                          (fuel . unleaded)
                          (steering . power-assisted)
                          (seat-colour . red)
                          (locking . manual)))
@end lisp

With a representation like this, it is easy to use the efficient
@code{assq-XXX} family of procedures (@pxref{Association Lists}) to
extract or change individual pieces of information:

@lisp
(assq-ref car1-properties 'fuel) @result{} unleaded
(assq-ref car1-properties 'transmission) @result{} manual

(assq-set! car1-properties 'seat-colour 'black)
@result{}
((colour . red)
 (transmission . manual)
 (fuel . unleaded)
 (steering . power-assisted)
 (seat-colour . black)
 (locking . manual)))
@end lisp

Hash tables also have keys, and exactly the same arguments apply to the
use of symbols in hash tables as in association lists.  The hash value
that Guile uses to decide where to add a symbol-keyed entry to a hash
table can be obtained by calling the @code{symbol-hash} procedure:

@deffn {Scheme Procedure} symbol-hash symbol
@deffnx {C Function} scm_symbol_hash (symbol)
Return a hash value for @var{symbol}.
@end deffn

See @ref{Hash Tables} for information about hash tables in general, and
for why you might choose to use a hash table rather than an association
list.


@node Symbol Variables
@subsubsection Symbols as Denoting Variables

When an unquoted symbol in a Scheme program is evaluated, it is
interpreted as a variable reference, and the result of the evaluation is
the appropriate variable's value.

For example, when the expression @code{(string-length "abcd")} is read
and evaluated, the sequence of characters @code{string-length} is read
as the symbol whose name is "string-length".  This symbol is associated
with a variable whose value is the procedure that implements string
length calculation.  Therefore evaluation of the @code{string-length}
symbol results in that procedure.

The details of the connection between an unquoted symbol and the
variable to which it refers are explained elsewhere.  See @ref{Binding
Constructs}, for how associations between symbols and variables are
created, and @ref{Modules}, for how those associations are affected by
Guile's module system.


@node Symbol Primitives
@subsubsection Operations Related to Symbols

Given any Scheme value, you can determine whether it is a symbol using
the @code{symbol?} primitive:

@rnindex symbol?
@deffn {Scheme Procedure} symbol? obj
@deffnx {C Function} scm_symbol_p (obj)
Return @code{#t} if @var{obj} is a symbol, otherwise return
@code{#f}.
@end deffn

Once you know that you have a symbol, you can obtain its name as a
string by calling @code{symbol->string}.  Note that Guile differs by
default from R5RS on the details of @code{symbol->string} as regards
case-sensitivity:

@rnindex symbol->string
@deffn {Scheme Procedure} symbol->string s
@deffnx {C Function} scm_symbol_to_string (s)
Return the name of symbol @var{s} as a string.  By default, Guile reads
symbols case-sensitively, so the string returned will have the same case
variation as the sequence of characters that caused @var{s} to be
created.

If Guile is set to read symbols case-insensitively (as specified by
R5RS), and @var{s} comes into being as part of a literal expression
(@pxref{Literal expressions,,,r5rs, The Revised^5 Report on Scheme}) or
by a call to the @code{read} or @code{string-ci->symbol} procedures,
Guile converts any alphabetic characters in the symbol's name to
lower case before creating the symbol object, so the string returned
here will be in lower case.

If @var{s} was created by @code{string->symbol}, the case of characters
in the string returned will be the same as that in the string that was
passed to @code{string->symbol}, regardless of Guile's case-sensitivity
setting at the time @var{s} was created.

It is an error to apply mutation procedures like @code{string-set!} to
strings returned by this procedure.
@end deffn

Most symbols are created by writing them literally in code.  However it
is also possible to create symbols programmatically using the following
@code{string->symbol} and @code{string-ci->symbol} procedures:

@rnindex string->symbol
@deffn {Scheme Procedure} string->symbol string
@deffnx {C Function} scm_string_to_symbol (string)
Return the symbol whose name is @var{string}.  This procedure can create
symbols with names containing special characters or letters in the
non-standard case, but it is usually a bad idea to create such symbols
because in some implementations of Scheme they cannot be read as
themselves.
@end deffn

@deffn {Scheme Procedure} string-ci->symbol str
@deffnx {C Function} scm_string_ci_to_symbol (str)
Return the symbol whose name is @var{str}.  If Guile is currently
reading symbols case-insensitively, @var{str} is converted to lowercase
before the returned symbol is looked up or created.
@end deffn

The following examples illustrate Guile's detailed behaviour as regards
the case-sensitivity of symbols:

@lisp
(read-enable 'case-insensitive)   ; R5RS compliant behaviour

(symbol->string 'flying-fish)    @result{} "flying-fish"
(symbol->string 'Martin)         @result{} "martin"
(symbol->string
   (string->symbol "Malvina"))   @result{} "Malvina"

(eq? 'mISSISSIppi 'mississippi)  @result{} #t
(string->symbol "mISSISSIppi")   @result{} mISSISSIppi
(eq? 'bitBlt (string->symbol "bitBlt")) @result{} #f
(eq? 'LolliPop
  (string->symbol (symbol->string 'LolliPop))) @result{} #t
(string=? "K. Harper, M.D."
  (symbol->string
    (string->symbol "K. Harper, M.D."))) @result{} #t

(read-disable 'case-insensitive)   ; Guile default behaviour

(symbol->string 'flying-fish)    @result{} "flying-fish"
(symbol->string 'Martin)         @result{} "Martin"
(symbol->string
   (string->symbol "Malvina"))   @result{} "Malvina"

(eq? 'mISSISSIppi 'mississippi)  @result{} #f
(string->symbol "mISSISSIppi")   @result{} mISSISSIppi
(eq? 'bitBlt (string->symbol "bitBlt")) @result{} #t
(eq? 'LolliPop
  (string->symbol (symbol->string 'LolliPop))) @result{} #t
(string=? "K. Harper, M.D."
  (symbol->string
    (string->symbol "K. Harper, M.D."))) @result{} #t
@end lisp

From C, there are lower level functions that construct a Scheme symbol
from a null terminated C string or from a sequence of bytes whose length
is specified explicitly.

@deffn {C Function} scm_str2symbol (const char * name)
@deffnx {C Function} scm_mem2symbol (const char * name, size_t len)
Construct and return a Scheme symbol whose name is specified by
@var{name}.  For @code{scm_str2symbol} @var{name} must be null
terminated; For @code{scm_mem2symbol} the length of @var{name} is
specified explicitly by @var{len}.
@end deffn

Finally, some applications, especially those that generate new Scheme
code dynamically, need to generate symbols for use in the generated
code.  The @code{gensym} primitive meets this need:

@deffn {Scheme Procedure} gensym [prefix]
@deffnx {C Function} scm_gensym (prefix)
Create a new symbol with a name constructed from a prefix and a counter
value.  The string @var{prefix} can be specified as an optional
argument.  Default prefix is @samp{@w{ g}}.  The counter is increased by 1
at each call.  There is no provision for resetting the counter.
@end deffn

The symbols generated by @code{gensym} are @emph{likely} to be unique,
since their names begin with a space and it is only otherwise possible
to generate such symbols if a programmer goes out of their way to do
so.  Uniqueness can be guaranteed by instead using uninterned symbols
(@pxref{Symbol Uninterned}), though they can't be usefully written out
and read back in.


@node Symbol Props
@subsubsection Function Slots and Property Lists

In traditional Lisp dialects, symbols are often understood as having
three kinds of value at once:

@itemize @bullet
@item
a @dfn{variable} value, which is used when the symbol appears in
code in a variable reference context

@item
a @dfn{function} value, which is used when the symbol appears in
code in a function name position (i.e. as the first element in an
unquoted list)

@item
a @dfn{property list} value, which is used when the symbol is given as
the first argument to Lisp's @code{put} or @code{get} functions.
@end itemize

Although Scheme (as one of its simplifications with respect to Lisp)
does away with the distinction between variable and function namespaces,
Guile currently retains some elements of the traditional structure in
case they turn out to be useful when implementing translators for other
languages, in particular Emacs Lisp.

Specifically, Guile symbols have two extra slots. for a symbol's
property list, and for its ``function value.''  The following procedures
are provided to access these slots.

@deffn {Scheme Procedure} symbol-fref symbol
@deffnx {C Function} scm_symbol_fref (symbol)
Return the contents of @var{symbol}'s @dfn{function slot}.
@end deffn

@deffn {Scheme Procedure} symbol-fset! symbol value
@deffnx {C Function} scm_symbol_fset_x (symbol, value)
Set the contents of @var{symbol}'s function slot to @var{value}.
@end deffn

@deffn {Scheme Procedure} symbol-pref symbol
@deffnx {C Function} scm_symbol_pref (symbol)
Return the @dfn{property list} currently associated with @var{symbol}.
@end deffn

@deffn {Scheme Procedure} symbol-pset! symbol value
@deffnx {C Function} scm_symbol_pset_x (symbol, value)
Set @var{symbol}'s property list to @var{value}.
@end deffn

@deffn {Scheme Procedure} symbol-property sym prop
From @var{sym}'s property list, return the value for property
@var{prop}.  The assumption is that @var{sym}'s property list is an
association list whose keys are distinguished from each other using
@code{equal?}; @var{prop} should be one of the keys in that list.  If
the property list has no entry for @var{prop}, @code{symbol-property}
returns @code{#f}.
@end deffn

@deffn {Scheme Procedure} set-symbol-property! sym prop val
In @var{sym}'s property list, set the value for property @var{prop} to
@var{val}, or add a new entry for @var{prop}, with value @var{val}, if
none already exists.  For the structure of the property list, see
@code{symbol-property}.
@end deffn

@deffn {Scheme Procedure} symbol-property-remove! sym prop
From @var{sym}'s property list, remove the entry for property
@var{prop}, if there is one.  For the structure of the property list,
see @code{symbol-property}.
@end deffn

Support for these extra slots may be removed in a future release, and it
is probably better to avoid using them.  (In release 1.6, Guile itself
uses the property list slot sparingly, and the function slot not at
all.)  For a more modern and Schemely approach to properties, see
@ref{Object Properties}.


@node Symbol Read Syntax
@subsubsection Extended Read Syntax for Symbols

The read syntax for a symbol is a sequence of letters, digits, and
@dfn{extended alphabetic characters}, beginning with a character that
cannot begin a number.  In addition, the special cases of @code{+},
@code{-}, and @code{...} are read as symbols even though numbers can
begin with @code{+}, @code{-} or @code{.}.

Extended alphabetic characters may be used within identifiers as if
they were letters.  The set of extended alphabetic characters is:

@example
! $ % & * + - . / : < = > ? @@ ^ _ ~
@end example

In addition to the standard read syntax defined above (which is taken
from R5RS (@pxref{Formal syntax,,,r5rs,The Revised^5 Report on
Scheme})), Guile provides an extended symbol read syntax that allows the
inclusion of unusual characters such as space characters, newlines and
parentheses.  If (for whatever reason) you need to write a symbol
containing characters not mentioned above, you can do so as follows.

@itemize @bullet
@item
Begin the symbol with the characters @code{#@{},

@item
write the characters of the symbol and

@item
finish the symbol with the characters @code{@}#}.
@end itemize

Here are a few examples of this form of read syntax.  The first symbol
needs to use extended syntax because it contains a space character, the
second because it contains a line break, and the last because it looks
like a number.

@lisp
#@{foo bar@}#

#@{what
ever@}#

#@{4242@}#
@end lisp

Although Guile provides this extended read syntax for symbols,
widespread usage of it is discouraged because it is not portable and not
very readable.


@node Symbol Uninterned
@subsubsection Uninterned Symbols

What makes symbols useful is that they are automatically kept unique.
There are no two symbols that are distinct objects but have the same
name.  But of course, there is no rule without exception.  In addition
to the normal symbols that have been discussed up to now, you can also
create special @dfn{uninterned} symbols that behave slightly
differently.

To understand what is different about them and why they might be useful,
we look at how normal symbols are actually kept unique.

Whenever Guile wants to find the symbol with a specific name, for
example during @code{read} or when executing @code{string->symbol}, it
first looks into a table of all existing symbols to find out whether a
symbol with the given name already exists.  When this is the case, Guile
just returns that symbol.  When not, a new symbol with the name is
created and entered into the table so that it can be found later.

Sometimes you might want to create a symbol that is guaranteed `fresh',
i.e. a symbol that did not exist previously.  You might also want to
somehow guarantee that no one else will ever unintentionally stumble
across your symbol in the future.  These properties of a symbol are
often needed when generating code during macro expansion.  When
introducing new temporary variables, you want to guarantee that they
don't conflict with variables in other people's code.

The simplest way to arrange for this is to create a new symbol but
not enter it into the global table of all symbols.  That way, no one
will ever get access to your symbol by chance.  Symbols that are not in
the table are called @dfn{uninterned}.  Of course, symbols that
@emph{are} in the table are called @dfn{interned}.

You create new uninterned symbols with the function @code{make-symbol}.
You can test whether a symbol is interned or not with
@code{symbol-interned?}.

Uninterned symbols break the rule that the name of a symbol uniquely
identifies the symbol object.  Because of this, they can not be written
out and read back in like interned symbols.  Currently, Guile has no
support for reading uninterned symbols.  Note that the function
@code{gensym} does not return uninterned symbols for this reason.

@deffn {Scheme Procedure} make-symbol name
@deffnx {C Function} scm_make_symbol (name)
Return a new uninterned symbol with the name @var{name}.  The returned
symbol is guaranteed to be unique and future calls to
@code{string->symbol} will not return it.
@end deffn

@deffn {Scheme Procedure} symbol-interned? symbol
@deffnx {C Function} scm_symbol_interned_p (symbol)
Return @code{#t} if @var{symbol} is interned, otherwise return
@code{#f}.
@end deffn

For example:

@lisp
(define foo-1 (string->symbol "foo"))
(define foo-2 (string->symbol "foo"))
(define foo-3 (make-symbol "foo"))
(define foo-4 (make-symbol "foo"))

(eq? foo-1 foo-2)
@result{} #t
; Two interned symbols with the same name are the same object,

(eq? foo-1 foo-3)
@result{} #f
; but a call to make-symbol with the same name returns a
; distinct object.

(eq? foo-3 foo-4)
@result{} #f
; A call to make-symbol always returns a new object, even for
; the same name.

foo-3
@result{} #<uninterned-symbol foo 8085290>
; Uninterned symbols print differently from interned symbols,

(symbol? foo-3)
@result{} #t
; but they are still symbols,

(symbol-interned? foo-3)
@result{} #f
; just not interned.
@end lisp


@node Keywords
@subsection Keywords
@tpindex Keywords

Keywords are self-evaluating objects with a convenient read syntax that
makes them easy to type.

Guile's keyword support conforms to R5RS, and adds a (switchable) read
syntax extension to permit keywords to begin with @code{:} as well as
@code{#:}.

@menu
* Why Use Keywords?::           Motivation for keyword usage.
* Coding With Keywords::        How to use keywords.
* Keyword Read Syntax::         Read syntax for keywords.
* Keyword Procedures::          Procedures for dealing with keywords.
* Keyword Primitives::          The underlying primitive procedures.
@end menu

@node Why Use Keywords?
@subsubsection Why Use Keywords?

Keywords are useful in contexts where a program or procedure wants to be
able to accept a large number of optional arguments without making its
interface unmanageable.

To illustrate this, consider a hypothetical @code{make-window}
procedure, which creates a new window on the screen for drawing into
using some graphical toolkit.  There are many parameters that the caller
might like to specify, but which could also be sensibly defaulted, for
example:

@itemize @bullet
@item
color depth -- Default: the color depth for the screen

@item
background color -- Default: white

@item
width -- Default: 600

@item
height -- Default: 400
@end itemize

If @code{make-window} did not use keywords, the caller would have to
pass in a value for each possible argument, remembering the correct
argument order and using a special value to indicate the default value
for that argument:

@lisp
(make-window 'default              ;; Color depth
             'default              ;; Background color
             800                   ;; Width
             100                   ;; Height
             @dots{})                  ;; More make-window arguments
@end lisp

With keywords, on the other hand, defaulted arguments are omitted, and
non-default arguments are clearly tagged by the appropriate keyword.  As
a result, the invocation becomes much clearer:

@lisp
(make-window #:width 800 #:height 100)
@end lisp

On the other hand, for a simpler procedure with few arguments, the use
of keywords would be a hindrance rather than a help.  The primitive
procedure @code{cons}, for example, would not be improved if it had to
be invoked as

@lisp
(cons #:car x #:cdr y)
@end lisp

So the decision whether to use keywords or not is purely pragmatic: use
them if they will clarify the procedure invocation at point of call.

@node Coding With Keywords
@subsubsection Coding With Keywords

If a procedure wants to support keywords, it should take a rest argument
and then use whatever means is convenient to extract keywords and their
corresponding arguments from the contents of that rest argument.

The following example illustrates the principle: the code for
@code{make-window} uses a helper procedure called
@code{get-keyword-value} to extract individual keyword arguments from
the rest argument.

@lisp
(define (get-keyword-value args keyword default)
  (let ((kv (memq keyword args)))
    (if (and kv (>= (length kv) 2))
        (cadr kv)
        default)))

(define (make-window . args)
  (let ((depth  (get-keyword-value args #:depth  screen-depth))
        (bg     (get-keyword-value args #:bg     "white"))
        (width  (get-keyword-value args #:width  800))
        (height (get-keyword-value args #:height 100))
        @dots{})
    @dots{}))
@end lisp

But you don't need to write @code{get-keyword-value}.  The @code{(ice-9
optargs)} module provides a set of powerful macros that you can use to
implement keyword-supporting procedures like this:

@lisp
(use-modules (ice-9 optargs))

(define (make-window . args)
  (let-keywords args #f ((depth  screen-depth)
                         (bg     "white")
                         (width  800)
                         (height 100))
    ...))
@end lisp

@noindent
Or, even more economically, like this:

@lisp
(use-modules (ice-9 optargs))

(define* (make-window #:key (depth  screen-depth)
                            (bg     "white")
                            (width  800)
                            (height 100))
  ...)
@end lisp

For further details on @code{let-keywords}, @code{define*} and other
facilities provided by the @code{(ice-9 optargs)} module, see
@ref{Optional Arguments}.


@node Keyword Read Syntax
@subsubsection Keyword Read Syntax

Guile, by default, only recognizes the keyword syntax specified by R5RS.
A token of the form @code{#:NAME}, where @code{NAME} has the same syntax
as a Scheme symbol (@pxref{Symbol Read Syntax}), is the external
representation of the keyword named @code{NAME}.  Keyword objects print
using this syntax as well, so values containing keyword objects can be
read back into Guile.  When used in an expression, keywords are
self-quoting objects.

If the @code{keyword} read option is set to @code{'prefix}, Guile also
recognizes the alternative read syntax @code{:NAME}.  Otherwise, tokens
of the form @code{:NAME} are read as symbols, as required by R5RS.

To enable and disable the alternative non-R5RS keyword syntax, you use
the @code{read-set!} procedure documented in @ref{User level options
interfaces} and @ref{Reader options}.

@smalllisp
(read-set! keywords 'prefix)

#:type
@result{}
#:type

:type
@result{}
#:type

(read-set! keywords #f)

#:type
@result{}
#:type

:type
@print{}
ERROR: In expression :type:
ERROR: Unbound variable: :type
ABORT: (unbound-variable)
@end smalllisp

@node Keyword Procedures
@subsubsection Keyword Procedures

The following procedures can be used for converting symbols to keywords
and back.

@deffn {Scheme Procedure} symbol->keyword sym
Return a keyword with the same characters as in @var{sym}.
@end deffn

@deffn {Scheme Procedure} keyword->symbol kw
Return a symbol with the same characters as in @var{kw}.
@end deffn


@node Keyword Primitives
@subsubsection Keyword Primitives

Internally, a keyword is implemented as something like a tagged symbol,
where the tag identifies the keyword as being self-evaluating, and the
symbol, known as the keyword's @dfn{dash symbol} has the same name as
the keyword name but prefixed by a single dash.  For example, the
keyword @code{#:name} has the corresponding dash symbol @code{-name}.

Most keyword objects are constructed automatically by the reader when it
reads a token beginning with @code{#:}.  However, if you need to
construct a keyword object programmatically, you can do so by calling
@code{make-keyword-from-dash-symbol} with the corresponding dash symbol
(as the reader does).  The dash symbol for a keyword object can be
retrieved using the @code{keyword-dash-symbol} procedure.

@deffn {Scheme Procedure} make-keyword-from-dash-symbol symbol
@deffnx {C Function} scm_make_keyword_from_dash_symbol (symbol)
Make a keyword object from a @var{symbol} that starts with a dash.
For example,

@example
(make-keyword-from-dash-symbol '-foo)
@result{} #:foo
@end example
@end deffn

@deffn {Scheme Procedure} keyword? obj
@deffnx {C Function} scm_keyword_p (obj)
Return @code{#t} if the argument @var{obj} is a keyword, else
@code{#f}.
@end deffn

@deffn {Scheme Procedure} keyword-dash-symbol keyword
@deffnx {C Function} scm_keyword_dash_symbol (keyword)
Return the dash symbol for @var{keyword}.
This is the inverse of @code{make-keyword-from-dash-symbol}.
For example,

@example
(keyword-dash-symbol #:foo)
@result{} -foo
@end example
@end deffn

@deftypefn {C Function} SCM scm_c_make_keyword (char *@var{str})
Make a keyword object from a string.  For example,

@example
scm_c_make_keyword ("foo")
@result{} #:foo
@end example
@c
@c  FIXME: What can be said about the string argument?  Currently it's
@c  not used after creation, but should that be documented?
@end deftypefn


@node Other Types
@subsection ``Functionality-Centric'' Data Types

Procedures and macros are documented in their own chapter: see
@ref{Procedures and Macros}.

Variable objects are documented as part of the description of Guile's
module system: see @ref{Variables}.

Asyncs, dynamic roots and fluids are described in the chapter on
scheduling: see @ref{Scheduling}.

Hooks are documented in the chapter on general utility functions: see
@ref{Hooks}.

Ports are described in the chapter on I/O: see @ref{Input and Output}.


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