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file: LISP, node: Top, up: (LANGUAGES)Lisp, next: Sources,

This file is a fast edit of the MACLISP Reference Manual Dated
March 6, 1976, so expect stuff to be out of date and to refer
to non-existent page numbers.  See other notes under Sources.

Please feel free to ^R this file

* MENU:

* Sources::			Where this info came from
				Where other info is
* Language::
    1. General Information
    2. Data Objects
    3. The Basic Actions of Lisp
* Function Descriptions::
    1. Predicates
    2. The Evaluator
    3. Manipulating List Structure
    4. Flow of Control
    5. Atomic Symbols
    6. Numbers
    7. Character Manipulation
    8. Arrays
    9. Mapping Functions
* Indices::
    Function Index
    Atom Index
    Concept Index

* System:(LISPA)
    1. The Top Level
    2. Break Points
    3. Control Characters
    4. Exceptional Condition Handling
    5. Debugging
    6. Storage Management
    7. Miscellaneous Functions

* Compiler:(LISPC)
    1. Peculiarities of the Compiler
    2. Declarations
    3. Running Compiled Functions
    4. Running the Compiler
    5. The Lisp Assembly Program
    6. Internal Implementation Details
    7. Calling Programs Written in Other Languages

* Input and Output:(LISPIO)
    1. The Reader
    2. The Printer
    3. Files
    4. Terminals
    5. Requests to the Host Operating System
    6. "Old I/O"
    7. "Moby I/O"

 Using Maclisp::					NO INFORMATION
    1. Getting Used to Lisp
    2. Extending the Language
    3. The Grinder
    4. Editors
    5. Implementing Subsystems with Maclisp
    6. Internal Implementation Details
    7. Maclisp Glossary
    8. Comparison with LISP 1.5
    9. Comparison with InterLISP



file: LISP, node: Sources, previous: Top, up: Top, next: Language,

The sources on LISP are spread out on ITS.  The bulk of this file
comes from a small portion of the 1976 MACLISP Reference Manual.
Other information sources are (check on MC: for current versions):

	.info.;	lisp cursor	7/26/77	talks about (cursorpos ...)
		lisp news		continually update list of changes
		lisp sfa	11/24/78 about software file arrays
		lspord >	3/4/77	? (1979: no such file)
		manual update	3/4/78
		newio stuff	1/27/79

X	lspman;	manual ascii	3/6/76	33% of the MACLISP Ref Manual
		intel >			how to convert Interlisp -> MACLISP
		new stuff	4/14/75	?
X		ch12 >		8/3/78	toplevel stuff
X		ch13 >		1/6/75	basic I/O
		ch14 >		7/21/77	compilation


	libdoc;			a users library full of goodies
	liblsp;

	tvlisp;			users library of TV hacks

	and your local LISP GURU


^--- an "X" in this column mean the file has been incorporated into this file




file: LISP, node: Language, previous: Sources, up: Top, next: General Information,
Source: MACLISP Manual 3/6/76


* MENU:

* General Information::
1.1     The Maclisp Language . . . 
1.2     Structure of the Manual  . 
1.3     Notational Conventions . . 

* Data Objects::

* The Basic Actions of Lisp::
3.1     Binding of Variables . . . 
3.2     Evaluation of Forms  . . . 
3.3     Application of Functions . 
3.4     Special Forms  . . . . . . 
3.5     Binding Context Pointers . 


file: LISP, node: General Information, previous: Language, up: Language, next: Data Objects,
Source: MACLISP Manual 3/6/76

1.  General Information
1.1     The Maclisp Language . . . 
1.2     Structure of the Manual  . 
1.3     Notational Conventions . . 


1.1  The Maclisp Language


   Maclisp is a dialect of  Lisp developed at M.I.T.'s Project MAC  and M.I.T.'s
Artificial Intelligence Laboratory  for use in artificial  intelligence research
and  related fields.   Maclisp  is descended  from the  commonly-known  Lisp 1.5
dialect; however, many features of the language have been changed or augmented.

   This document is intended both as a reference source for the language  and as
a user's guide to three implementations.  These are, in chronological order, the
M.I.T. Artificial Intelligence Lab's  implementation on the DEC  pdp-10 computer
under  their  operating   system  ITS,  hereafter   referred  to  as   "the  ITS
implementation,"  Project MAC's  implementation  on Honeywell's  version  of the
Multics system, hereafter referred  to as "the Multics implementation,"  and the
version  that runs  on  the DEC  pdp-10  under DEC's  TOPS-10  operating system,
hereafter  called "the  DEC-10 implementation."  The DEC-10  implementation also
runs under  TENEX by  means of  a TOPS-10  emulator.  Since  the ITS  and DEC-10
implementations are closely related, they are sometimes referred to collectively
as  the  pdp-10  implementation.    There  are  reputed  to  be   several  other
implementations.

   These implementations  are mostly  compatible; however,  some implementations
have extra features designed to exploit peculiar features of the system on which
they run, and some implementations are temporarily missing some  features.  Most
programs  will work  on any  implementation, although  it is  possible  to write
machine-dependent code if you try hard enough.

   The Maclisp system  is structured as an  environment, which is  essentially a
set  of  names and  bindings  of those  names  to data  structures  and function
definitions.   The  environment contains  a  large number  of  useful functions.
These functions can be used through an interpreter to define other functions, to
control the environment, to do useful work, etc.

   The interpreter is the basic user  interface to the system.  This is  how the
user enters "commands." When Maclisp is not doing anything else, such as running
a program, it waits for the user  to enter a Lisp form.  This form  is evaluated
and  the value  is  printed out.   The  form may  call  upon one  of  the system
functions (or a user-defined function,  of course) to perform some  useful task.
The evaluation  of a  form may  initiate the  execution of  a large  and complex
program,  perhaps never  returning to  the "top  level" interpreter,  or  it may
perform some  simple action and  immediately wait for  the user to  type another
form.

   It is also possible to get  into the interpreter while a program  is running,
using  the break  facility.  This  is primarily  used in  debugging  and related
programming activities.

   The functions invoked by the top-level interpreter may be  executable machine
programs, or they may themselves  be interpreted.  This is entirely a  matter of
choice and convenience.  The system functions are mostly machine programs.  User
functions are usually first used interpretively.  After they work,  the compiler
may be applied  to them, turning  them into machine  programs which can  then be
loaded into the environment.

   All of this is done  within a single consistent language, Lisp,  whose virtue
is that the data structure is simple and general enough that programs may easily
operate on programs, and that the program structure is simple and general enough
that it can be used as a command language.

.bp
1.2  Structure of the Manual
Source: MACLISP Manual 3/6/76


   The manual is generally  structured into sections on particular  topics; each
section contains  explanatory text and  function definitions,  interspersed.  In
general,  each  section  contains both  elementary  and  complex  material, with
complexity increasing toward the end of the section.  An axiomatic, step-by-step
development is not used.  Frequently  the more complex information in  a section
will assume knowledge from other sections which appear later in the manual.  The
new user is advised to skip around, reading early chapters and early sections of
chapters first.

   Often descriptions of Lisp functions will be given not only in prose but also
in terms of other Lisp functions.  These are as accurate as possible, but should
not be  taken too  literally.  Their  main purpose is  to serve  as a  source of
examples.

   Accessing information in the manual is dependent on both the user's  level of
ability and the purpose for which  she or he is using the manual.   Though cover
to cover reading is not recommended (though not excluded), it is  suggested that
someone who has  never previously seen this  manual browse through  it, touching
the beginning of each  subdivision that is listed  in the Table of  Contents, in
order to familiarize himself or herself with the material that it  contains.  To
find an answer  to some particular  question, one must  use one of  the provided
access methods.  Since the manual is structured by topics one can use  the Table
of Contents that is found at the beginning of the manual, and the  more detailed
tables of contents  found at the  beginning of each of  the six major  parts, to
find where information of a general class will be found.  Entry into  the manual
is also facilitated by  the Glossary and the  Concept Index, which are  found at
the end.   Also at  the end of  the manual  are a Function  Index and  an Atomic
Symbol Index which are  probably most useful to  a regular and repeated  user of
the dialect, or to  an experienced user of  another dialect, who wishes  to find
out the answer to a question about a specific function.  When one section of the
manual assumes knowledge of another section a page number reference to the other
section will generally be given.

.bp
1.3  Notational Conventions
Source: MACLISP Manual 3/6/76


   There are some conventions of  notation that must be mentioned at  this time,
due to their being used in examples.

   Most numbers are in octal  radix (base eight).  Numbers with a  decimal point
and spelled-out numbers are in decimal radix.  It is important to  remember that
by default Maclisp inputs and outputs  all numbers in octal radix.  If  you want
to change this, see the variables base and ibase.

   A combination  of the characters  equal sign and  greater than  symbol, "=>",
will be used in examples of  Lisp code to mean evaluation.  For instance,  "F =>
V" means that evaluating the form F produces the value V.

   All uses of the phrase "Lisp reader," unless further qualified, refer to that
part of the Lisp  system which reads input, and  not to the person  reading this
document.

   The terms  "S-expression" and "Lisp  object" are synonyms  for "any  piece of
Lisp data."

   The character "$" always stands for dollar-sign, never for "alt mode," unless
that is specifically stated.

   The two characters  accent acute, "'", and  semi-colon, ";", are  examples of
what are called macro characters.  Though the macro character facility, which is
explained in Part 5, is not of immediate interest to a new user of  the dialect,
these two macro characters come preset by the Lisp system and are  useful.  When
the Lisp reader encounters an accent acute, or quote mark, it reads in  the next
S-expression and encloses it in  a quote-form, which prevents evaluation  of the
S-expression.  That is:

                                   'some-atom

                                  turns into:

                               (quote some-atom)

                                      and

                                 '(cons 'a 'b)
                                   turns into

                       (quote (cons (quote a) (quote b)))

   The semi-colon (;) is used  as a commenting character.  When the  Lisp reader
encounters it, the remainder of the line is discarded.

   The  term  "newline"  is used  to  refer  to that  character  or  sequence of
characters which indicates the end of a line.  This is implementation dependent.
In Multics Maclisp, newline is the Multics newline character, octal 012.  In ITS
Maclisp, newline  is carriage  return (octal 015),  optionally followed  by line
feed (octal  012.)  In dec-10  Maclisp, newline is  carriage return  followed by
line feed.

   All  Lisp  examples  in  this  manual  are  written  according  to  the  case
conventions of the Multics implementation, which uses both upper and  lower case
letters  and spells  the names  of most  system functions  in lower  case.  Some
implementations of  Maclisp use only  upper case letters  because they  exist on
systems which are not, or have not always been, equipped with  terminals capable
of  generating and  displaying  the full  ascii character  set.   However, these
implementations will accept input in lower case and translate it to  upper case,
unless the user has explicitly said not to.

file: LISP, node: Data Objects, previous: General Information, up: Language, next: The Basic Actions of Lisp,
Source: MACLISP Manual 3/6/76


   Lisp works with pieces of data called "objects" or "S-expressions." These can
be simple "atomic" objects or  complex objects compounded out of  other objects.
Functions,  the basic  units of  a Lisp  program, are  also objects  and  may be
manipulated as data.

   Objects  come in  several types.   All  types are  manifest; that  is,  it is
possible for a  program to tell what  type an object is  just by looking  at the
object itself, so it  is not necessary to declare  the types of variables  as in
some other languages.  One can  make declarations, however, in order to  aid the
compiler in producing optimal code.  (See part 4.2.)

   It is important to know that  Lisp represents objects as pointers, so  that a
storage cell (a  "variable") will hold  any object, and  the same object  may be
held by several different storage cells.  For example, the same identical object
may be a component of two different compound objects.

   The data-types are divided into  three broad classes:  the atomic  types, the
non-atomic types, and  the composite types.  Objects  are divided into  the same
three classes  according to their  type.  Atomic objects  are basic  units which
cannot be broken down by ordinary chemical means (car and cdr), while non-atomic
objects are structures constructed out of other objects.  Composite  objects are
indivisible, atomic,  entities which  have other  objects associated  with them.
These other objects may be examined and replaced.

   The atomic data types are numbers, atomic symbols, strings, and subr-objects.
Atomic symbols can also be regarded as composite.  See below.

   In Lisp numbers can be represented by three types of atomic objects: fixnums,
flonums, and bignums.  A fixnum  is a fixed-point binary integer whose  range of
values  is  machine-dependent.   A  flonum  is  a  floating-point  number  whose
precision and range of values  are machine-dependent.  A bignum is  an infinite-
precision integer.  It is impossible to get "overflow" in bignum  arithmetic, as
any  integer  can  be  represented by  a  bignum.   However,  fixnum  and flonum
arithmetic is faster than bignum arithmetic and requires less memory.  Sometimes
the  word  "fixnum"  is used  to  include  both fixnums  and  bignums  (i.e. all
integers); in  this manual,  however, the word  "fixnum" will  never be  used to
include bignums unless that is explicitly stated.
   The  printed  representations  for  numbers  are  as  follows:  a  fixnum  is
represented  as a  sequence of  digits in  a specified  base, usually  octal.  A
trailing decimal point indicates a  decimal base.  A flonum is represented  as a
set of digits containing an embedded or leading decimal point and/or  a trailing
exponent.  The exponent is introduced by  an upper or lower case "e".   A bignum
looks like a fixnum except that it has enough digits that it will not fit within
the range available to  fixnums.  Any number may be  preceded by a + or  - sign.
Some examples of fixnums are 4,  -1232, -191., +46.   An example of a  bignum is
1565656565656565656565656565656565.  Some  examples of  flonums are:   4.0, .01,
-6e5, 4.2e-1.

   One of the most important Lisp data types is the atomic symbol.  In fact, the
word "atom" is often used to mean just atomic symbols, and not the  other atomic
types.  An atomic symbol has associated with it a name, a value, and  possibly a
list  of "properties".   The name  is  a sequence  of characters,  which  is the
printed representation  of the  atomic symbol.   This name  is often  called the
"pname," or  "print-name." A pname  may contain any  ascii character  except the
null character, which  causes trouble in  some implementations.  For  example, a
certain atomic symbol  would be represented externally  as foo; internally  as a
structure containing the value, the pname "foo", and the properties.

   There are  two special atomic  symbols, t and  nil.  These always  have their
respective selves as values and their values may not be changed.  nil is used as
a  "marker"  in many  contexts;  it is  essential  to the  construction  of data
structures  such as  lists.  t  is usually  used when  an antithesis  to  nil is
required for some purpose, e.g.  to represent the logical conditions  "true" and
"false." Another property of the special  atomic symbol nil is that its  car and
its cdr are always nil.

   The value  of an  atomic symbol  can be any  object of  any type.   There are
functions to set  and get the  value of a  symbol.  Because atomic  symbols have
values associated with them,  they can be used  as variables in programs  and as
"dummy arguments"  in functions.  It  is also possible  for an atomic  symbol to
have no value, in which case it is said to be "undefined" or "unbound."

   The property list of an atomic symbol is explained on page 2-48.  It  is used
for such things  as recording the fact  that an atomic symbol  is the name  of a
function.

   An atomic symbol  with one or  no characters in its  pname is often  called a
"character object" and used to represent an ascii character.  The  atomic symbol
with a zero-length  pname represents the ascii  null character, and  the symbols
with  one-character  pnames  represent  the  character  which  is  their  pname.
Functions which take character objects as input usually also accept a string one
character long  or a  fixnum equal to  the ascii-code  value for  the character.
Character objects are always interned on the obarray (see page 2-54).

   Another  Lisp data  type is  the string.   This is  a sequence  of characters
(possibly zero-length).  Strings are used  to hold messages to be typed  out and
to manipulate text when the structure of the text is not appropriate for the use
of "list processing."  The printed representation of  a string is a  sequence of
characters enclosed in double-quotes, e.g. "foo".   If a " is to be  included in
the string, it is written twice, e.g. "foo""bar" is foo"bar.  In implementations
without strings,  atomic symbols are  used instead.  The  pdp-10 implementations
currently lack strings.

   A "subr-object" is a special atomic data-type whose use is normally hidden in
the  implementation.  A  subr-object  represents executable  machine  code.  The
functions built  into the Lisp  system are subr-objects,  as are  user functions
that have been compiled.  A  subr-object has no printed representation,  so each
system function has an atomic symbol  which serves as its name.  The  symbol has
the subr-object as a property.

   One composite  data type  is the  array.  An  array consists  of a  number of
cells, each of  which may contain  any Lisp object.  The  cells of an  array are
accessed by subscripting; each cell is  named by a tuple of integers.   An array
may have one or more dimensions; the upper limit on the number of  dimensions is
implementation-defined.  An array is not always associated with an atomic symbol
which is its name.  Rather,  an array is always designated by  an array-pointer,
which is  a special kind  of atomic Lisp  object.  Frequently,  an array-pointer
will be placed on  the property list of a  symbol under the indicator  array and
then that symbol will be used as  the name of the array, since symbols  can have
mnemonic names and  a reasonable printed representation.   See page 2-85  for an
explanation of how to create, use, and delete arrays.

   Another composite data  type is the file-object,  which is described  on part
5.3.

   The  sole  non-atomic  data  type  is the  "cons."   A  cons  is  a structure
containing  two  components,  called  the "car"  and  the  "cdr"  for historical
reasons.  (These are  names of fields  in an IBM  7094 machine word.)  These two
components may be any Lisp object,  even another cons (in fact, they  could even
be the same cons).  In this way complex structures can be built up out of simple
conses.  Internally a cons is represented in a form similar to:

               _____________________________________
               |                 |                 |
               |     car         |      cdr        |
               _|__________________|__________________|

where the boxes represent  cells of memory large  enough to hold a  pointer, and
"car" and "cdr"  are two pointers to  objects.  The printed representation  of a
cons is the "dotted-pair" notation (A . B) where A is the car and B is the cdr.

   Another way  to write the  internal representation of  a cons, which  is more
convenient for large structures, is:

                ---> o -----> cdr
                    |
                    |
                    V
                   car

   There are three  Lisp functions associated with  conses: cons, car,  and cdr.
The  function cons  combines its  two  arguments into  a cons;  (1 .  2)  can be
generated by evaluating (cons 1 2).  The function car returns the  car component
of its argument, and the function cdr returns the cdr component of its argument.

   One type of structure, built out of conses, that is used quite often,  is the
"list."  A  list is  a row  of objects, of  arbitrary length.   A list  of three
things 1, 2, and 3  is constructed by (cons 1 (cons  2 (cons 3 nil))); nil  is a
special atom that is used  to mark the end of  a list.  The structure of  a list
can be diagrammed as:

                ---> o ----> o ----> o ----> nil
                    |       |       |
                    |       |       |
                    V       V       V
                    1       2       3

   From this it can be  seen that the car of  a list is its first  element, that
the cdr of a list is a list  of the elements after the first, and that  the list
of no elements is the same as nil.

   This list of 1,  2, and 3 could be  represented in the dot-notation  used for
conses as  (1 . (2 . (3  . nil))).  However, a more convenient notation  for the
printed representation of lists has been defined:  the "list-notation" (1  2 3).
It is  also possible to  have a hybrid  of the two  notations which is  used for
structures which are almost  a list except that they  end in an atom  other than
nil.  For example, (A . (B . (C . D))) can be represented as (A B C . D).

   A list not  containing any elements is  perfectly legal and  frequently used.
This zero-length list is  identified with the atom nil.   It may be typed  in as
either nil or ().

file: LISP, node: The Basic Actions of Lisp, previous: Data Objects, up: Language, next: Binding of Variables,
Source: MACLISP Manual 3/6/76

* MENU:

* Binding of Variables::
* Evaluation of Forms:: 
* Application of Functions::
* Special Forms:: 
* Binding Context Pointers::


file: LISP, node: Binding of Variables, previous: The Basic Actions of Lisp, up: The Basic Actions of Lisp, next: Application of Functions,
Source: MACLISP Manual 3/6/76


   The  basic  primitives  of  programming in  Lisp  are  variables,  forms, and
functions.  A variable is an atomic symbol which has a value associated with it;
the symbol is said to  be bound to that value.   The value may of course  be any
Lisp object whatsoever.  The  atomic symbol acts simply  as a name by  which the
program may refer to the value while it is processing it.

   This is similar to the  concept of variables in other  programming languages.
However, Lisp's concept of the scope  of names is subtly different from  that of
most "block-structured" languages.  At  a given moment, a variable  may actually
have several bindings in existence.   Only the most recent, or  current binding,
can be used.  When a new binding  is created, the previous one is pushed  onto a
stack.  It will become accessible again when the binding which superseded  it is
removed.   Creation  and removal  of  bindings is  synchronized  with subroutine
calling  (and with  certain  special forms  described below)  so  this mechanism
corresponds  closely  to  the "local  variables"  concept  of  other programming
languages.   However,  Lisp considers  that  there is  only  one  variable whose
binding changes, rather than several separate variables which happen to have the
same  name.  Any  reference  to a  variable,  even from  outside  the particular
program which gave it its current binding, gets the current binding and  not one
determined by "scope  rules."  It is possible  to simulate the other  concept of
scope of names by using binding context pointers, which are described later (see
page 1-22).

   Unlike many other languages, Lisp  does not combine the concepts of  name and
storage.  Many languages associate with  a variable (a name) a piece  of storage
which can hold one object of a particular type, such as a floating point number.
The variable's  value resides in  this storage.  It  is then impossible  for two
variables to really have "the same" value; one could have a copy of the value of
another but not the same identical object.

   The situation in Lisp is quite  different.  Binding a variable to a  value is
not copying the value into storage associated with that variable.   Values exist
as separate objects  in their own  right and in  their own storage.   Binding is
simply an association between a  variable and a value; consequently there  is no
reason why two variables cannot have truly identical values.  Similarly, erasing
the binding between a variable and its value does not destroy or throw  away the
value; it simply breaks  the association.  Of course,  if there is no  other use
for the value the storage it occupies will eventually be reclaimed by the system
and put to more productive use.

   Often these processes of creating a new binding of a variable to a  value and
reverting to  a previous binding  are referred to  as binding and  unbinding the
variable, respectively.

   A slightly different way of creating a binding between a variable and a value
is assignment.  When  a variable is  bound to a  value, the previous  binding is
saved and can be restored, but when  a variable has a value assigned to  it, the
previous binding  is not  saved, but is  simply replaced.   Thus binding  may be
regarded  as creating  a new  level  of usage  of a  variable,  while assignment
switches a variable to a different value within the same level.  For instance, a
subroutine  or function  may bind  a variable  to an  initial value  when  it is
entered, and  then proceed to  make use of  that variable, possibly  assigning a
different value to it  from time to time.   The initial binding of  the variable
establishes the (temporary) ownership of that variable by the subroutine.

   Due to the subtlety of  the distinction between binding and  assignment, some
people  have  proposed that  assignment  be eliminated  wherever  possible.  The
Maclisp do function can often be useful in this regard.

   There are several program constructs by which a variable can be bound.  These
will be explained after forms and functions have been introduced.

3.2  Evaluation of Forms


   The  process of  "executing" a  Lisp program  consists of  the  evaluation of
forms.  Evaluation takes a form and produces from it a value (any  Lisp object),
according to  a strict  set of  rules which  might be  regarded as  the complete
semantics of Lisp.

   If the form  is atomic, it is  evaluated in a way  which depends on  its data
type.  An atomic symbol is a variable; it evaluates to the value to which  it is
currently bound.  If it is not bound, an error occurs.  (See part 3.4.) A number
or a string is a literal  constant; it evaluates to itself.  The  special atomic
symbols t and nil are also treated as constants.  A constant can also be created
by use of the quote special form; the value of (quote x) is x.

   If  the form  is a  list, its  first element  specifies the  operation  to be
performed, and its remaining elements specify arguments to that operation.  Non-
atomic forms  come in  two types:   special forms,  which include  the necessary
programming  operations  such  as  assignment  and  conditionals,  and  function
references,  in which  the "operation"  is a  function which  is applied  to the
specified  arguments.   Thus  functional  composition  is  the  method  by which
programs are built up out of  parts - as distinguished from composition  of data
structures, for  example.  Lisp functions  correspond closely to  subroutines in
other programming languages.

   A function  may be  either a primitive  which is  directly executable  by the
machine,  called a  subr  (short for  "subroutine"),  or a  function  defined by
composition  of  functions  and  special  forms,  called  an  expr   (short  for
"expression.") Most subrs are built in to the language, but it is possible for a
user to convert his exprs into  subrs by using the compiler (see part  4.)  This
gains speed and compactness at some cost in debugging features.

   There is additional complexity because special forms are actually implemented
as if they were function references.  There is a special type of subr  called an
fsubr  which is  used  for this  purpose.  An  fsubr  is permitted  to  make any
arbitrary  interpretation  of  its  argument  specification  list,   instead  of
following the standard procedure which is described below.  It is  also possible
to define a special form by an expr, which is then called a fexpr.  Most  of the
built-in special forms are handled specially by the compiler.  They are compiled
as the appropriate code rather than as a call to the fsubr.

   Other types  of functions are  lsubr, which  is just a  subr with  a variable
number  of  arguments,  lexpr,  which  is an  expr  with  a  variable  number of
arguments, and  macro, which is  a type of  special form whose  result is  not a
value, but another form; this allows a "transformational" type of semantics.

   Consider the form

                                (F A1 A2 ... An)


   The evaluator first  examines F to  see if it is  a function which  defines a
special form, i.e. an fsubr, a fexpr, or a macro.  If so, F is consulted  and it
decides how to produce  a value.  If not, F  must be an ordinary  function.  The
sub-forms  A1 through  An are  evaluated, producing  n arguments,  and  then the
definition of F is applied  to the arguments.  (Application is described  in the
following section.) This yields a result (some Lisp object), which is then taken
as the value of the form.

   An atomic  form of some  random type, such  as a subr-object,  a file,  or an
array-pointer, evaluates to  something random, often  itself; or else  causes an
error depending on the convenience  of the implementation.  Note that  an array-
pointer is different from  an atomic symbol which happens  to be the name  of an
array; such an atomic symbol is evaluated the same as any other atomic symbol.

file: LISP, node: Application of Functions, previous: Binding of Variables, up: The Basic Actions of Lisp, next: Special Forms,
Source: MACLISP Manual 3/6/76

   When a non-atomic form is  evaluated, the function specified by that  form is
combined with  the arguments specified  by that form  to produce a  value.  This
process  is  called application;  the  function is  said  to be  applied  to the
arguments.

   The first  step in application  is to convert  the function-specifier  into a
functional  expression  (sometimes  confusingly  called  a  functional  form.) A
functional expression is a Lisp object  which is stylized so that Lisp  can know
how to apply it to arguments.   The rules for this conversion will  be described
after the types of functional expressions have been explained.

   There are basically two types of functional expression.   A lambda-expression
is a functional expression which specifies some variables which are to  be bound
to the arguments, and  some forms which are  to be evaluated.  One  would expect
the forms to depend on the variables.  The value of the last form is used as the
value  of the  application of  the lambda-expression.   Any preceding  forms are
present purely for their side-effects.  A lambda-expression looks like:

                     (lambda (a b c d)
                         form1
                         form2
                         form3)

   Here a,  b, c,  and d  are the variables  to be  bound to  the values  of the
arguments,  called the  lambda-variables.  If  at a  certain moment  the current
binding of a was the one  created by this lambda-expression, a would be  said to
be lambda-bound.   Clearly this  lambda-expression is  a function  which accepts
four arguments.  The application of the functional expression to  four arguments
produces a value by evaluating form1, then form2, and then form3.  The  value of
form3 is the value of the whole form.  For example, the value of the form

                    ((lambda (a b) b) 3 4)

is 4.  The  functional expression used  is a very  simple one which  accepts two
arguments and returns the second one.

   If we grant the existence of a primitive addition operation, whose functional
expression may be designated by +, then the value of the form


                    ((lambda (a b) (+ a b)) 3 4)

is 7.  Actually,

                    (+ 3 4)

evaluates to the same thing.

   The  second basic  type of  functional  expression is  the subr,  which  is a
program  directly executable  by the  machine.  The  arguments of  the  form are
conveyed  to  this  program  in a  machine-dependent  manner,  it  performs some
arbitrary computation, and it returns a result.  The built in primitives  of the
language are subrs, and the user may write lambda-expressions which make  use of
these subrs to define  his own functions.  The  compiler may be used  to convert
user functions into subrs if extra efficiency is required.

   It  is  extremely  convenient  to  be  able  to  assign  names  to functional
expressions.  Otherwise the  definition of a function  would have to  be written
out in full each time it was used, which would be impossibly cumbersome.

   Lisp uses atomic symbols to name functions.  The "property list" mechanism is
used to associate an atomic symbol with a functional expression.  (See page 2-48
for an  explanation of  property lists.)  Because the  binding mechanism  is not
used, it is  possible for the  same name to  be used for  both a variable  and a
function with no conflict.  Usually the defun special form is used  to establish
the association between a function name and a functional expression.

   Thus, the car of a form  may be either a functional expression itself,  or an
atomic symbol which names a functional expression.  In the latter case, the name
of  the  "property"  which  associates  the  symbol  with  the  expression gives
additional information:

   A lambda-expression is normally placed under the expr property.  This defines
an ordinary expr.

   If  a lambda-expression  is placed  under the  fexpr property,  it  defines a
special form.  In that  case, the first lambda-variable  is bound to the  cdr of
the form being evaluated.  For example, if foo is a fexpr, and (foo (a b) (c d))
is evaluated, then  foo's lambda-variable would  be bound to  ((a b) (c  d)).  A
second lambda-variable may optionally be included in a fexpr.  It will  be bound
to a "binding  context pointer" to  the context of  the evaluation of  the form.
   If a  lambda-expression with  one lambda-variable is  placed under  the macro
property,  it defines  the "macro"  special form  mentioned above.   The lambda-
expression is applied to the entire form, as a single argument, and the value is
a new form that is evaluated in place of the original form.

   If a subr-object is placed under the subr property, it defines a subr.   If a
subr-object is placed  under the fsubr property,  it defines a special  form.  A
subr-object  under  the lsubr  property  defines a  subr  which  accepts varying
numbers of arguments.

   There  are some  additional refinements.   A lambda-expression  which accepts
varying numbers of arguments, called a lexpr, looks as follows:

                    (lambda n
                        form1
                        form2)

The  single,  unparenthesized,  lambda-variable  n is  bound  to  the  number of
arguments.  The function arg, described on page 2-10, may be used to  obtain the
arguments.

   Another  property  which  resembles a  functional  property  is  the autoload
property.  If Lisp encounters an autoload property while searching  the property
list of a  symbol for functional  properties, it loads  in the file  of compiled
functions  specified by  the property,  then searches  the property  list again.
Presumably the file would contain  a definition for the function  being applied,
and  that  definition would  be  found the  second  time through.   In  this way
packages  of  functions  which  are  not  always  used  can  be  present  in the
environment only when needed.

   An array may also  be used as a  function.  The arguments are  the subscripts
and the  value is the  contents of the  selected cell of  the array.   An atomic
symbol  with an  array property  appearing in  the function  position in  a form
causes that array to be used.

   If the function-specifier of a form doesn't meet any of the above tests, Lisp
evaluates it and tries again.  In this way, "functional variables" and "computed
functions" can  be used.   However, it is  better to  use the  funcall function.
(See page 2-11.)

   There are some other cases of lesser importance:

   There is an obscure type of functional expression called  a label-expression.
It looks like
                        (label name (lambda (...) ...))

The  atomic symbol  name  is bound  to  the enclosed  lambda-expression  for the
duration of the application of the label-expression.  Thus if name is used  as a
functional variable this temporary definition  will be used.  This is  mostly of
historical interest and is rarely used in actual programming.

   Another type  of functional  expression is the  funarg.  A  funarg is  a list
beginning with the atomic symbol  funarg, as you might expect, and  containing a
function and a binding context pointer.  Applying a funarg causes  the contained
function to  be applied in  the contained binding  context instead of  the usual
context.  funargs are created by the *function special form.

   An expr property may be an atomic symbol rather than a lambda-expression.  In
this case, the atomic  symbol is used as  the function.  The original  symbol is
simply a synonym for it.

   In  addition to  the variety  of application  just described,  which  is used
internally by  the evaluation procedure,  there is a  similar but  not identical
application procedure available through the function apply.  The main difference
is that the function and the arguments are passed to apply separately.  They are
not encoded into a form, consequently macros are not accepted by this version of
application.  Note that what  is passed to apply is  a list of arguments,  not a
list of expressions which, evaluated, would yield arguments.

file: LISP, node: Special Forms, previous: Application of Functions, up: The Basic Actions of Lisp, next: Binding Context Pointers,
Source: MACLISP Manual 3/6/76

   This section  briefly describes some  of the special  forms in  Maclisp.  For
full details on a specific special form, consult the Function Index in the back.

Constants

     (quote x) evaluates to the S-expression x.

     (function x)  evaluates to  the functional expression  x.  There  is little
     real  difference  between  quote  and function.   The  latter  is  simply a
     mnemonic reminder to anyone who reads the program - including  the compiler
     - that the specified expression is supposed to be some kind of function.

Conditionals

     Conditionals control whether or not certain forms are  evaluated, depending
     on the results of evaluating other forms.  Thus both the value and the side
     effects of the conditional form can be controlled.

        (cond (predicate form1 form2...) (predicate form1 form2...)...)

     is a general conditional form.  The lists of a predicate and some forms are
     called clauses.  The  cond is evaluated by  considering the clauses  one by
     one in the order they are written.  The predicate of a clause is evaluated,
     and if the result is true, that is, anything other than nil, then the forms
     in that clause are evaluated and the cond is finished without examining the
     remaining clauses.  If the result is not true, i.e. if it is nil,  then the
     next clause is examined in the same way.  If all the clauses are exhausted,
     that is not an error.  The value of a cond is the value of the last form it
     evaluates, which could be  nil if no predicate is  true, or the value  of a
     predicate if that predicate is true but has no forms in its clause.

     (and form1 form2 form3...) evaluates  the forms in succession until  one is
     nil or the  forms are exhausted,  and the result is  the value of  the last
     form evaluated.

     (or form1 form2 form3...) evaluates  the forms until one is non-nil  or the
     forms  are  exhausted,  and  the  result is  the  value  of  the  last form
     evaluated.

Non-Local Exits

     (catch form tag) evaluates the  form, but if the special form  (throw value
     tag)  is encountered,  and the  tags are  the same,  the  catch immediately
     returns the value without further ado.  See page 2-40 for the full details.

Iteration

     (prog  (variable...)  form-or-tag ...)  allows  Fortranoid  "programs" with
     goto's, local variables, and return's to be written.

     (do ...) is the special form for iteration.  See page 2-34 for  the details
     of prog and do.

Defining Functions

     (defun  name  (arg1  arg2...)  form1  form2...)  defines  an  (interpreted)
     function.  See page 2-56 for full details.

Error Control

     (break name t) causes ";bkpt name"  to be typed out and gives control  to a
     read-eval-print loop so that the  user can examine and change the  state of
     the world.  When he is satisfied, the user can cause the break to  return a
     value.  See part 3.2 for the details of break.

     (errset form) evaluates the form, but if an error occurs the  errset simply
     returns nil.  If no error occurs, the value is a list whose  single element
     is what the value of the form would have been without errset.

Assignment

     (setq var1 value1 var2 value2...) assigns the values to the variables.  The
     values are forms which are evaluated.

     (store (array  subscript1 subscript2...)  value) assigns  the value  to the
     array cell selected by subscripting.  See part 2.8 for  further information
     on arrays.




Miscellaneous Parameters

     (status  name -optional  args-) returns  miscellaneous parameters  of LISP.
     name is a mnemonic name for what is to be done.

     (sstatus name -optional args-) sets miscellaneous parameters.

     See part 3.7 for the details of status and sstatus.

Pretty-Printing

     (grindef x) prettily prints the  value and function definition (if  any) of
     the atomic symbol  x.  Indentation is used  to reveal structure,  the quote
     special form is represented by ', etc. See part 6.3 for the details.

Tracing

     (trace name)  causes the function  name to print  a message whenever  it is
     called and  whenever it returns.   See part 3.5  for the many  features and
     options of trace.

file: LISP, node: Binding Context Pointers, previous: Special Forms, up: The Basic Actions of Lisp, next: Function Descriptions,
Source: MACLISP Manual 3/6/76

   There  is a  special type  of  object called  a binding  context  pointer, or
sometimes an "a-list pointer", which can  be used to refer to a  binding context
(a set  of bindings of  variables and  values which was  extant at  a particular
instant.) Due to the stack implementation of Maclisp, a binding  context pointer
is only valid while control is  nested within the binding context it  names.  It
is not  possible to exit  from within a  binding context but  keep it  around by
retaining a pointer to it.

   A binding context pointer is either a negative fixnum or nil.  nil  means the
"global" or "top level" binding context.  The negative fixnum is a special value
of implementation dependent  meaning which should be  obtained only from  one of
the four following sources:  the function evalframe, the function  errframe, the
special form *function, or the second lambda-variable of a fexpr.

   The only use for  binding context pointers is  to pass them to  the functions
eval and  apply to  specify the  binding context  in which  variables are  to be
evaluated  and  assignments  are  to  be  performed  during  that  evaluation or
application.  Binding  context pointers are  also used internally  by *function.
When it generates a funarg, it  puts in the funarg the functional  expression it
was  given and  a binding  context pointer  designating the  binding environment
current at the time *function was called.

file: LISP, node: Function Descriptions, previous: Binding Context Pointers, up: Top, next: Predicates,
Source: MACLISP Manual 3/6/76


* MENU:

* Predicates::

* The Evaluator::

* Manipulating List Structure::
3.1     Conses
3.2     Lists
3.3     Alteration of List Structure
3.4     Tables
3.5     Sorting

* Flow of Control::
4.1     Conditionals
4.2     Iteration
4.3     Non-local Exits
4.4     Causing and Controlling Errors

* Atomic Symbols::
5.1     The Value Cell
5.2     The Property List
5.3     The Print-Name
5.4     Interning of Symbols
5.5     Defining Atomic Symbols as Functions

* Numbers::
6.1     Number Predicates
6.2     Comparison . . . 
6.3     Conversion . . . 
6.4     Arithmetic . . . 
6.5     Exponentiation and Logarithm Functions
6.6     Trigonometric Functions  . . . . . . .
6.7     Random Functions . . . . . . . . . . .
6.8     Logical Operations on Numbers  . . . .

* Character Manipulation::
7.1     Character Objects  . . . . . . . . . .

* Arrays::

* Mapping Functions::


file: LISP, node: Predicates, previous: Function Descriptions, up: Function Descriptions, next: The Evaluator,
Source: MACLISP Manual 3/6/76


   A  predicate is  a  function which  tests  for some  condition  involving its
argument and returns t if that condition is true, or nil if it is not true.

   The  following  predicates are  for  checking data  types.   These predicates
return t if their argument is of the type indicated by the name of the function,
nil if it is of some other type.  Note that the name of most predicates  ends in
the letter p, by convention.


atom                SUBR 1 arg

     The atom predicate returns nil if its argument is a dotted-pair or  a list,
     or t  if it  is any kind  of atomic  object such as  a number,  a character
     string, or an atomic symbol.


fixp                SUBR 1 arg

     The fixp  predicate returns  t if  its argument  is a  fixnum or  a bignum,
     otherwise nil.


floatp              SUBR 1 arg

     The floatp predicate returns  t if its argument is  a flonum, nil if  it is
     not.


bigp                SUBR 1 arg

     The  predicate  bigp  returns  t  if its  argument  is  a  bignum,  and nil
     otherwise.


numberp             SUBR 1 arg

     The numberp predicate returns t if its argument is any kind of  number, nil
typep               SUBR 1 arg

     typep is a general  function for constructing type-predicates.   It returns
     an atomic symbol describing the type of its argument, chosen from the list

             (fixnum flonum bignum list symbol string array random)

     symbol means  atomic symbol.   list means a  list or  a cons.   array means
     array-pointer.   random  is for  all  types  that don't  fit  in  any other
     category.  Thus numberp could have been defined by:

        (defun numberp (x)
           (and (memq (typep x) '(fixnum flonum bignum))
                t))


The following two functions only exist in the Multics implementation.


stringp             SUBR 1 arg

     The stringp predicate returns t if its argument is a string, otherwise nil.


subrp               SUBR 1 arg

     The subrp predicate returns  t if its argument  is a "subr" object,  i.e. a
     pointer to the machine code for a compiled or system function.  Example:

            (subrp (get 'car 'subr)) => t


The following are a more miscellaneous set of predicates.


eq                  SUBR 2 args

     (eq x y) => t  if x and y are  exactly the same object, nil  otherwise (cf.
     equal).   It  should be  noted  that things  that  print the  same  are not
     necessarily eq to each other.   In particular, numbers with the  same value
     need not be eq, and two similar lists are usually not eq.  In  general, two
     atomic symbols  with the same  print-name are eq,  but it is  possible with
     maknam or multiple obarrays to generate symbols which have the  same print-
     name but are not eq.  Examples:

                (eq 'a 'b) => nil
                (eq 'a 'a) => t
                (eq '(a . b) '(a . b)) => nil (usually)
                (eq (cons 'a 'b) (cons 'a 'b)) => nil (always)
                (setq x '(a . b)) (eq x x) => t since it is
                             the same copy of (a . b) in both arguments.
                (setq x (setq y 17)) (eq x y) => t or nil
                              depending on the implementation.  You can
                              never rely on numbers being eq.


equal               SUBR 2 args

     The equal  predicate returns  t if its  arguments are  similar (isomorphic)
     objects. (cf.  eq) Two numbers  are equal  if they have  the same  value (a
     flonum is never equal to a  fixnum though).  Two strings are equal  if they
     have the same length, and the characters composing them are the  same.  All
     other atomic  objects are equal  if and  only if they  are eq.   For dotted
     pairs and lists, equal is defined recursively as the two car's  being equal
     and the two cdr's being equal.  Thus equal could have been defined by:

            (defun equal (x y)
                (or (eq x y)
                    (and (numberp x) (numberp y) (numequal x y))
                    (and (not (atom x))
                         (not (atom y))
                         (equal (car x) (car y))
                         (equal (cdr x) (cdr y)))))

            if there was an auxiliary function for numeric equality:

           (defun numequal (x y)
                 (and (eq (typep x) (typep y))
                      (zerop (difference x y))))

     This  numequal function  is not  the same  as the  Maclisp numeric-equality
     function, =, because the latter only compares non-big numbers.

     As a consequence of  the above definition, it  can be seen that  equal need
     not  terminate when  applied  to looped  list structure.   In  addition, eq
     always implies equal.  An intuitive definition of equal (which is not quite
     correct) is that two objects are  equal if they look the same  when printed
     out.


not                 SUBR 1 arg

     not returns t if its argument is nil, otherwise nil.


null                SUBR 1 arg

     This is  the same  as not.   Both functions  are provided  for the  sake of
     clarity.  null should  be used to  check if something  is nil and  return a
     logical value.  not should be used to invert the sense of a  logical value.
     Even though Lisp uses nil to represent logical "false," you  shouldn't make
     understanding your program depend on this.  For example, one often writes

        (cond ((not (null x)) ... )
              ( ... ))

        rather than

        (cond (x ... )
              ( ... ))

     There is no  loss of efficiency since  these will compile into  exactly the
     same instructions.


   See also the number predicates (page 2-59).

file: LISP, node: The Evaluator, previous: Predicates, up: Function Descriptions, next: Manipulating List Structure,
Source: MACLISP Manual 3/6/76


eval                LSUBR 1 or 2 args

     (eval  x) evaluates  x, as  a form,  atomic or  otherwise, and  returns the
     result.

     (eval x  p) evaluates  x in the  context specified  by the  binding context
     pointer p.  Example:

          (setq x 43 foo 'bar)
          (eval (list 'cons x 'foo))
               => (43 . bar)


apply               LSUBR 2 or 3 args

     (apply f y) applies the function f to the list of arguments y.  Unless f is
     an fsubr or fexpr, such as cond or and, which evaluates its arguments  in a
     funny way, the  arguments in the list  y are used without  being evaluated.
     Examples:

            (setq f '+) (apply f '(1 2 3)) => 6
            (setq f '-) (apply f '(1 2 3)) => -4
            (apply 'cons '((+ 2 3) 4)) =>
                     ((+ 2 3) . 4) not (5 . 4)

     (apply  f  y  p)  works  like apply  with  two  arguments  except  that the
     application is  done with  the variable bindings  specified by  the binding
     context pointer p.


quote               FSUBR

     The special form (quote x) returns x without trying to evaluate  it.  quote
     is used to include constants in a form.  For convenience, the read function
     normally  converts any  S-expression preceded  by the  apostrophe  or acute
     accent character (') into the quote special form.  For example,


                    (setq x '(some list))

     is converted by the reader to:

                    (setq x (quote (some list)))

     which when evaluated causes the variable  x to be set to the  constant list
     value  shown.   For more  information  on input  syntax,  see  the detailed
     discussion in part 5.1.

     quote could have been defined by:

          (defun quote fexpr (x) (car x))


function            FSUBR

     function is like quote except that its argument is a functional expression.
     To  the interpreter,  quote and  function are  identical, but  the compiler
     needs  to be  able to  distinguish between  a random  piece of  data, which
     should be left alone, and a function, which should be compiled into machine
     code.  Example:

        (mapcar (function (lambda (p q)
                             (cond ((eq p '*) q)
                                   (t (list p '= q)) )))
                first-list-of-things
                (compute-another-list) )

     calls  mapcar with  three arguments,  the first  of which  is  the function
     defined  by  the  lambda-expression.  The  actual  value  passed  to mapcar
     depends on whether the form  has been compiled.  If it is  interpreted, the
     lambda-expression  written above  will be  passed.  If  it is  compiled, an
     automatically-generated  atomic  symbol  with  the  compiled  code  for the
     lambda-expression as its subr property will be passed.  The usual  thing to
     do with functional arguments is to invoke them via apply or  funcall, which
     accept both the compiled and the interpreted functional forms.

     function makes no attempt to solve the "funarg problem."   *function should
     be used for this purpose.

*function           FSUBR

     The value of (*function f) is  a "funarg" of the function f.  A  funarg can
     be used like a function.  It has the additional property that it contains a
     binding context pointer so that the values of variables are bound  the same
     during  the  application of  the  funarg as  at  the time  it  was created,
     provided that the binding environment in which the funarg was created still
     exists on the stack. Hence if  foo is a function that accepts  a functional
     argument, such as

          (defun foo (f)
              (append one-value (f the-other-value) ))

          or, better

          (defun foo (f)
              (append one-value (funcall f the-other-value) ))

          then

          (foo (*function bar))

          works, but

          (foo (prog (x y z)
                  (do something)
                  (return (*function bar)) ))

     does  not if  bar intends  to reference  the prog  variables x,  y,  and z.
     *function is intended to help  solve the "funarg problem," however  it only
     works in some easy cases.  Funargs generated by *function are  intended for
     use as functional arguments and cannot be returned as values  of functional
     applications.  Thus, the user should be careful in his use of  *function to
     make  sure that  his use  does not  exceed the  limitations of  the Maclisp
     funarg mechanism.

     It is possible to assign a  value to a variable when a previous  binding of
     that variable has  been made current by  a funarg.  The assignment  will be
     executed in  the proper  context.  (This has  not always  been the  case in
     Maclisp; it is a fairly new feature.)

     A funarg has the form
comment             FSUBR

     comment  ignores  its  arguments and  returns  the  atomic  symbol comment.
     Example:

        (defun foo (x)
            (cond ((null x) 0)
                  (t (comment x has something in it)
                     (1+ (foo (cdr x))))))

     Usually it is preferable to comment code using the  semicolon-macro feature
     of the standard input syntax.  This allows the user to add comments  to his
     code which are ignored by the lisp reader.

     Example:

        (defun foo (x)
            (cond ((null x) 0)
                  (t (1+ (foo (cdr x))))     ;x has something in it
              ))

     A  problem  with such  comments  is that  they  are discarded  when  the S-
     expression is read into lisp.  If it is edited within lisp and printed back
     into  a file,  the comments  will be  lost.  However,  most users  edit the
     original file and read the changes into lisp, since this allows them to use
     the editor of their choice.  Thus this is not a real problem.


prog2               LSUBR 2 or more args

     The expressions in a prog2 form are evaluated from left to right, as in any
     lsubr-form.  The  result is  the second argument.   prog2 is  most commonly
     used to evaluate an expression with side effects, then return a value which
     needs to be computed before the side effects happen.
     Examples:

            (prog2 (do-this) (do-that)) ;just get 2 things evaluated

            (setq x (prog2 nil y        ;parallel assignment
                           (setq y x))) ;which exchanges x and y

            (defun prog2 nargs (arg 2)) ;a lexpr definition for prog2
progn               LSUBR 1 or more args

     The expressions in a progn form are evaluated from left to right, as usual,
     and the result is the value of  the last one.  In other words, progn  is an
     lsubr which does  nothing but return  its last argument.   Although lambda-
     expressions, prog-forms, do-forms, cond-forms, and iog-forms all  use progn
     implicitly, that is, they allow  multiple forms in their bodies,  there are
     occasions when one needs to evaluate a number of forms for side-effects and
     make them appear to be a single form.  progn serves this purpose. Example:

          (progn (setq a (cdr frob)) (eq (car a) (cadr a)))

          might be used as the antecedent of a cond clause.

        progn could have been defined by:

        (defun progn nargs
            (and (> nargs 0)
                 (arg nargs)))


progv               FSUBR

     progv is a special form to provide the user with extra control over lambda-
     binding.   It binds  a list  of variables  to a  list of  values,  and then
     evaluates  some forms.   The  lists of  variables and  values  are computed
     quantities; this is what makes progv different from lambda, prog, and do.

                  (progv var-list value-list form1 form2 ... )

     first evaluates var-list and  value-list.  Then the variables are  bound to
     the values.   In compiled  code the  variables must  be special,  since the
     compiler has no way of  knowing what symbols might appear in  the var-list.
     If too few values are  supplied, the remaining variables are bound  to nil.
     If too many values are supplied, the excess values are ignored.

     After the variables have been bound to the values, the forms are evaluated,
     and finally the variable bindings  are undone.  The result returned  is the
     value of the last form.  Note that the "body" of a progv is similar to that
     of progn, not that of prog.
     Example:


        (setq a 'foo b 'bar)

        (progv (list a b 'b) (list b) (list a b foo bar))
            => (foo nil bar nil)

     During the evaluation of the body  of this progv, foo is bound to  bar, bar
     is bound to nil, b is bound to nil, and a remains bound to foo.


arg                 SUBR 1 arg

     (arg nil),  when evaluated  during the  application of  a lexpr,  gives the
     number of arguments supplied to that lexpr.  This is primarily  a debugging
     aid, since lexprs  also receive their number  of arguments as the  value of
     their lambda-variable.

     (arg i), when evaluated during the application of a lexpr, gives  the value
     of the i'th argument to the lexpr.  i must be a fixnum in this case.  It is
     an  error if  i is  less than  1 or  greater than  the number  of arguments
     supplied to the lexpr.

     Example:

        (defun foo nargs            ;define a lexpr foo.
            (print (arg 2))         ;print the second argument.
            (+ (arg 1)              ;return the sum of the first
               (arg (- nargs 1))))  ;and next to last arguments.


setarg              SUBR 2 args

     setarg is used only during the  application of a lexpr.  (setarg i  x) sets
     the  lexpr's i'th  argument to  x.  i  must be  greater than  zero  and not
     greater than the number of arguments passed to the lexpr.  After  (setarg i
     x) has been done, (arg i) will return x.






listify             SUBR 1 arg

     (listify n)  efficiently manufactures  a list of  n of  the arguments  of a
     lexpr.   With a  positive argument  n, it  returns a  list of  the  first n
     arguments of the lexpr.  With a  negative argument n, it returns a  list of
     the last (abs n) arguments of the lexpr.  Basically, it works as if defined
     as follows:

            (defun listify (n)
                 (cond ((minusp n)
                        (listify1 (arg nil) (+ (arg nil) n 1)))
                       (t
                        (listify1 n 1)) ))

            (defun listify1 (n m)      ; auxiliary function.
                 (do ((i n (1- i))
                      (result nil (cons (arg i) result)))
                     ((< i m) result) ))


funcall             LSUBR 1 or more args

     (funcall f a1 a2  ... an) calls the function  f with the arguments  a1, a2,
     ..., an.   It is similar  to apply except  that the separate  arguments are
     given to funcall, rather than a list  of arguments.  If f is a fexpr  or an
     fsubr there must be exactly one argument.  f may not be a macro.  Example:

                (setq cons 'plus)
                (cons 1 2) => (1 . 2)
                (funcall cons 1 2) => 3


subrcall            FSUBR

     subrcall  is  used  to  invoke  a  subr-pointer  directly,  rather  than by
     referring  to  an atomic  symbol  of  which the  subr-pointer  is  the subr
     property.  The form is:

                         (subrcall type p a1 a2 ... an)

     All arguments except the first  are evaluated.  type is the type  of result
     expected: fixnum, flonum, or nil (any  type).  p is the subr pointer  to be
     called.   a1  through  an are  the  arguments  to be  passed  to  the subr.
     subrcall compiles into efficient machine code.


lsubrcall           FSUBR

     lsubrcall is identical to subrcall except that the subr-pointer  called has
     to be an lsubr instead of a subr.  This is because many Lisps use different
     internal calling sequences for lsubrs than for subrs.


arraycall           FSUBR

     arraycall is similar to subrcall and lsubrcall except that an array-pointer
     is used instead  of a subr-pointer.  The  first argument of  arraycall must
     correspond to the type  that the array was  given when it was  created.  An
     arraycall expression may be used as the first argument to store.


symeval             SUBR 1 arg

     symeval is used to get the  value of an atomic symbol, when  the particular
     symbol which will be  used is not known  when the program is  written, (for
     example in  a language interpreter  written in Lisp.)   If the  argument to
     symeval  is not  an atomic  symbol, or  is an  atomic symbol  but  does not
     currently have a  value, an error is  signalled.  The advantage  of symeval
     over eval is that it is  compiled into very efficient code (which  will not
     detect the above-mentioned error, so watch out.)

file: LISP, node: Manipulating List Structure, previous: The Evaluator, up: Function Descriptions, next: Conses,
Source: MACLISP Manual 3/6/76

* MENU:

* Conses::
* Lists::
* Alteration of List Structure::
* Tables::
* Sorting::

file: LISP, node: Conses, previous: Manipulating List Structure, up: Manipulating List Structure, next: Lists,
Source: MACLISP Manual 3/6/76

car                 SUBR 1 arg

     Returns the first component of a cons.

     Example:  (car '(a b)) => a


cdr                 SUBR 1 arg

     Returns the second component of a cons.

     Example:  (cdr '(a b c)) => (b c)


car                 SWITCH

cdr                 SWITCH

     Officially car and cdr are only applicable to lists.  However, as  a matter
     of convenience the car and cdr of nil are nil.  This allows programs to car
     and cdr off the ends of  lists without having to check, which  is sometimes
     helpful.  Furthermore, some old programs apply car and cdr to objects other
     than lists in order to  hack with the internal representation.   To provide
     control over this, the value of car can be set to control which  data types
     are subject to the car operation.  Similarly, the value of cdr controls the
     cdr  operation.   Illegal operations  will  cause errors.   For  reasons of
     efficiency, this error checking is only enabled in (*rset t) mode (see part
     3.5) and is  mostly turned off in  compiled programs.  The values  to which
     the switches may be set are:






          Value      Operation applicable to

          list       lists.
          nil        lists and nil.
          symbol     lists, nil, and symbols.
          t          anything.

     The default value of the switches is nil.


c...r               SUBR 1 arg

     All the compositions of up to four car's and cdr's are defined as functions
     in their own right.  The names begin with c and end with r, and  in between
     is a sequence of a's and d's corresponding to the composition  performed by
     the function.

     For example,
                     (cddadr x) = (cdr (cdr (car (cdr x))))

     Some  of the  most commonly  used  ones are:  cadr, which  gets  the second
     element of a list; caddr, which  gets the third element of a  list; cadddr,
     which gets the fourth element of a list; caar, to car twice.

     The car'ing and cdr'ing  operations of these functions have  error checking
     under the control of the car and cdr switches explained above, just  as the
     car and cdr functions themselves do.


cons                SUBR 2 args

     This is a primitive  function to construct a  new dotted pair whose  car is
     the first argument to cons, and  whose cdr is the second argument  to cons.
     Thus the following  identities hold (except  when numbers are  involved; as
     always numbers are not well-behaved with respect to eq):

           (eq (car (cons x y)) x) => t
           (eq (cdr (cons x y)) y) => t




        Examples:
            (cons 'a 'b) => (a . b)
            (cons 'a (cons 'b (cons 'c nil))) => (a b c)
            (cons 'a '(b c d e f)) => (a b c d e f)


ncons               SUBR 1 arg

     (ncons x) = (cons x nil) = (list x)


xcons               SUBR 2 args

     xcons ("exchange cons") is like cons except that the order of  arguments is
     reversed.

     Example:
                            (xcons 'a 'b) => (b . a)

file: LISP, node: Lists, previous: Conses, up: Manipulating List Structure, next: Alteration of List Structure,
Source: MACLISP Manual 3/6/76


last                SUBR 1 arg

     last returns the last cons of the list which is its argument.

        Example:
                (setq x '(a b c d))
                (last x) => (d)
                (rplacd (last x) '(e f))
                x => (a b c d e f)

     last could have been defined by:

        (defun last (x)
            (cond ((null x) x)
                  ((null (cdr x)) x)
                  ((last (cdr x))) ))

     In some implementations,  the null check above  may be replaced by  an atom
     check, which  will catch  dotted lists.   Code which  depends on  this fact
     should not be  written though, because  all implementations are  subject to
     change on this point.


length              SUBR 1 arg

     length  returns the  length of  its argument,  which must  be a  list.  The
     length of a list is the number of top-level conses in it.

        Examples:
                (length nil) => 0
                (length '(a b c d)) => 4
                (length '(a (b c) d)) => 3

     length could have been defined by:






        (defun length (x)
            (cond ((null x) 0)
                  ((1+ (length (cdr x)))) ))
        or by:

        (defun length (x)
            (do ((n 0 (1+ n))
                 (y x (cdr y)))
                ((null y) n) ))

     The warning about dotted lists given under last applies also to length.


list                LSUBR 0 or more args

     list constructs and returns a list of its arguments.

     Example:
              (list 3 4 'a (car '(b . c)) (+ 6 -2)) => (3 4 a b 4)

     list could have been defined by:

        (defun list nargs
            (do ((n nargs (1- n))
                 (s nil (cons (arg n) s)))
                ((zerop n) s) ))
     (This depends on parallel assignment to the control variables of do.)


append              LSUBR 0 or more args

     The arguments  to append  are lists.   The result  is a  list which  is the
     concatenation of the arguments.  The arguments are not changed (cf. nconc).
     For example,

             (append '(a b c) '(d e f) nil '(g)) => (a b c d e f g)

     To make a copy of  the top level of a list,  that is, to copy the  list but
     not its elements, use (append x nil).


     A  version of  append  which only  accepts  two arguments  could  have been
     defined by:

        (defun append2 (x y)
            (cond ((null x) y)
                  ((cons (car x) (append2 (cdr x) y)) )))

     The generalization to  any number of arguments  could then be made  using a
     lexpr:

        (defun append argcount
            (do ((i (1- argcount) (1- i))
                 (val (arg argcount) (append2 (arg i) val)))
                ((zerop i) val) ))


reverse             SUBR 1 arg

     Given a list as argument, reverse creates a new list whose elements are the
     elements of its argument taken  in reverse order.  reverse does  not modify
     its argument, unlike nreverse which is faster but does modify its argument.
     Example:

                   (reverse '(a b (c d) e)) => (e (c d) b a)

        reverse could have been defined by:

        (defun reverse (x)
            (do ((l x (cdr l))         ; scan down argument,
                 (r nil                ; putting each element
                    (cons (car l) r))) ; into list, until
                ((null l) r)))         ; no more elements.


nconc               LSUBR 0 or more args

     nconc takes lists as arguments.   It returns a list which is  the arguments
     concatenated  together.  The  arguments  are changed,  rather  than copied.
     (cf. append)

     Example:
                   (nconc '(a b c) '(d e f)) => (a b c d e f)
     Note that the constant (a b c) has  now been changed to (a b c d e  f).  If
     this form is evaluated again, it will yield (a b c d e f d e f).  This is a
     danger you always have to watch out for when using nconc.

     nconc could have been defined by:

        (defun nconc (x y)      ;for simplicity, this definition
            (cond ((null x) y)  ;only works for 2 arguments.
                  (t (rplacd (last x) y) ;hook y onto x
                      x)))      ;and return the modified x.


nreverse            SUBR 1 arg

     nreverse reverses its  argument, which should be  a list.  The  argument is
     destroyed by rplacd's all through the list (cf. reverse).

     Example:
                         (nreverse '(a b c)) => (c b a)

        nreverse could have been defined by:

        (defun nreverse  (x)
            (cond ((null x) nil)
                  ((nreverse1 x nil))))

        (defun nreverse1 (x y)          ;auxiliary function
            (cond ((null (cdr x)) (rplacd x y))
                  ((nreverse1 (cdr x) (rplacd x y)))))
                  ;; this last call depends on order of argument evaluation.


nreconc             SUBR 2 args

     (nreconc x y) is exactly the same as (nconc (nreverse x) y) except  that it
     is more efficient.

     nreconc could have been defined by:

        (defun nreconc (x y)
            (cond ((null x) y)
                  ((nreverse1 x y)) ))
     using the same nreverse1 as above.

file: LISP, node: Alteration of List Structure, previous: Lists, up: Manipulating List Structure, next: Tables,
Source: MACLISP Manual 3/6/76


   The functions  rplaca and  rplacd are  used to  make alterations  in already-
existing list structure.   The structure is  not copied but  physically altered;
hence caution should  be exercised when using  these functions as  strange side-
effects can occur if portions of list structure become shared unbeknownst to the
programmer.  The nconc, nreverse,  and nreconc functions already  described have
the same property.   However, they are normally  not used for  this side-effect;
rather, the list-structure modification is purely for efficiency  and compatible
non-modifying functions are provided.

rplaca              SUBR 2 args

     (rplaca  x y)  changes the  car of  x to  y and  returns (the  modified) x.
     Example:

            (setq g '(a b c))

            (rplaca (cdr g) 'd) => (d c)

     Now g => (a d c)


rplacd              SUBR 2 args

     (rplacd  x y)  changes the  cdr of  x to  y and  returns (the  modified) x.
     Example:

            (setq x '(a b c))

            (rplacd x 'd) => (a . d)

     Now x => (a . d)

     See also setplist (page 2-51).






subst               SUBR 3 args

     (subst x y z) substitutes x for all occurrences of y in z, and  returns the
     modified copy  of z.   The original  z is  unchanged, as  subst recursively
     copies all of z replacing elements eq to y as it goes.  If x and y are nil,
     z  is  just  copied, which  is  a  convenient way  to  copy  arbitrary list
     structure.

     Example:

        (subst 'Tempest 'Hurricane
               '(Shakespeare wrote (The Hurricane)))
            => (Shakespeare wrote (The Tempest))

     subst could have been defined by:

        (defun subst (x y z)
            (cond ((eq z y) x)    ;if item eq to y, replace.
                  ((atom z) z)    ;if no substructure, return arg.
                  ((cons (subst x y (car z))  ;otherwise recurse.
                         (subst x y (cdr z))))))


sublis              SUBR 2 args

     sublis  makes substitutions  for atomic  symbols in  an  S-expression.  The
     first argument  to sublis is  an association list  (see the  next section).
     The second argument  is the S-expression in  which substitutions are  to be
     made.  sublis looks at all atomic symbols in the S-expression; if an atomic
     symbol appears in  the association list occurrences  of it are  replaced by
     the object it is associated with.  The argument is not modified; new conses
     are created where necessary and only where necessary, so the  newly created
     structure shares as much of its substructure as possible with the old.  For
     example, if  no substitutions  are made,  the result  is eq  to the  old S-
     expression.
     Example:

            (sublis '((x . 100) (z . zprime))
                    '(plus x (minus g z x p) 4))
               => (plus 100 (minus g zprime 100 p) 4)

     In some implementations sublis works by putting temporary sublis properties

file: LISP, node: Tables, previous: Alteration of List Structure, up: Manipulating List Structure, next: Sorting,
Source: MACLISP Manual 3/6/76


   Maclisp includes several functions which simplify the maintenance  of tabular
data structures of  several varieties.  The simplest  is a plain list  of items,
which models (approximately) the concept  of a set.  There are functions  to add
(cons), remove (delete, delq), and search for (member, memq) items in a list.

   Association lists are very commonly  used.  An association list is a  list of
dotted pairs.   The car  of each pair  is a  "key" and the  cdr is  "data".  The
functions assoc and assq may be used to retrieve the data, given the key.

   Structured records can  be stored as association  lists or as  stereotyped S-
expressions  where each  element of  the structure  has a  certain  car-cdr path
associated with it.  There  are no built-in functions  for these but it  easy to
define macros to implement them (see part 6.2).

   Simple list-structure is very convenient, but may not be efficient enough for
large data bases because  it takes a long time  to search a long  list.  Maclisp
includes some hashing functions  (sxhash, maknum) which aid in  the construction
of more efficient, hairier structures.


member              SUBR 2 args

     (member x y) returns nil if x is not a member of the list y.  Otherwise, it
     returns the  portion of y  beginning with the  first occurrence of  x.  The
     comparison is made by equal.  y is searched on the top level only.

        Example:
                (member 'x '(1 2 3 4)) => nil
                (member 'x '(a (x y) c x d e x f)) => (x d e x f)


     Note that the  value returned by  member is eq to  the portion of  the list
     beginning with x.  Thus rplaca on the result of member may be used,  if you
     first check to make sure member did not return nil.
     Example:

        (catch (rplaca (or (member x z)
                           (throw nil lose))
                       y)
     member could have been defined by:

        (defun member (x y)
            (cond ((null y) nil)
                  ((equal x (car y)) y)
                  ((member x (cdr y))) ))


memq                SUBR 2 args

     memq  is like  member, except  eq is  used for  the comparison,  instead of
     equal.  memq could have been defined by:

        (defun memq (x y)
            (cond ((null y) nil)
                  ((eq x (car y)) y)
                  ((memq x (cdr y))) ))


delete              LSUBR 2 or 3 args

     (delete  x  y) returns  the  list y  with  all top-level  occurrences  of x
     removed.  equal  is used for  the comparison.  The  argument y  is actually
     modified (rplacd'ed) when instances of x are spliced out.  delete should be
     used for value, not for effect.  That is, use

        (setq a (delete 'b a))

        rather than

        (delete 'b a))


        The latter is not equivalent when the first element of the value of a is
        b.

     (delete x y n) is like (delete x y) except only the first n instances  of x
     are deleted.  n is allowed to be zero.  If n is greater than the  number of
     occurrences of  x in the  list, all occurrences  of x in  the list  will be
     deleted.

     Example:

        (delete 'a '(b a c (a b) d a e)) => (b c (a b) d e)

        delete could have been defined by:

        (defun delete nargs        ; lexpr for 2 or 3 args
            (delete1 (arg 1)       ; pass along arguments...
                     (arg 2)
                     (cond ((= nargs 3) (arg 3))
                           (123456789.)))) ; infinity

        (defun delete1 (x y n)       ;auxiliary function
            (cond ((or (null y) (zerop n)) y)
                  ((equal x (car y)) (delete1 x
                                              (cdr y)
                                              (1- n)))
                  ((rplacd y (delete1 x (cdr y) n)))))


delq                LSUBR 2 or 3 args

     delq  is the  same as  delete except  that eq  is used  for  the comparison
     instead of equal.


sxhash              SUBR 1 arg

     sxhash computes a hash code of an S-expression, and returns it as a fixnum,
     which may be positive or negative.   A property of sxhash is that  (equal x
     y) implies  (= (sxhash x)  (sxhash y)).  The  number returned by  sxhash is
     some  possibly  large  number  in the  range  allowed  by  fixnums.   It is
     guaranteed that:

     1) sxhash for an atomic symbol will always be positive.

     2) sxhash  of any particular  expression will be  constant in  a particular
     implementation for all time, probably.

     3)  Two  different  implementations  may  hash  the  same  expression  into
     different values.

     4) sxhash of any object of type random will be zero.
     5) sxhash of a fixnum will = that fixnum.

        Here is an example of how to use sxhash in maintaining
        hash tables of S-expressions:

     (defun knownp (x)    ;look up x in the table
       (prog (i bkt)
         (setq i (plus 76 (remainder (sxhash x) 77)))
           ;The remainder should be reasonably randomized between
           ;-76 and 76, thus table size must be > 175 octal.
         (setq bkt (table i))
           ;bkt is thus a list of all those expressions that hash
           ;into the same number as does x.
         (return (member x bkt))))

     To write an "intern" for S-expressions, one could

     (defun sintern (x)
       (prog (bkt i tem)
         (setq bkt (table (setq i (+ 2n-2 (\ (sxhash x) 2n-1)))))
             ;2n-1 and 2n-1 stand for a power of 2 minus one and
             ;minus two respectively.  This is a good choice to
             ;randomize the result of the remainder operation.
         (return (cond ((setq tem (member x bkt))
                        (car tem))
                       (t (store (table i) (cons x bkt))
                          x)))))


assoc               SUBR 2 args

     (assoc x y) looks  up x in the association  list (list of dotted  pairs) y.
     The value is the first dotted pair whose car is equal to x, or nil if there
     is none such.

        Examples:
             (assoc 'r '((a . b) (c . d) (r . x) (s . y) (r . z)))
                =>  (r . x)

             (assoc 'fooo '((foo . bar) (zoo . goo))) => nil

     It is okay to rplacd the result of assoc as long as it is not nil,  if your

        Example:
            (setq values '((x .  100) (y  . 200) (z .  50)))
            (assoc 'y values) => (y . 200)
            (rplacd (assoc 'y values)  201)
            (assoc 'y values)  => (y . 201) now
               (One should always be careful about using rplacd however)

     A typical  trick is  to say (cdr  (assoc x  y)).  Since the  cdr of  nil is
     guaranteed to be nil, this yields nil if no pair is found (or if a  pair is
     found whose cdr is nil.)

        assoc could have been defined by:

        (defun assoc (x y)
            (cond ((null y) nil)
                  ((equal x (caar y)) (car y))
                  ((assoc x (cdr y))) ))


assq                SUBR 2 args

     assq is  like assoc except  that the comparison  uses eq instead  of equal.
     assq could have been defined by:

        (defun assq (x y)
            (cond ((null y) nil)
                  ((eq x (caar y)) (car y))
                  ((assq x (cdr y))) ))


sassoc              SUBR 3 args

     (sassoc x y  z) is like  (assoc x y) except  that if x  is not found  in y,
     instead of  returning nil sassoc  calls the function  z with  no arguments.
     sassoc could have been defined by:

        (defun sassoc (x y z)
            (or (assoc x y)
                (apply z nil)))

     sassoc  and sassq  (see below)  are of  limited use.   These  are primarily
sassq               SUBR 3 args

     (sassq x  y z)  is like (assq  x y)  except that if  x is  not found  in y,
     instead of  returning nil  sassq calls  the function  z with  no arguments.
     sassq could have been defined by:

        (defun sassq (x y z)
            (or (assq x y)
                (apply z nil)))


maknum              SUBR 1 arg

     (maknum x) returns a positive fixnum which is unique to the object  x; that
     is, (maknum x) and  (maknum y) are numerically equal  if and only if  (eq x
     y).  This can be used in hashing.

     In the  pdp-10 implementations,  maknum returns the  memory address  of its
     argument.   In  the  Multics  implementation,  an  internal  hash  table is
     employed.

     Note  that unlike  sxhash, maknum  will  not return  the same  value  on an
     expression which has been printed out and read back in again.


munkam              SUBR 1 arg

     munkam is the  opposite of maknum.  Given  a number, it returns  the object
     which was given to maknum to  get that number.  It is inadvisable  to apply
     munkam to a number which did not come from maknum.

file: LISP, node: Sorting, previous: Tables, up: Manipulating List Structure, next: Flow of Control,
Source: MACLISP Manual 3/6/76


   Several functions are provided for sorting arrays and lists.  These functions
use algorithms which always terminate no matter what sorting predicate  is used,
provided  only that  the predicate  always terminates.   The array  sort  is not
necessarily stable, that  is equal items may  not stay in their  original order.
However the list sort is stable.

   After sorting, the argument (be it list or array) is rearranged internally so
as  to  be completely  ordered.   In the  case  of an  array  argument,  this is
accomplished by permuting the elements of the array, while in the list case, the
list is  reordered by  rplacd's in  the same  manner as  nreverse.  Thus  if the
argument should not  be clobbered, the  user must sort  a copy of  the argument,
obtainable by fillarray or append, as appropriate.

   Should the comparison predicate cause an error, such as a wrong type argument
error, the state of  the list or array  being sorted is undefined.   However, if
the error is corrected the sort will, of course, proceed correctly.

   Both sort and sortcar handle the  case in which their second argument  is the
function alphalessp in a more  efficient manner than usual.  This  efficiency is
primarily due to elimination of argument checks at comparison time.


sort                SUBR 2 args

     The first argument to sort is an array (or list), the second a predicate of
     two arguments.  Note that a "number array" cannot be sorted.  The predicate
     must be applicable to all the objects in the array or list.   The predicate
     should take  two arguments,  and return non-nil  if and  only if  the first
     argument is strictly less than the second (in some appropriate sense).

     The sort function proceeds to sort the contents of the array or  list under
     the  ordering imposed  by  the predicate,  and  returns the  array  or list
     modified into sorted  order, i.e. its  modified first argument.   Note that
     since  sorting  requires  many  comparisons, and  thus  many  calls  to the
     predicate,  sorting will  be much  faster if  the predicate  is  a compiled
     function rather than interpreted.




        Example:

        (defun mostcar (x)
            (cond ((atom x) x)
                  ((mostcar (car x)))))

        (sort 'fooarray
              (function (lambda (x y)
                (alphalessp (mostcar x) (mostcar y)))))

     If fooarray contained these items before the sort:

        (Tokens (The lion sleeps tonight))
        (Carpenters (Close to you))
        ((Rolling Stones) (Brown sugar))
        ((Beach Boys) (I get around))
        (Beatles (I want to hold your hand))

     then after the sort fooarray would contain:

        ((Beach Boys) (I get around))
        (Beatles (I want to hold your hand))
        (Carpenters (Close to you))
        ((Rolling Stones) (Brown sugar))
        (Tokens (The lion sleeps tonight))


sortcar             SUBR 2 args

     sortcar is  exactly like sort,  but the  items in the  array or  list being
     sorted should all be non-atomic.  sortcar takes the car of each item before
     handing two items to the predicate.   Thus sortcar is to sort as  mapcar is
     to maplist.

file: LISP, node: Flow of Control, previous: Sorting, up: Function Descriptions, next: Conditionals,
Source: MACLISP Manual 3/6/76

* MENU:

* Conditionals::
* Iteration::
* Non-local Exits::
* Causing and Controlling Errors::



   Maclisp provides a variety of structures for flow of control.

   Functional application is the basic method for construction of programs.  All
operations are written as the  application of a function to  arguments.  Maclisp
programs  are often  written  as a  large  collection of  small  functions which
implement simple operations.   Some of the functions  work by calling  others of
the functions, thus defining some operations in terms of others.

   Recursion  exists  when  a  function  calls  itself.   This  is  analogous to
mathematical induction.

   Iteration is a control structure present in most languages.  It is similar to
recursion but sometimes less useful and sometimes more useful.  Maclisp contains
a generalized iteration facility.  The iteration facility also permits those who
like "gotos" to use them.

   Conditionals allow control to branch  depending on the value of  a predicate.
and  and or  are basically  one-arm conditionals,  while cond  is  a generalized
multi-armed conditional.

   Nonlocal  exits are  similar to  a  return, except  that the  return  is from
several levels of  function calling rather than  just one, and is  determined at
run time.   These are  mostly used for  applications such  as escaping  from the
middle of a function when it is discovered that the algorithm is not applicable.

   Errors are  a type of  non-local exit  used by the  Lisp interpreter  when it
discovers a condition that it does not like.  Errors have the additional feature
of correctability, which  allows a user-specified  function (most often  a break
loop), to get a chance to come in and correct the error or at least inspect what
was happening  and determine what  caused it, before  the nonlocal  exit occurs.
This is explained in detail on part 3.4.

   Maclisp does not directly provide "hairy control structure" such  as multiple
processes, backtracking, or continuations.


file: LISP, node: Conditionals, previous: Flow of Control, up: Flow of Control, next: Iteration,
Source: MACLISP Manual 3/6/76

and                 FSUBR

     (and form1 form2...) evaluates the forms one at a time, from left to right.
     If  any  form  evaluates  to  nil,  and  immediately  returns  nil  without
     evaluating the  remaining forms.   If all the  forms evaluate  non-nil, and
     returns  the value  of the  last one.   and can  be used  both  for logical
     operations, where  nil stands for  False and  t stands for  True, and  as a
     conditional expression.

        Examples:
             (and x y)

             (and (setq temp (assq x y))
                  (rplacd temp z))

             (and (null (errset (something)))
                  (princ "There was an error."))

     Note: (and) => t, which is the identity for this operation.


or                  FSUBR

     (or form1 form2...) evaluates the forms one by one from left to  right.  If
     a form evaluates to nil, or  proceeds to evaluate the next form.   If there
     are no more  forms, or returns  nil.  But if  a form evaluates  non-nil, or
     immediately returns that value without evaluating any remaining  forms.  or
     can be used both for logical  operations, where nil stands for False  and t
     for True, and as a conditional expression.

     Note:  (or) => nil, the identity for this operation.


cond                FSUBR

     The  cond  special form  consists  of  the word  cond  followed  by several
     clauses.  Each  clause consists  of a  predicate followed  by zero  or more
     forms.  Sometimes the predicate is called the antecedent and the  forms are
     called the consequents.

        (cond (antecedent consequent consequent...)
              (antecedent ...)
              ... )

     The idea is  that each clause  represents a case  which is selected  if its
     predicate is satisfied and the predicates of all preceding clauses  are not
     satisfied.  When a case is selected, its consequent forms are evaluated.

     cond  processes  its  clauses  in order  from  left  to  right.   First the
     predicate of the current clause  is evaluated.  If the result is  nil, cond
     advances to the next clause.   Otherwise, the cdr of the clause  is treated
     as a list of forms, or consequents, which are evaluated in order  from left
     to  right.   After   evaluating  the  consequents,  cond   returns  without
     inspecting any remaining  clauses.  The value of  the cond special  form is
     the value of the last consequent evaluated, or the value of  the antecedent
     if there were no consequents in  the clause.  If cond runs out  of clauses,
     that is, if every antecedent is  nil, that is, if no case is  selected, the
     value of the cond is nil.

        Example:
            (cond ((zerop x)    ;First clause:
                   (+ y 3))     ; (zerop x) is antecedent.
                                ; (+ y 3) is consequent.
                  ((null y)     ;A clause with 2 consequents:
                   (setq x 4)   ; this
                   (cons x z))  ; and this.
                  (z)           ;A clause with no consequents:
                                ; the antecedent is just z.
               )                ;This is the end of the cond.

     This is like the traditional Lisp 1.5 cond except that it is  not necessary
     to have exactly one consequent in each clause, and it is permissible to run
     out of clauses.


file: LISP, node: Iteration, previous: Conditionals, up: Flow of Control, next: Non-local Exits,
Source: MACLISP Manual 3/6/76



prog                FSUBR

     prog  is  the "program"  special  form.  It  provides  temporary variables,
     sequential evaluation of statements, and the ability to do "gotos."  A prog
     looks something like:

        (prog (var1 var2...)
         tag1
            statement1
            statement2
         tag2
            statement3
            . . .
          )

     var1, var2,  ... are  temporary variables.   When the  prog is  entered the
     values of  these variables  are saved.  When  the prog  is exited  they are
     restored.  The variables are initialized  to nil when the prog  is entered,
     thus they are said  to be "bound to  nil" by the prog.   However, variables
     which have been declared fixnum or  flonum will be initialized to 0  or 0.0
     instead,  but  only in  compiled  programs.  You  should  be  careful about
     relying on the initial value of prog-variables.

     The part of a prog after the temporary variable list is the body.   An item
     in the body may be an atomic symbol or a number, which is a tag, or  a non-
     atomic form, which is a statement.

     prog,   after  binding   the  temporary   variables,  processes   its  body
     sequentially.  tags  are skipped  over;  statements  are evaluated  but the
     values are ignored.  If the end  of the body is reached, prog  returns nil.
     If (return x) is evaluated, prog stops processing its body and  returns the
     value x.   If (go tag)  is evaluated, prog  jumps to the  part of  the body
     labelled with the tag.   The argument to go  is not evaluated unless  it is
     non-atomic.

     It should be noted  that the Maclisp prog is  an extension of the  Lisp 1.5
     prog, in  that go's and  return's may  occur in more  places than  Lisp 1.5
     allowed.  However, the Lisp compilers implemented on ITS, Multics,  and the
     DECsystem 10 for Maclisp require that go's and return's be lexically within
     the scope of the prog. This makes a function which does not contain a prog,
     but which does contain a go or return uncompilable.

     See also the do special form,  which uses a body similar to prog.   The do,
     catch, and  throw special forms  are included in  Maclisp as an  attempt to
     encourage goto-less programming style,  which leads to more  readable, more
     easily  maintained  code.   The  programmer  is  recommended  to  use these
     functions instead of prog wherever reasonable.

     Example:

        (prog (x y z)  ;x, y, z are prog variables  - temporaries.
           (setq y (car w) z (cdr w))     ;w is a free variable.
        loop
           (cond ((null y) (return x))
                 ((null z) (go err)))
        rejoin
           (setq x (cons (cons (car y) (car z))
                         x))
           (setq y (cdr y)
                 z (cdr z))
           (go loop)
        err
           (break are-you-sure? t)
           (setq z y)
           (go rejoin))


do                  FSUBR

     The do  special form  provides a  generalized "do  loop" facility,  with an
     arbitrary number of "index variables" whose values are saved when the do is
     entered and restored when it is  left, i.e. they are bound by the  do.  The
     index  variables  are  used  in the  iteration  performed  by  do.   At the
     beginning they are initialized to specified values, and then at the  end of
     each trip  around the loop  the values of  the index variables  are changed
     according  to  specified rules.   do  allows the  programmer  to  specify a
     predicate which determines when the iteration will terminate.  The value to
     be returned as the result of the form may optionally be specified.

     do comes in two varieties.

     The newer variety of do looks like:

        (do ((var init repeat)...)
            (end-test exit-form...)
            body...)

     The  first item  in the  form  is a  list of  zero or  more  index variable
     specifiers.   Each index  variable specifier  is a  list of  the name  of a
     variable var,  an initial value  init, which defaults  to nil  (or possibly
     zero, as mentioned under prog) if it is omitted, and a repeat value repeat.
     If repeat is omitted, the var is not changed between loops.

     All  assignment  to  the  index variables  is  done  in  parallel.   At the
     beginning of  the first iteration,  all the inits  are evaluated,  then the
     vars are saved, then the vars  are setq'ed to the values of the  inits.  To
     put it another way, the vars  are lambda-bound to the values of  the inits.
     Note  that the  inits are  evaluated  before the  vars are  bound.   At the
     beginning of  each succeeding  iteration those vars  that have  repeats get
     setq'ed  to the  values of  their respective  repeats.  Note  that  all the
     repeats are evaluated before any of the vars is changed.

     The second element  of the do-form  is a list  of an end  testing predicate
     end-test and zero or more forms, the exit-forms.  At the beginning  of each
     iteration, after processing of the repeats, the end-test is  evaluated.  If
     the result  is nil, execution  proceeds with  the body of  the do.   If the
     result is not nil, the exit-forms are evaluated from left to right and then
     do returns.  The value of the do is the value of the last exit-form, or nil
     if there were no exit-forms.   Note that the second element of  the do-form
     resembles a cond clause.

     If the second element  of the form is nil,  there is no end-test  nor exit-
     forms, and the body of the do is executed only once.  In this type of do it
     is an  error to  have repeats.   This type of  do is  a "prog  with initial
     values."

     If the second element  of the form is  the S-expression (nil), there  is no
     end-test or exit-forms, and the body  of the do is executed over  and over.
     This is  a "do  forever." The  infinite loop  can be  terminated by  use of
     return or throw.

     The remainder of the do-form constitutes a prog-body.  When the end  of the
     body is reached, the next iteration  of the do begins.  If return  is used,
     The older variety of do is:

     (do var init repeat end-test body...)

     The first time through the loop  var gets the value of init;  the remaining
     times through the loop it  gets the value of repeat, which  is re-evaluated
     each time.  Note that init is  evaluated before the value of var  is saved.
     After var is set, end-test is evaluated.  If it is non-nil, the do finishes
     and returns nil.  If the end-test is nil, the body of the loop is executed.
     The body  is like a  prog body.  go  may be used.   If return is  used, its
     argument is the value of the do.   If the end of the prog body  is reached,
     another loop begins.

     Examples of the older variety of do:

        (setq n (cadr (arraydims x)))
        (do i 0 (1+ i) (= i n)
                (store (x i) 0))      ;zeroes out the array x

        (do zz x (cdr zz) (or (null zz) (zerop (f (car zz)))))
                           ; this applies f to each element of x
                           ; continuously until f returns zero.

     Examples of the new form of do:

             (do ((n (cadr (arraydims x)))
                  (i 0 (1+ i)))
                 ((= i n)
               (store (x i) 0))
                     ;this is like the example above,
                     ;except n is local to the do

             (do ((x) (y) (z)) (nil) body)
        is like
             (prog (x y z) body)

     except  that when  it runs  off the  end  of  the body,  do loops  but prog
     returns nil.  On the other hand,

             (do ((x) (y) (z)) nil body)

        is identical to the prog above (it does not loop.)

        (do ((x y (f x))) ((p x)) body)

        is like

        (do x y (f x) (p x) body)

     The construction

        (do ((x e (cdr x)) (oldx x x)) ((null x)) body)

     exploits parallel assignment to  index variables.  On the  first iteration,
     the value of oldx  is whatever value x had  before the do was  entered.  On
     succeeding iterations, oldx contains the  value that x had on  the previous
     iteration.

     In either form of do, the body may contain no forms at all.  Very  often an
     iterative algorithm can be  most clearly expressed entirely in  the repeats
     and exit-forms of a new-style do, and the body is empty.

        (do ((x x (cdr x))
             (y y (cdr y))
             (z nil (cons (f x y) z))) ;exploits parallel
            ((or (null x) (null y))    ; assignment.
             (nreverse z))             ;typical use of nreverse.
            )                          ;no do-body required.

        is like (maplist 'f x y).


go                  FSUBR

     The (go tag) special form is used  to do a "go-to" within the body of  a do
     or a prog.  If  the tag is an atom,  it is not evaluated.  Otherwise  it is
     evaluated and should yield an atom.  Then go transfers control to the point
     in the  body labelled by  a tag  eq or =  to the one  given.  (Tags  may be
     either atomic symbols or numbers).  If there is no such tag in the body, it
     is an unseen-go-tag error.

     "Computed" go's should be avoided in compiled code, or altogether.



        Example:

        (prog (x y z)
          (setq x some frob)
        loop
          do something
          (and some predicate (go loop))  ;regular go
          do something more
          (go (cond ((minusp x) 'loop)    ;"computed go"
                    (t 'endtag)))
        endtag
          (return z))


return              SUBR 1 arg

     return  is used  to return  from a  prog or  a do.   The value  of return's
     argument  is returned  by prog  or  do as  its value.   In  addition, break
     recognizes  the typed-in  S-expression (return  value) specially.   If this
     form is typed at a break, value will be evaluated and returned as the value
     of break.  If  not at the  top level of  a form typed  at a break,  and not
     inside a prog or do, return will cause a fail-act error.
     Example:

        (do ((x x (cdr x))
             (n 0 (* n 2)))
            ((null x) n)
         (cond ((atom (car x))
                (setq n (1+ n)))
               ((memq (caar x) '(sys boom bleah))
                (return n))))

file: LISP, node: Non-local Exits, previous: Iteration, up: Flow of Control, next: Causing and Controlling Errors,
Source: MACLISP Manual 3/6/76

catch               FSUBR

     catch is the Maclisp function for doing structured non-local exits.
     (catch x) evaluates x and returns its value, except that if during the
     evaluation of x (throw y) should be evaluated, catch immediately returns
     y without further evaluating x.

     catch may also be used with a second argument, not evaluated, which is
     used as a tag to distinguish between nested catches.  (catch x b) will
     catch a (throw y b) but not a (throw y z).  throw with only one argument
     always throws to the innermost catch.  catch with only one argument
     catches any throw.  It is an error if throw is done when there is no
     suitable catch.
     Example:

	(catch (mapcar (function (lambda (x) (cond ((minusp x)
						    (throw x negative))
						   (t (f x)))))
		       y)
	       negative)

     which returns a list of f of each element of y if y is all positive,
     otherwise the first negative member of y.

     The user of catch and throw is advised to stick to the 2 argument
     versions, which are no less efficient, and tend to reduce the likelihood
     of bugs. The one argument versions exist primarily as an easy way to fix
     old Lisp programs which use errset and err for non-local exits.  This
     latter practice is rather confusing, because err and errset are supposed
     to be used for error handling, not general program control.

     The catch-tag break is used by the break function.







throw               FSUBR

     throw is used with catch as a structured non-local exit mechanism.

     (throw x) evaluates x and throws the value back to the most recent
     catch.

     (throw x tag) throws the value of x back to the most recent catch
     labelled with tag or unlabelled.  catch'es with tags not eq to tag are
     skipped over. x is evaluated but tag is not.

     See the description of catch for further details.

file: LISP, node: Causing and Controlling Errors, previous: Non-local Exits, up: Flow of Control, next: Atomic Symbols,
Source: MACLISP Manual 3/6/76

   See the complete description of the Maclisp error system (part 3.4)  for more
information about how these functions work.

error               LSUBR 0 to 3 args

     This is a function which  allows user functions to signal their  own errors
     using the Maclisp error system.

     (error) is the same as (err).

     (error message)  signals a simple  error; no datum  is printed and  no user
     interrupt is signalled.  The error message typed out is message.

     (error message datum)  signals an error with  message as the message  to be
     typed out and datum as the Lisp object to be printed in the  error message.
     No user interrupt is signalled.

     (error message datum  uint-chn) signals an error  but first signals  a user
     interrupt on channel uint-chn, provided  that there is such a  channel, and
     it has a  non-nil service function,  and the special  conditions concerning
     errset (see  part 3.4) are  satisfied.  uint-chn is  the name of  the user-
     interrupt channel to  be used (an atomic  symbol); see part 3.4.2.   If the
     service function returns  an atom, error goes  ahead and signals  a regular
     error.  If the service function returns a list, error returns as  its value
     the car of that list.  In this case it was a "correctable" error.   This is
     the only case  in which error  will return; in  all other cases  control is
     thrown back to top level, or to the nearest enclosing errset.


errset              FSUBR

     The special  form (errset  form flag) is  used to  trap an  expected error.
     errset evaluates the form.  If an error occurs during the evaluation of the
     form,  the error  is prevented  from escaping  from inside  the  errset and
     errset returns nil.  If no errors occur, a list of one element,  the result
     of the evaluation, is returned.  The result is listified so that there will
     no ambiguity if it is nil.  errset may also be made to return any arbitrary
     value by use of the err function.

     The flag is optional.  If present, it is evaluated before the form.   If it
     is nil,  no error message  will be  printed if an  error occurs  during the
     evaluation of the form.  If it is  not nil, or if it is omitted,  any error
     messages generated will be printed.

     Examples:

     If you are not sure x is a number:

                           (errset (setq x (add1 x)))

     This example may not work in compiled code if the compiler chooses to open-
     code the  add1 rather than  calling the add1  subroutine.  In  general, one
     must be extremely foolhardy to depend on error checking in compiled code.

     To suppress the error message if the value of a is not an atomic symbol:

                             (errset (set a b) nil)

     To do the same but generate one's own message:

              (or (errset (set a b) nil)
                  (error '(not a variable) a))


err                 FSUBR

     (err) causes an error which is handled the same as a Lisp error except that
     there is no preliminary user interrupt, and no message is typed out.

     (err x)  is like (err)  except that  if control returns  to an  errset, the
     value of the errset will be the result of evaluating x, instead of nil.

     (err x nil) is the same as (err x).

     (err x t) is like (err x) except that x is not evaluated until  just before
     the errset returns it.  That is, x is evaluated after unwinding the pdl and
     restoring the bindings.

     Note: some people use err  and errset where catch and throw  are indicated.
     This is a very poor programming practice.  See writeups of catch  and throw
     for details.

file: LISP, node: Atomic Symbols, previous: Causing and Controlling Errors, up: Function Descriptions, next: The Value Cell,
Source: MACLISP Manual 3/6/76

* MENU:

* The Value Cell::
* The Property List::
* The Print-Name::
* Interning of Symbols::
* Defining Atomic Symbols as Functions::


file: LISP, node: The Value Cell, previous: Atomic Symbols, up: Atomic Symbols, next: The Property List,
Source: MACLISP Manual 3/6/76

   Each atomic symbol has associated with  it a value cell, which is a  piece of
storage that can refer to one  Lisp object.  This object is called  the symbol's
value, since it is what is returned if the symbol is evaluated.  The  binding of
atomic  symbols  to  values  allows  them to  be  used  in  programming  the way
"variables" are used in other languages.

   The value cell can also be empty,  in which case the symbol has no  value and
is said  to be  unbound or  undefined.  This is  the initial  state of  a newly-
created atomic symbol.  Attempting to evaluate an unbound symbol causes an error
to be signalled.

   An object can be  placed into a symbol's  value cell by lambda-binding  or by
assignment.   (See page  1-11.)  The  difference is  in how  closely  the value-
changing is associated with control structure and in whether it is  considered a
side-effect.


setq                FSUBR

     The  setq  special form  is  used  to assign  values  to  variables (atomic
     symbols.) setq processes  the elements of  its form in  pairs, sequentially
     from left  to right.   The first  member of  each pair  is a  variable, the
     second is a form  which evaluates to a  value.  The form is  evaluated, but
     the variable is not.  The value-binding  of the variable is made to  be the
     value specified.  You must  not setq the special atomic-symbol  constants t
     and nil.  The value returned by  setq is the last value assigned,  i.e. the
     result of the evaluation of the last element of the setq-form.

     Example:  (setq x (+ 1 2 3) y (cons x nil))

     This returns (6) and gives x a value of 6 and y a value of (6).

     Note that the first assignment is completed before the second assignment is
     started, resulting in the second use of x getting the value assigned in the
set                 SUBR 2 args

     set is like setq except that the first argument is evaluated; also set only
     takes one pair of arguments.  The first argument must evaluate to an atomic
     symbol, whose value  is changed to the  value of the second  argument.  set
     returns the value of its second argument.  Example:

            (set (cond ((predicate) 'atom1) (t 'atom2))
                        'stba)

     evaluates to stba and gives either atom1 or atom2 a value of stba.

        set could have been defined by:

        (defun set (x y)
            (eval (list 'setq x (list 'quote y))))

        Alternatively, setq could have been defined by:

        (defun setq fexpr (x)
          ((lambda (var val rest)
             (set var val)
             (cond ((null rest) val)
                   ((apply (function setq) rest)) ))   ;if more, recurse
           (car x)
           (eval (cadr x))
           (cddr x)))


symeval             SUBR 1 arg

     (symeval a) returns the  value of a, which  must be an atomic  symbol.  The
     compiler produces highly  optimal code for  symeval, making it  much better
     than eval when the value of  a symbol needs to be taken and  the particular
     symbol to be used varies.

boundp              SUBR 1 arg

     The argument to boundp must be an  atomic symbol.  If it has a value,  t is
     returned.  Otherwise nil is returned.


makunbound          SUBR 1 arg

     The argument to makunbound must be an atomic symbol.  Its value is removed,
     i.e. it becomes unbound.

        Example:
                (setq a 1)
                a => 1
                (makunbound 'a)
                a => unbnd-vrbl error.

     makunbound returns its argument.

file: LISP, node: The Property List, previous: The Value Cell, up: Atomic Symbols, next: The Print-Name,
Source: MACLISP Manual 3/6/76


   A property-list  is a list  with an  even number of  elements.  Each  pair of
elements constitutes a property; the first element is called the "indicator" and
the second is called the  "value" or, loosely, the "property." The  indicator is
generally an atomic symbol which serves as the name of the property.   The value
is any Lisp object.

   For  example, one  type of  functional  property uses  the atom  expr  as its
indicator.  In the case of an expr-property, the value is a list  beginning with
lambda.

   An example of a property list with two properties on it is:

                    (expr (lambda (x) (plus 14 x)) foobar t)

   The first property has indicator expr and value (lambda (x) (plus 14 x)), the
second property has indicator foobar and value t.

   Each  atomic symbol  has associated  with it  a property-list,  which  can be
retrieved with the  plist function.  It is  also possible to  have "disembodied"
property  lists  which are  not  associated  with any  symbol.   These  keep the
property  list on  their cdr,  so the  form of  a disembodied  property  list is
(<anything> . plist).  The way  to create a disembodied property list  is (ncons
nil).  Atomic symbols also (usually) keep their property list on their  cdr, but
you aren't allowed  to know that.   Use the plist  function to get  the property
list of a symbol.

   Property lists are useful for associating "attributes" with symbols.  Maclisp
uses properties to remember function definitions.  The compiler  uses properties
internally  to keep  track of  some of  what it  knows about  the program  it is
compiling.

   The user  familiar with Lisp  1.5 will  want to note  that the  property list
"flags" which are allowed  on Lisp 1.5 property  lists do not exist  in Maclisp.
However, the same effect can be  achieved by using properties with a value  of t
or nil.

   Some property names are used  internally by Maclisp, and should  therefore be
avoided in user code.  These include args, array, autoload, expr,  fexpr, fsubr,
lsubr, macro, pname, sublis, subr, value, used by the Lisp system proper; arith,
*array,  atomindex,  *expr,  *fexpr,  *lexpr,  numfun,  number,  numvar,  ohome,
special, sym, used by the compiler; grindfn, grindmacro, used by the grinder.


get                 SUBR 2 args

     (get x y) gets x's y-property.  x can be an atomic symbol or  a disembodied
     property list.  The value of x's y-property is returned, unless x has no y-
     property in which case nil is returned.   It is not an error for x to  be a
     number, but nil will always be returned since numbers do not  have property
     lists.
     Example:

        (get 'foo 'bar)
          => nil                 ;initially foo has no bar property
        (putprop 'foo 'zoo 'bar) ;give foo a bar property
          => zoo
        (get 'foo 'bar)          ;retrieve that property
          => zoo
        (plist 'foo)             ;look at foo's property list
        => (bar zoo ...other properties...)

        get could have been defined by:

        (defun get (x y)
          (do ((z (cond ((numberp x) nil)
                        ((atom x) (plist x))
                        (t (cdr x)))
                  (cddr z)))
              ((or (null z) (eq y (car z)))
               (cadr z))))

     This relies  on the  fact that  the car  and the  cdr of  nil are  nil, and
     therefore (cadr z) is nil if z is nil.


getl                SUBR 2 args

     (getl x y) is  like get except that y  is a list of indicators  rather than
     just a single indicator.  getl searches x's property list until  a property
     whose indicator appears in the list y is found.

     The portion of x's property list beginning with the first such  property is
     returned.  The car of this is the indicator (property name) and the cadr is
     the property value.  getl returns nil if none of the indicators in y appear
     on the property list of x.  getl could have been defined by:

        (defun getl (x pl)
           (do ((q (plist x) (cddr q))) ; scan down P-list of x
               ((or (null q) (memq (car q) pl))
                q)))

     This  definition is  simplified and  doesn't take  numbers  and disembodied
     property lists into account.


putprop             SUBR 3 args

     (putprop x y  z) gives x  a z-property of  y and returns  y.   x may  be an
     atomic symbol or a disembodied property list.  After somebody does (putprop
     x y z), (get x z) will return y.

     Example:
                          (putprop 'Nixon 'not 'crook)

     If the symbol already  has a property with  the same name that  property is
     removed first.  This ensures that getl will always find the  property which
     was put on most recently.  For instance, if you were to redefine an expr as
     a subr,  and then  redefine it  as an  expr again,  this effect  of putprop
     causes the evaluator to find the latest definition always.

     A lisp definition of the basic putprop without the complications of numbers
     and disembodied property lists might be:

        (defun putprop (x y z)
          (remprop x z)
          (setplist x (cons z (cons y (plist x))))
          y)






defprop             FSUBR

     defprop  is a  version  of putprop  with no  argument-evaluation,  which is
     sometimes more convenient for typing.  For instance,

                          (defprop foo bar oftenwith)

     is equivalent to

                         (putprop 'foo 'bar 'oftenwith)


remprop             SUBR 2 args

     (remprop x y)  removes x's y-property, by  splicing it out of  x's property
     list.   The value  is nil  if x  had no  y-property.  If  x did  have  a y-
     property, the value is a list  whose car is the property, and whose  cdr is
     part of x's property list, similar to (cdr (getl x '(y))).

     x may be an atomic symbol or a disembodied property list.  Example:

                              (remprop 'foo 'expr)

     undefines the function foo, assuming it was defined by

                              (defun foo (x) ... )


plist               SUBR 1 arg

     (plist x) returns the property list of the atomic symbol x.


setplist            SUBR 2 args

     (setplist x l) sets the property list of the atomic symbol x to l.  This is
     to  be used  with  caution, since  in some  implementations  property lists
     contain internal system properties  which are essential to the  workings of
     the Lisp system.


file: LISP, node: The Print-Name, previous: The Property List, up: Atomic Symbols, next: Interning of Symbols,
Source: MACLISP Manual 3/6/76


   Each  atomic symbol  has an  associated character  string called  its "print-
name," or  "pname" for  short.  This character  string is  used as  the external
representation  of the  symbol.  If  the string  is typed  in, it  is read  as a
reference to the symbol.  If the  symbol is to be print'ed, the string  is typed
out.

   See also page 2-79 for some other functions which have to do with pnames.


samepnamep          SUBR 2 args

     The arguments to samepnamep must evaluate to atomic symbols or to character
     strings.  The result is t if they have the same pname, nil  otherwise.  The
     pname  of  a  character  string is  considered  to  be  the  string itself.
     Examples:

               (samepnamep 'xyz (maknam '(x y z))) => t

               (samepnamep 'xyz (maknam '(w x y))) => nil

               (samepnamep 'x "x") => t


alphalessp          SUBR 2 args

     (alphalessp x  y), where x  and y evaluate  to atomic symbols  or character
     strings, returns t if the  pname of x occurs earlier in  alphabetical order
     than the pname of y.  The  pname of a character string is considered  to be
     the string itself.  Examples:

               (alphalessp 'x 'x1) => t

               (alphalessp 'z 'q) => nil

               (alphalessp "x" 'y) => t

     Note that the "alphabetical order" used by alphalessp is actually the ASCII
     collating sequence.   Consequently all upper  case letters come  before all
     lower case letters.
pnget               SUBR 2 args

     (pnget symbol  n) returns  the pname  of the  symbol as  a list  of fixnums
     containing  packed  n-bit bytes.   The  legal  values of  n  depend  on the
     implementation; in the pdp-10 implementation, 6 (SIXBIT) and 7  (ASCII) are
     allowed.  If this seems obscure, that's because it is.  Example:

        (pnget 'MUMBLERATOR 7) =>
                    (-311246236550 -351327625542 -270_33)


pnput               SUBR 2 args

     This is a sort of inverse  of pnget.  (pnput (pnget foo 7) flag)  returns a
     symbol with the same pname as foo.  The symbol is interned if flag  is non-
     nil.

file: LISP, node: Interning of Symbols, previous: The Print-Name, up: Atomic Symbols, next: Defining Atomic Symbols as Functions,
Source: MACLISP Manual 3/6/76


   One normally wants  to refer to  the same (eq)  atomic symbol every  time the
same  pname  is typed.   Maclisp  implements  this through  what  is  called the
obarray.  The obarray is a hash-table of atomic symbols.  These symbols are said
to be interned, or registered in the obarray.  Whenever a pname is read  in Lisp
input, the  obarray is searched  for a symbol  with the same  pname.  If  one is
found, the pname is considered to refer to that symbol.  If not, a new symbol is
created and added to the obarray.

   The  representation  of an  obarray  is a  Lisp  array.  The  first  510. (or
thereabouts) elements  of the array  contain lists which  are buckets of  a hash
table.  The  last 128. elements  of the array  contain the  "character objects,"
symbols  with   1-character  pnames.    (These  entries   contain  nil   if  the
corresponding  symbol has  not  yet been  interned.) The  character  objects are
treated specially  for efficiency.  There  are usually one  or two  unused array
elements between these two areas.

   In order to allow for multiple name spaces, Maclisp allows multiple obarrays.
An  obarray  can  be  made  "current"  by  binding  the  symbol  obarray  to the
appropriate  array-pointer.  See  page  2-85 for  details on  how  to manipulate
obarrays and arrays in general.

   It is  possible to have  a symbol  interned on several  obarrays at  the same
time.  It is also possible to have two different (non-eq) symbols with  the same
pname interned  on different  obarrays.  Furthermore  it is  possible to  have a
symbol  which is  not interned  on any  obarray, which  is called  an uninterned
symbol.   These  are  useful  for  purely-internal  functions,  but   can  cause
difficulty in debugging  since they can't be  accessed directly.  Such  a symbol
can be accessed via some data structure that contains it, set up by  the program
that created it.

   Normally symbols  are never removed  from obarrays.  It  is possible  for the
user to explicitly remove  a symbol from the  current obarray.  There is  also a
feature by  which "truly  worthless" symbols may  be removed  automatically (see
part 3.6).





intern              SUBR 1 arg

     (intern x), where x is  an atomic symbol, returns the unique  atomic symbol
     which is  "interned on the  obarray" and has  the same pname  as x.   If no
     symbol on the  current obarray has  the same pname  as x, then  intern will
     place x itself on the obarray, and return it as the value.


remob               SUBR 1 arg

     The argument to  remob must be  an atomic symbol.   It is removed  from the
     current obarray if it is  interned on that obarray.  This makes  the atomic
     symbol inaccessible to any S-expressions  that may be read in or  loaded in
     the future.  remob returns nil.


copysymbol          SUBR 2 args

     A subr  of two arguments.   The first  argument must be  a symbol,  and the
     second should be t  or nil.  The result  is a new, uninterned  symbol, with
     the same pname as the argument.  "Uninterned" means that the symbol has not
     been placed on any  obarray.  If the second  argument is t, the  new symbol
     will be given the  same value as the original  and will have a copy  of its
     property  list.   Thus the  new  will start  out  with the  same  value and
     properties as the  old, but if  it is setq'ed  or putprop'ed, the  value or
     property of the old  will not be changed.   If the second argument  is nil,
     the new  symbol has no  value and no  properties (except  possibly internal
     system properties.)


gensym              LSUBR 0 or 1 args

     gensym creates and returns a new atomic symbol, which is not interned on an
     obarray  (and therefore  is not  recognized by  read.) The  atomic symbol's
     pname is of the form prefix number, e.g. g0001.  The number  is incremented
     each time.

     If gensym  is given  an argument,  a numeric  argument is  used to  set the
     number.  The pname of an atomic-symbol argument is used to set  the prefix.
     For example:



          if   (gensym) => g0007
          then (gensym 'foo) => f0008
               (gensym 40) => f0032
          and  (gensym) => f0033

     Note that the number is in  decimal and always four digits, and  the prefix
     is always one character.

file: LISP, node: Defining Atomic Symbols as Functions, previous: Interning of Symbols, up: Atomic Symbols, next: Numbers,
Source: MACLISP Manual 3/6/76


   Atomic symbols may be used as  names for functions.  This is done  by putting
the actual function (a subr-object or a lambda-expression) on the  property list
of  the  atomic  symbol  as  a "functional  property,"  i.e.  under  one  of the
indicators expr, fexpr, macro, subr, lsubr, or fsubr.

   Array  properties  (see  page  2-85) are  also  considered  to  be functional
properties, so an atomic symbol which is  the name of an array is also  the name
of a function, the accessing function of that array.

   When  an atomic  symbol  which is  the name  of  a function  is  applied, the
function which it names is substituted.


defun               FSUBR

     defun is used for defining functions.  The general form is:

                (defun name  type (lambda-variable...)
                       body...)

     However, name and type may  be interchanged.  type, which is  optional, may
     be expr, fexpr, or macro.  If it is omitted, expr is assumed.  Examples:

          (defun addone (x) (1+ x))             ;defines an expr

          (defun quot fexpr (x) (car x))        ;defines a fexpr

          (defun fexpr quot (x) (car x))        ;is the same

          (defun zzz expr x                     ;this is how you
                     (foo (arg 1)(arg 2)))      ; define a lexpr.

     The first example above is really just defining a synonym.  Another  way to
     do this is:
                            (defprop addone 1+ expr)

     That is, an atomic  functional property indicates synonyming.  This  can be
     particularly useful to  define a macro  by an expr or  fexpr, or even  by a
     subr.
     The functions defprop and putprop may also be used for defining functions.

     There is a feature by which, when a file of functions has been compiled and
     loaded into  the lisp  environment, the file  may be  edited and  then only
     those  functions  which  were  changed  may  be  loaded   for  interpretive
     execution.  This is done by compiling with the "E" switch, and then reading
     in the source  file with the variable  defun bound non-nil.   Each function
     will have an  expr-hash property maintained,  which contains the  sxhash of
     the interpreted definition of  the function.  defun will only  redefine the
     function if this hash-code  has changed.  This feature is  rather dangerous
     since reasonable alterations to the function definition may not  change the
     sxhash  and  consequently may  not  take effect.   Because  of  its general
     losingness, this feature is only available in the pdp-10 implementation and
     sometimes not even there.

        defun could have been defined by:

        (defun defun fexpr (x)  ;circular, but you get the idea
          (prog (name type body)

            ; first, analyze the form, get arguments.
            (cond ((memq (car x) '(expr fexpr macro))
                   (setq type (car x)
                         name (cadr x)
                         body (cddr x)))
                  ((memq (cadr x) '(expr fexpr macro))
                   (setq name (car x)
                         type (cadr x)
                         body (cddr x)))
                  ((setq name (car x)
                         type 'expr
                         body (cdr x))))

            (setq body (cons 'lambda body))









            ; now, check for expr-hash hair.
            (cond ((and defun
                        (get name 'expr-hash)
                        (= (get name 'expr-hash)
                           (sxhash body)))
                     )
                  ; actually make the definition.
                  ((putprop name body type)))
            (return name)))


args                LSUBR 1 or 2 args

     (args f) tells you the number of arguments expected by the function  f.  If
     f wants n  arguments, args returns (nil  . n).  If f  can take from m  to n
     arguments, args returns  (m . n).  If  f is an fsubr  or a lexpr,  expr, or
     fexpr, the results are meaningless.

     (args f x), where x is (nil .  n) or (m . n), sets the number  of arguments
     desired  by  the function  f.   This only  works  for  compiled, non-system
     functions.


sysp                SUBR 1 arg

     The sysp predicate  takes an atomic symbol  as an argument.  If  the atomic
     symbol is the name of a system function (and has not been  redefined), sysp
     returns  the type  of  function (subr,  lsubr, or  fsubr).   Otherwise sysp
     returns nil.  Examples:

            (sysp 'foo) => nil  (presumably)

            (sysp 'car) => subr

            (sysp 'cond) => fsubr

file: LISP, node: Numbers, previous: Defining Atomic Symbols as Functions, up: Function Descriptions, next: Number Predicates,
Source: MACLISP Manual 3/6/76

* MENU:

* Number Predicates::
* Comparison::
* Conversion::
* Arithmetic::
* Exponentiation and Logarithm Functions::
* Trigonometric Functions::
* Random Functions::
* Logical Operations on Numbers::

For a description of the various types of numbers used in Maclisp, see part 1.2.


file: LISP, node: Number Predicates, previous: Numbers, up: Numbers, next: Comparison,
Source: MACLISP Manual 3/6/76

zerop               SUBR 1 arg

     The zerop  predicate returns  t if its  argument is  fixnum zero  or flonum
     zero.  (There  is no  bignum zero.)  Otherwise  it returns  nil.  It  is an
     error if the argument is not a number.  If that is possible signp should be
     used.


plusp               SUBR 1 arg

     The plusp  predicate returns  t if  its argument  is strictly  greater than
     zero, nil if it is zero or negative.  It is an error if the argument is not
     a number.


minusp              SUBR 1 arg

     The minusp predicate returns t if its argument is a negative number, nil if
     it is  a non-negative  number.  It  is an error  if the  argument is  not a
     number.


oddp                SUBR 1 arg

     The oddp predicate  returns t if its  argument is an odd  number, otherwise
     nil.  The argument must be a fixnum or a bignum.






signp               FSUBR

     The signp  predicate is used  to test the  sign of a  number.  (signp  c x)
     returns t  if x's  sign satisfies the  test c,  nil if it  does not.   x is
     evaluated but c is not.  The result is always nil if x is not a  number.  c
     can be one of the following:

                  l       means    x<0
                  le        "      x<_0
                  e         "      x=0
                  n         "      x=/0
                  ge        "      x>_0
                  g         "      x>0

     Examples:
         (signp le -1) => t
         (signp n 0) => nil
         (signp g '(foo . bar)) => nil


haulong             SUBR 1 arg

     (haulong x) returns the number of significant bits in x.  x can be a fixnum
     or a  bignum.  The result  is the  least integer not  less than  the base-2
     logarithm of |x|+1.

        Examples:
            (haulong 0) => 0
            (haulong 3) => 2
            (haulong -7) => 3
            (haulong 12345671234567) => 40.

file: LISP, node: Comparison, previous: Comparison, up: Numbers, next: Conversion,
Source: MACLISP Manual 3/6/76


=                   SUBR 2 args

     (= x  y) is  t if x  and y  are numerically equal.   x and  y must  be both
     fixnums or both flonums.  Use equal to compare bignums.


greaterp            LSUBR 2 or more args

     greaterp compares its arguments, which must be numbers, from left to right.
     If any argument is not greater than the next, greaterp returns nil.  But if
     the  arguments  to  greaterp  are strictly  decreasing,  the  result  is t.
     Examples:

                (greaterp 4 3) => t
                (greaterp 1 1) => nil
                (greaterp 4.0 3.6 -2) => t
                (greaterp 4 3 1 2 0) => nil


>                   SUBR 2 args

     (> x y) is t if x is  strictly greater than y, and nil otherwise.  x  and y
     must be both fixnums or both flonums.


lessp               LSUBR 2 or more args

     lessp compares its  arguments, which must be  numbers, from left  to right.
     If any argument is not less  than the next, lessp returns nil.  But  if the
     arguments to lessp are strictly increasing, the result is t.  Examples:

                (lessp 3 4) => t
                (lessp 1 1) => nil
                (lessp -2 3.6 4) => t
                (lessp 0 2 1 3 4) => nil




<                   SUBR 2 args

     (< x y) is t if x is strictly less than y, and nil otherwise.  x and y must
     be both fixnums or both flonums.


max                 LSUBR 1 or more args

     max returns the  largest of its arguments,  which must be numbers.   If any
     argument is a flonum, the result will be a flonum.  Otherwise, it will be a
     fixnum or a bignum depending on its magnitude.


min                 LSUBR 1 or more args

     min returns the smallest of  its arguments, which must be numbers.   If any
     argument is a flonum, the result will be a flonum.  Otherwise, it will be a
     fixnum or a bignum depending on its magnitude.

file: LISP, node: Conversion, previous: Comparison, up: Numbers, next: Arithmetic,
Source: MACLISP Manual 3/6/76


fix                 SUBR 1 arg

     (fix x)  converts x to  a fixnum  or a bignum  depending on  its magnitude.
     Examples:

          (fix 7.3) => 7
          (fix -1.2) => -2
          (fix 104) => 104


float               SUBR 1 arg

     (float x) converts x to a flonum.  Example:

          (float 4) => 4.0
          (float 3.27) => 3.27


abs                 SUBR 1 arg

     (abs x) => |x|,  the absolute value of the  number x.  abs could  have been
     defined by:

        (defun abs (x) (cond ((minusp x) (minus x))
                             (t x) ))


minus               SUBR 1 arg

     minus  returns the  negative of  its  argument, which  can be  any  kind of
     number.  Examples:

                (minus 1) => -1
                (minus -3.6) => 3.6





haipart             SUBR 2 args

     (haipart  x  n) extracts  n  leading  or trailing  bits  from  the internal
     representation of x.  x may be a  fixnum or a bignum.  n must be  a fixnum.
     The value  is returned  as a  fixnum or a  bignum.  If  n is  positive, the
     result  contains  the  n  high-order significant  bits  of  |x|.   If  n is
     negative, the  result contains the  |n| low-order bits  of |x|.  If  |n| is
     bigger than the number of significant bits in x, |x| is returned.

        Examples:
            (haipart 34567 7) => 162

            (haipart 34567 -5) => 27

            (haipart -34567 -5) => 27

file: LISP, node: Arithmetic, previous: Conversion, up: Numbers, next: Exponentiation and Logarithm Functions,
Source: MACLISP Manual 3/6/76


                               General Arithmetic

   These functions will  perform arithmetic on any  kind of numbers,  and always
yield an  exact result, except  when used with  flonums.  (Flonums  have limited
precision and range.) Conversions to flonum or bignum representation are done as
needed.  Flonum representation will be used if any of the arguments are flonums;
otherwise fixnum  representation will be  used if the  result can fit  in fixnum
form, or bignum representation if it cannot.

   The two sections after this one describe other arithmetic functions which are
more efficient but less powerful.

plus                LSUBR 0 or more args

     plus returns the sum of its arguments, which may be any kind of numbers.


difference          LSUBR 1 or more args

     difference returns its first argument minus the rest of its  arguments.  It
     works for any kind of numbers.


times               LSUBR 0 or more args

     times  returns the  product of  its arguments.   It works  for any  kind of
     numbers.


quotient            LSUBR 1 or more args

     quotient returns its first argument  divided by the rest of  its arguments.
     The arguments may any kind of number.

        Examples:
          (quotient 3 2)  => 1      ;fixnum division truncates.

          (quotient 3 2.0) =>  1.5  ;but flonum division does not..

add1                SUBR 1 arg

     (add1 x) => x+1.  x may be any kind of number.


sub1                SUBR 1 arg

     (sub1 x) => x-1.  x may be any kind of number.


remainder           SUBR 2 args

     (remainder x y) =>  the remainder of the division  of x by y.  The  sign of
     the remainder is the same as the sign of the dividend.  The  arguments must
     be fixnums or bignums.


gcd                 SUBR 2 args

     (gcd x y) => the greatest common divisor of x and y.  The arguments must be
     fixnums or bignums.


expt                SUBR 2 args

                   z
     (expt x z) = x

     The exponent z may be  a bignum if the base x  is 0, 1, or -1;  otherwise z
     should be a fixnum.  x may be any kind of number.

     As a special feature,  expt allows its second  argument to be a  flonum, in
     which  case  the  first  argument   is  converted  to  a  flonum   and  the
     exponentiation  is  performed  in floating  point,  using  logarithms.  The
     result is a flonum in this case.
.bp
                               Fixnum Arithmetic
Source: MACLISP Manual 3/6/76


   These functions require their arguments to be fixnums and produce only fixnum
results.   If the  true result,  which  would be  returned by  the  more general
functions described previously, is too large to be represented as a  fixnum, the
result actually returned will be truncated to an implementation-dependent number
of  bits,  which  is  36.  (including  the  sign)  in  the  Multics  and  pdp-10
implementations.   The  compiler   produces  highly-optimized  code   for  these
operations.

+                   LSUBR 0 or more args

     + returns the sum of its arguments.  The arguments must be fixnums, and the
     result is always a fixnum.  Examples:

                (+ 2 6 -1) => 7
                (+ 3) => 3      ;trivial case
                (+) => 0        ;identity element


-                   LSUBR 0 or more args

     This  is  the  fixnum-only subtraction  function.   With  one  argument, it
     returns the number's negation.  With more than one argument, it returns the
     first argument minus the rest of the arguments.

                (-) => 0, the identity element
                (- 3) => -3
                (- 5 3) => 2
                (- 2 6 -1) => -3
        etc.


*                   LSUBR 0 or more args

     * returns the product of its arguments.  Examples:

                (* 4 5 -6) => -120.
                (* 3) => 3           ;trivial case
                (*) => 1             ;identity element

/                   LSUBR 0 or more args

     This is the fixnum-only  division function.  The arguments must  be fixnums
     and the result of the division is truncated to an integer and returned as a
     fixnum.  Note that the name of this function must be typed in as  //, since
     Lisp uses / as an escape character.

     If used with more than one  argument, it divides the first argument  by the
     rest of  the arguments.   If used with  only one  argument, it  returns the
     fixnum reciprocal of that number, which is -1, 0, 1, or undefined depending
     on whether the number is -1, large, 1, or 0.

               (//) => 1, the identity element.
               (// 20. 5) => 4
               (// 100. 3 2) => 16.
               etc.


1+                  SUBR 1 arg

     (1+ x) => x+1.  x must be a fixnum.  The result is always a fixnum.


1-                  SUBR 1 arg

     (1- x) => x-1.  x must be a fixnum.  The result is always a fixnum.


\                   SUBR 2 args

     (\ x y) returns the remainder of x divided by y, with the sign of x.  x and
     y must be fixnums.  Examples:

               (\ 5 2) => 1
               (\ 65. -9.) => 2
               (\ -65. 9.) => -2


\\                  SUBR 2 args

     This subr  of two arguments  is like gcd,  but only accepts  fixnums.  This
     makes it faster than gcd.
^                   SUBR 2 args

     ^ is the fixnum only  exponentiation function.  It is somewhat  faster than
     expt, but requires its arguments to be fixnums, uses fixnum arithmetic, and
     always returns a fixnum result, which will be incorrect if the  true result
     is too large to be represented as a fixnum.
.bp
                               Flonum Arithmetic
Source: MACLISP Manual 3/6/76


   These functions  require their  arguments to be  flonums, and  always produce
flonum results.  If the true result is too large or too small to  be represented
as a flonum, an arithmetic underflow or overflow error will occur.  (In the pdp-
10  implementation these  errors  are not  detected in  compiled  programs.) The
compiler produces highly-optimized code for these operations.

+$                  LSUBR 0 or more args

     +$ returns the sum of its arguments.

        Examples:
                (+$ 4.1 3.14) => 7.24
                (+$  2.0 1.5  -3.6)  => -0.1
                (+$ 2.6) => 2.6         ;trivial case
                (+$)  => 0.0            ;identity element


-$                  LSUBR 0 or more args

     This  is the  flonum-only subtraction  function.  When  used with  only one
     argument,  it returns  the number's  negation.  Otherwise,  it  returns the
     first argument minus the rest of the arguments.

               (-$) => 0.0, the identity element
               (-$ x)  => the negation of x.
               (-$ 6.0 2.5) => 4.5
               (-$ 2.0 1.5 -3.6) => 3.1
               etc.


*$                  LSUBR 0 or more args

     *$ returns the product of its arguments.  Examples:

             (*$ 3.0 2.0 4.0) => 24.0
             (*$ 6.1) => 6.1            ;trivial case
             (*$) => 1.0                ;identity element


/$                  LSUBR 0 or more args

     This is  the flonum-only division  function.   Note that  the name  of this
     function must be typed in as //$, since Lisp uses / as an escape character.
     This function computes the reciprocal if given only one argument.  If given
     more than one argument, it divides the first by the rest.

               (//$) => 1.0, the identity element
               (//$ 5.0) => 0.2
               (//$ 6.28 3.14) => 2.0
               (//$ 100.0 3.0 2.0) => 16.5
               etc.


1+$                 SUBR 1 arg

     (1+$ x) => x+1.0.  x must be a flonum.  The result is always a flonum.


1-$                 SUBR 1 arg

     (1-$ x) => x-1.0.  x must be a flonum.  The result is always a flonum.


^$                  SUBR 2 args

     ^$ is the flonum-only exponentiation function.  The first argument  must be
     a flonum, the second must be a fixnum (repeat, a fixnum), and the result is
     a flonum.  To raise a flonum to a flonum power, use (expt x y) or  (exp (*$
     y (log x))).

file: LISP, node: Exponentiation and Logarithm Functions, previous: Arithmetic, up: Numbers, next: Trigonometric Functions,
Source: MACLISP Manual 3/6/76


sqrt                SUBR 1 arg

     (sqrt x) =>  a flonum which is  the square root of  the number x.   This is
     more  accurate than  (expt x  0.5).  The  following code,  which is  due to
     Gosper, should be written if the square root of a bignum is desired.  It is
     essentially a  Newton iteration, with  appropriate precautions  for integer
     truncation.

          (defun bsqrt (n)
             (bsqrt1 (abs n)
                     (expt 2 (// (1+ (haulong n)) 2))))

          (defun bsqrt1 (n guess)
                 ((lambda (next)
                    (cond ((lessp next guess)
                           (bsqrt1 n next))
                          (t guess)))
                  (quotient (plus guess (quotient n guess))
                            2)))


exp                 SUBR 1 arg

                 x
     (exp x) => e


log                 SUBR 1 arg

     (log x) => the natural logarithm of x.

file: LISP, node: Trigonometric Functions, previous: Exponentiation and Logarithm Functions, up: Numbers, next: Random Functions,
Source: MACLISP Manual 3/6/76


sin                 SUBR 1 arg

     (sin x) gives the  trigonometric sine of x.  x  is in radians.  x may  be a
     fixnum or a flonum.


cos                 SUBR 1 arg

     (cos x) returns the cosine of x.  x is in radians.  x may be a fixnum  or a
     flonum.


atan                SUBR 2 args

     (atan x  y) returns  the arctangent  of x/y, in  radians.  x  and y  may be
     fixnums or flonums.  y may be 0 as long as x is not also 0.

file: LISP, node: Random Functions, previous: Trigonometric Functions, up: Numbers, next: Logical Operations on Numbers,
Source: MACLISP Manual 3/6/76


random              LSUBR 0 to 2 args

     (random) returns a random fixnum.

     (random nil) restarts the random sequence at its beginning.

     (random x), where x is a fixnum, returns a random fixnum between 0  and x-1
     inclusive.  A useful function is:

        (defun frandom ()
            (//$ (float (random 10000.)) 10000.0)))

     which returns a random flonum between 0.0 and 1.0.

     (random n1 n2) sets  the random number seed  from the pair of  integers n1,
     n2.


zunderflow          SWITCH

     If an intermediate  or final flonum  result in the  interpretive arithmetic
     functions  (times,  *$,  expt,  etc.)  is  too  small  in  magnitude  to be
     represented by the  machine, corrective action  will be taken  according to
     the zunderflow switch.

     If the value of zunderflow is non-nil, the offending result will be  set to
     0.0 and computation  will proceed.  If the  value of zunderflow is  nil, an
     error will be signalled.  nil is the initial value.

     In the pdp-10 implementation compiled code is not affected by zunderflow if
     the  arithmetic  in  question was  open-coded  by  the  compiler.  Instead,
     computation proceeds using a result with a binary exponent 256  higher than
     the correct exponent.  In  the Multics implementation zunderflow  works the
     same for compiled code as for interpreted code.

     See (sstatus divov), which controls division by zero (part 3.7).


file: LISP, node: Logical Operations on Numbers, previous: Random Functions, up: Numbers, next: Character Manipulation,
Source: MACLISP Manual 3/6/76


   These  functions  may  be  used freely  for  bit  manipulation;  the compiler
recognizes them and produces efficient code.

boole               LSUBR 3 or more args

     (boole k x y) computes a bit by bit Boolean function of the fixnums x and y
     under the control of k.  k must  be a fixnum between 0 and 17  (octal).  If
     the  binary representation  of k  is  abcd, then  the truth  table  for the
     Boolean operation is:

               y
        ___|_0__1_
          0| a  c
        x  |
          1| b  d

     If boole has more than three arguments, it goes from left to right; thus

                  (boole k x y z) = (boole k (boole k x y) z)

     The most common values for k are 1 (and), 7 (or), 6 (xor).  You can get the
     complement, or logical negation, of x by (boole 6 x -1).

           The following macros are often convenient:

        (defun logand macro (x)
          (subst (cdr x) 'f '(boole 1 . f)))

        (defun logor macro (x)
          (subst (cdr x) 'f '(boole 7 . f)))

        (defun logxor macro (x)
          (subst (cdr x) 'f '(boole 6 . f)))


     Alternatively, these could be defined with macrodef (see part 6.2):

        (macrodef logand x (boole 1 . x))

        (macrodef logor x (boole 7 . x))

        (macrodef logxor x (boole 6 . x))


lsh                 SUBR 2 args

     (lsh x y), where x and y are fixnums, returns x shifted left y bits if y is
     positive, or  x shifted right  |y| bits if  y is negative.   Zero-bits are
     shifted in to fill unused positions.  The result is undefined if |y|  > 36.
     The number 36 is implementation  dependent, but this is the number  used in
     both the Multics and pdp-10 implementations.  Examples:

                (lsh 4 1) => 10 (octal)
                (lsh 14 -2) => 3
                (lsh -1 1) => -2


rot                 SUBR 2 args

     (rot x y) returns as a fixnum the 36-bit representation of x,  rotated left
     y bits if y is positive, or rotated right |y| bits if y is negative.  x and
     y must be fixnums.   The results are undefined if  |y| > 36.  As  with lsh,
     the number 36 depends on the implementation.  Examples:

            (rot 1 2) => 4
            (rot -1 7) => -1
            (rot 601234 36.) => 601234
            (rot 1 -2) => 200000000000
            (rot -6 6) => -501


The following feature only exists in the pdp-10 implementation.

     The internal representation of flonums may be hacked using these functions.
     lsh or rot applied to  a flonum operates on the internal  representation of
     the  flonum and  returns a  fixnum  result.  For  example, (lsh  0.5  0) =>
     200400000000 (octal).  The following function also exists:
fsc                 SUBR 2 args

     (fsc  x y)  performs a  FSC instruction  on the  two numbers  x and  y, and
     returns the result as a flonum.  Consult the pdp-10 processor manual if you
     want to use this.

     x  and  y   may  be  fixnums  or   flonums;  fsc  just  uses   the  machine
     representations of the numbers.  If y is greater than 777777 octal, the FSC
     instruction is omitted and  the possibly-unnormalized flonum with  the same
     machine representation as x is returned.

file: LISP, node: Character Manipulation, previous: Logical Operations on Numbers, up: Function Descriptions, next: Arrays,
Source: MACLISP Manual 3/6/76

	Character Objects
	Character Strings

7.1  Character Objects


   An  atomic symbol  with a  one-character pname  is often  called  a character
object  and  used to  represent  the ascii  character  which is  its  pname.  In
addition the atomic  symbol with a zero-length  pname represents the  ascii null
character.  Functions which take a character object as an argument  usually also
accept a string one character long or a fixnum equal to the ascii-code value for
the character.  Character objects are  always interned on the obarray  (see page
2-54), so they may be compared with the function eq.


ascii               SUBR 1 arg

     (ascii x), where x is a number, returns the character object for  the ascii
     code x.

     Examples:

     (ascii 101) => A

     (ascii 56) => /.


getchar             SUBR 2 args

     (getchar x n), where x is an  atomic symbol and n is a fixnum,  returns the
     n'th character  of x's pname;  n = 1  selects the leftmost  character.  The
     character is returned as a character object.  nil is returned if n  is out
     of bounds.







getcharn            SUBR 2 args

     getcharn is the same as getchar except that the character is returned  as a
     fixnum instead of a character object.


maknam              SUBR 1 arg

     maknam takes as its argument a list of characters and returns an uninterned
     atomic symbol whose pname is constructed from the list of  characters.  The
     characters  may  be  represented  either as  fixnums  (ascii  codes)  or as
     character objects.  Example:

                          (maknam '(a b 60 d)) => ab0d


implode             SUBR 1 arg

     implode is the  same as maknam except  that the resulting atomic  symbol is
     interned.  It is more efficient than doing (intern (maknam x)), although it
     is less efficient than plain maknam which should be used when  interning is
     not required.


readlist            SUBR 1 arg

     The argument to  readlist is a list  of characters.  The characters  may be
     represented either as fixnums  (ascii codes) or as character  objects.  The
     characters in the  list are assembled into  an S-expression as if  they had
     been typed  into read  (see part 5.1.)  If macro  characters are  used, any
     usage in the macro character function of read, readch, tyi, or  tyipeek not
     explicitly specifying an input  file takes input from  readlists's argument
     rather than from an I/O device or a file.  This causes macro  characters to
     work as you would expect.

        Examples:
            (readlist '(a b c)) => abc
            (readlist '( /( p r 151 n t /  /' f o o /) ))
                => (print (quote foo))  ;ascii 151 = "i"

     Note the use of the slashified special characters left  parenthesis, space,
     quote, right parenthesis in the argument to readlist.
explode             SUBR 1 arg

     (explode x)  returns a list  of characters, which  are the  characters that
     would be typed  out if (prin1 x)  were done, including slashes  for special
     characters but not including extra newlines inserted to  prevent characters
     from running  off the  right margin.   Each character  is represented  by a
     character object.  Example:

        (explode '(+ /12 3)) => ( /( + /  // /1  /2 /  /3 /) )
                ;Note the presence of slashified spaces in this list.


explodec            SUBR 1 arg

     (explodec x)  returns a list  of characters which  are the  characters that
     would be  typed out if  (princ x) were  done, not including  extra newlines
     inserted to prevent characters from running off the right  margin.  Special
     characters  are  not  slashified.   Each  character  is  represented  by  a
     character object.  Example:

        (explodec '(+ /12 3)) => ( /( + /  /1 /2 /  /3 /) )


exploden            SUBR 1 arg

     (exploden x)  returns a list  of characters which  are the  characters that
     would be  typed out if  (princ x) were  done, not including  extra newlines
     inserted to prevent characters from running off the right  margin.  Special
     characters are not slashified.   Each character is represented by  a number
     which is the ascii code for that character.  cf. explodec.  Example:

        (exploden '(+ /12 3)) => (50 53 40 61 62 40 63 51)


flatsize            SUBR 1 arg

     (flatsize x) returns  the number of characters  prin1 would use to  print x
     out.




flatc               SUBR 1 arg

     (flatc x) returns the number of characters princ would use to print  x out,
     without slashifying special characters.
.bp
7.2  Character Strings
Source: MACLISP Manual 3/6/76


   These  character  string  functions  only exist  at  present  in  the Multics
implementation of Maclisp.  A predicate to test if your implementation has these
functions is
                            (status feature strings)

   These functions all accept atomic  symbols in place of strings  as arguments;
in this case  the pname of the  atomic symbol is used  as the string.   When the
value of one of these functions is described as a string, it is always  a string
and never an atomic symbol.  Also see the functions on page 2-52.


catenate            LSUBR 0 or more args

     The arguments are character strings.   The result is a string which  is all
     the arguments concatenated together.  Example:

          (catenate "foo" "-" "bar") => "foo-bar"


index               SUBR 2 args

     index is like the PL/I builtin function index.  The arguments are character
     strings.  The position  of the first occurrence  of the second  argument in
     the first is returned, or 0 if there is none.  Examples:

          (index "foobar" "ba") => 4
          (index "foobar" "baz") => 0
          (index "goobababa" "bab") => 4


stringlength        SUBR 1 arg

     The argument  to stringlength must  be a character  string.  The  number of
     characters in it is returned.  Examples:

          (stringlength "foo") => 3
          (stringlength "") => 0


substr              LSUBR 2 or 3 args

     This is like the  PL/I substr builtin.  (substr x  m n) returns a  string n
     characters long, which is a portion of the string x beginning with its m'th
     character and proceeding for n characters.  m and n must be fixnums, x must
     be a string.

     (substr x m) returns  the portion of the  string x beginning with  its m'th
     character and continuing until the end of the string.  Examples:

          (substr "foobar" 3 2) => "ob"
          (substr "resultmunger" 6) => "tmunger"


get_pname           SUBR 1 arg

     (get_pname x) returns the pname of  x as a character string.  x must  be an
     atomic symbol.


make_atom           SUBR 1 arg

     make_atom returns an atomic symbol,  uninterned, whose pname is given  as a
     character string argument.  Example:

          (make_atom "foo") => foo      ;which is not eq to a
                                        ;foo that is read in.

file: LISP, node: Arrays, previous: Character Manipulation, up: Function Descriptions, next: Mapping Functions,
Source: MACLISP Manual 3/6/76



   As explained in part 1.2, an array is a group of cells which may contain Lisp
objects.  The individual cells are selected by numerical subscripts.

   An array is  designated by a special  atomic object called  an array-pointer.
Array-pointers can be returned by the array-creation functions array and *array.
An array-pointer  may either be  used directly  to refer to  the array,  or, for
convenience in  referring to  the array  through input/output  media, it  may be
placed on the property list of  an atomic symbol under the indicator  array, and
then that symbol can be used as the name of the array.

   There are several types of arrays.  The main types are ordinary arrays, whose
cells can hold any type of object, and number arrays, whose cells can  only hold
numbers.  Number arrays permit more efficient code to be compiled  for numerical
applications, and take less space than an ordinary array which contains the same
number of  numbers.  See  the array*  declaration (part  4.2) and  the arraycall
function (page 2-12).

   When an array is created its  type must be declared by giving a  "type code."
The type code  for ordinary arrays  is t.  For number  arrays, the type  code is
either fixnum or flonum.   A particular number array  can only hold one  type of
numbers because its cells contain the machine representation of the  number, not
the Lisp-object representation.

   Some other types  of arrays are:   un-garbage-collected arrays, with  a type-
code of  nil, which are  the same as  ordinary arrays except  that they  are not
protected  by  the garbage  collector  and  therefore can  be  used  for certain
esoteric  hacks;  obarrays, with  a  type-code  of obarray,  which  are  used to
maintain tables of known atomic symbols  so that the same atomic symbol  will be
referenced when the same pname is typed in; and readtables, with a  type-code of
readtable, which  are used to  remember the syntax  specifications for  the Lisp
input reader.  Normally, there is  only one readtable and one  obarray, supplied
by the  system, but the  user may create  additional readtables and  obarrays in
order to  provide special  non-Lisp environments or  to gain  additional control
over the Lisp environment.   Lisp functions such as read  can be made to  use an
additional readtable or obarray by re-binding the variable readtable or obarray,
respectively.

   An array-pointer may  also be dead,  in which case it  does not point  to any
array.  One of the functions array, *array, or *rearray may be used  to revivify
a dead array-pointer.

   The functions array and *array are used to create arrays.  The first argument
may be an atomic  symbol, which makes that atomic  symbol the name of  an array,
putting an array-pointer  on its property  list, or redefining  an array-pointer
that was already on the property list to point to the new  array.  Alternatively
the first argument may be an  array pointer, which causes that array  pointer to
be redefined to point to a new array, or it may be nil, which causes a new array
pointer to be  created and returned.  Except  in the latter case,  array returns
its first argument.  *array always  returns the array pointer, never  the atomic
symbol.

   A readtable or an obarray may not be created with  user-specified dimensions.
The dimensions are always determined  by Lisp.  Other types of arrays  allow any
reasonable number (at least 3,  anyway) of dimensions to be specified  when they
are  created.  The  subscripts range  from 0  up to  1 less  than  the dimension
specified.

   Ordinary  and un-garbage-collected  arrays  are initialized  to  nil.  Fixnum
arrays are initialized to 0.  Flonum arrays are initialized to 0.0.

   Obarrays are initialized  according to the third  argument given to  array or
*array.  nil causes a completely empty obarray to be created.  Not even nil will
be interned on this obarray.   t causes the current obarray (value of the symbol
obarray)  to be  copied.  An  array-pointer which  is an  obarray, or  an atomic
symbol which names an  obarray, causes that obarray  to be copied.  If  no third
argument is given, the current obarray is copied.

   Readtables are initialized  in a similar fashion.   If the third  argument of
array or *array is nil, then the current readtable is copied.  If it is  t, then
the  readtable  being  created  is  initialized  to  the  initial  standard Lisp
readtable,  including the  macro characters  ' and  ;.  (Note  that this  is the
opposite of the t-nil convention  for obarrays.  This is for  compatibility with
the makreadtable function, which  no longer exists.) An array-pointer  or symbol
of a readtable to be copied may  also be given.  If no third argument  is given,
the current readtable is copied.

   An array-pointer may be redefined  to an entirely different type and  size of
array, using  the *array  function.  It  remains the  same array-pointer,  eq to
itself.  If a variable was setq'ed to the array-pointer, that variable  will now
indicate the  new array.   If a symbol  has that  array-pointer on  its property
list, it will now be the name of the new array.

   The *rearray  function can  be used to  redefine the  size or  arrangement of
dimensions of an array without losing its contents, or to make  an array-pointer
not point to any array (become dead).  If there is only one argument, the array-
pointer is  killed, the  array's contents are  discarded, and  the array-pointer
becomes a "dead array" as described  above.  *array may now be used  to redefine
it as a new array.

   If more than one argument is  given to *rearray, they are the  same arguments
as to *array.  *rearray with more than one argument cannot be used to change the
type of an array, and cannot operate on a readtable or an obarray, but it can be
used  to  change  the  dimensions  of an  array.   The  modified  array  will be
initialized from its old contents rather than  nil, 0, or 0.0.  The elements are
taken  in row-major  order for  initialization purposes,  and if  there  are not
enough,  nil, 0,  or 0.0  will be  used to  fill the  remaining elements  of the
modified array, according to the type.

   The Multics implementation also has a type of arrays called  external arrays.
External  arrays  reside  in  a Multics  segment  rather  than  within  the Lisp
environment.  They  behave much like  fixnum arrays, and  should be  declared as
such to the compiler.  To create an external array, use a form such as

                      (array foo external pointer length)

The pointer is  a packed pointer  to the beginning of  the array, i.e.  a fixnum
whose first six octal digits are  the segment number and whose second  six octal
digits are the word  address.  The length is the  number of words in  the array.
External arrays can only have  one dimension, can only contain fixnums,  and are
not initialized  when they are  created.  They cannot  usefully be saved  by the
save function.  This  type of array can  be used for communication  between Lisp
programs and  Multics programs  or subsystems written  in other  languages, when
large amounts of numerical data or machine words must be passed back  and forth.
See also defpl1 (part 4.6).

   If you want the range of subscripts on arrays to be checked, it  is necessary
to set the *rset flag non-nil (i.e. run in (*rset t) mode) and to avoid  the use
of in-line array accessing  (i.e. the array* declaration) in  compiled programs.
The amount of checking performed when *rset is nil and/or compiled code  is used
depends on the implementation.


      Here is an example of a use of arrays:

      (defun matrix-multiply (arr1 arr2 result)
         (and (eq (typep arr1) 'symbol)       ;convert arguments
              (setq arr1 (get arr1 'array)))  ;to array-pointers
         (and (eq (typep arr2) 'symbol)
              (setq arr2 (get arr2 'array)))
         (and (eq (typep result) 'symbol)
              (setq result (get result 'array)))
         (do ((ii (cadr (arraydims result)))  ;get relevant
              (jj (caddr (arraydims result))) ;dimensions
              (kk (cadr (arraydims arr2))))
             ()
           (do i 0 (1+ i) (= i ii)        ;result := arr1 x arr2
             (do j 0 (1+ j) (= j jj)
               (do ((k 0 (1+ k))
                    (r 0.0))
                   ((= k kk)
                    (store (arraycall flonum result i j) r))
                 (setq r (+$ r (*$ (arraycall flonum arr1 i k)
                                   (arraycall flonum arr2 k j)
                    )))))))
         result)


*array              LSUBR 3 or more args

     (*array x  y b1 b2  ... bn) defines  x to be  an n-dimensional  array.  The
     first subscript may  range from 0 to  b1 minus 1, the  second from 0  to b2
     minus 1,  etc.  y  is the  type of array,  as explained  above.  It  may be
     chosen from among:  t, nil, fixnum, flonum, readtable, obarray.


array               FSUBR

     (array x y b1 b2 ... bn) has the same effect as (*array (quote x) (quote y)
     b1 b2 ... bn).  This special form is provided for your typing convenience.




*rearray            LSUBR 1 or more args

     *rearray is used to redefine the dimensions of an array.

     (*rearray x) kills the array-pointer  x, or the array-pointer which  is the
     array property of the atomic symbol x.  The storage used by  the associated
     array is reclaimed.  The value returned is  t if x was an array, nil  if it
     was not.

     (*rearray x type dim1 dim2 ...  dimn) is like (*array x type dim1  dim2 ...
     dimn) except that the contents of the previously existing array named x are
     copied into  the new array  named x.  If  it is a  multi-dimensional array,
     row-major order  is used.  This  means the last  subscript varies  the most
     rapidly as the array is traversed.


store               FSUBR

     The special form (store array-ref value) is used to store an object  into a
     particular cell  of an array.   The first element  of the  form, array-ref,
     must be a subscripted reference to an array, or an invocation of arraycall.
     By coincidence, certain other forms work as array-ref, for  instance (apply
     f l)  where f  turns out  to be an  array.  The  second element,  value, is
     evaluated and stored into the specified cell of the array.  store evaluates
     its second "argument" before its first "argument".

        Examples:

        (store (data i j) (plus i j))

        (store (sine-values (fix (*$ x 100.0)))
               (sin x))

        (store (arraycall fixnum az i j) 43)


arraydims           SUBR 1 arg

     (arraydims x),  where x  is an array-pointer  or an  atomic symbol  with an
     array property, returns a list of  the type and bounds of the  array.  Thus
     if A was defined by (array A t 10 20),

fillarray           SUBR 2 args

     (fillarray a l) fills the array  a with consecutive items from the  list l.
     If the array is too short to  contain all the items in the list,  the extra
     items are ignored.  If the list is too short to fill up the array, the last
     element of  the list is  used to fill  each of the  remaining cells  in the
     array.

     (fillarray x y) fills the array x  from the contents of the array y.   If y
     is bigger than x, the extra elements are ignored.  If y is smaller  than x,
     the rest  of x is  unchanged.  x and  y must be  atomic symbols  which have
     array properties, or  array-pointers.  The two arrays  must be of  the same
     type, and they may not be readtables or obarrays.

     The list-into-array case of fillarray could have been defined by:

        (defun fillarray (a x)
            (do ((x x (or (cdr x) x))
                 (n 0 (1+ n))
                 (hbound (cadr (arraydims a))))
                ((= n hbound))
              (store (a n) (car x))
             )
            a)

     An  extension to  the above  definition is  that fillarray  will  work with
     arrays of more  than one dimension, filling  the array in  row-major order.
     fillarray returns its first argument.


listarray           LSUBR 1 or 2 args

     (listarray array-name) takes the elements of the array specified  by array-
     name and returns them as the elements of a list.  The length of the list is
     the size of the array and the elements are present in the list in  the same
     order as they are stored  in the array, starting with the  zero'th element.
     If the array has more than one dimension row-major order is used.

     (listarray  array-name n)  is the  same, except  that at  most the  first n
     elements will be listed.

     array-name  may be  an array-pointer  or an  atomic symbol  with  an array-
   Number arrays  may be efficiently  saved in the  file system and  restored by
using the functions loadarrays and dumparrays.


loadarrays          SUBR 1 arg

     (loadarrays file-spec) reloads the arrays  in the file, and returns  a list
     of 3-lists, of the form:

                         ( (newname oldname size) ...)

     newname  is a  gensym'ed atom,  which is  the name  of the  reloaded array.
     (newname ought to be an array-pointer, but this function was defined before
     array-pointers were invented.)  oldname is the name  the array had  when it
     was dumped.  size is the number of elements in the array.


dumparrays          SUBR 2 args

     (dumparrays (array1 array2 ...) file-spec) dumps the listed arrays into the
     specified file.  The arrays must be fixnum or flonum arrays.

     In both of  the above, the file-spec  argument is dependent on  the system.
     In ITS or DEC-10 Lisp, the file-spec is a list of zero to four items, as in
     uread, and the same defaults  apply.  In Multics Lisp, the file-spec  is an
     atomic symbol or  a string which  gives the pathname  of the segment  to be
     used.   The defaults  and other  features of  the Lisp  I/O system  are not
     applied.  Only a segment may be specified, not a stream.

     As  a  special  compatibility  feature,  in  Multics  Lisp  loadarrays will
     recognize a pdp-10 dumparrays file.   (One can be moved to  Multics through
     the ARPA Network File Transfer  Protocol if the "type image"  and "bytesize
     36" commands are employed.)  The pnames will be converted to lower case and
     flonums will be converted to the H6880 machine  representation.  dumparrays
     can create a  file which pdp-10  loadarrays can read,  including upper-case
     pnames and pdp-10 format flonums, if it is invoked as follows:

     (dumparrays (array1 array2...) '(pdp10 file-spec))

file: LISP, node: Mapping Functions, previous: Arrays, up: Function Descriptions,
Source: MACLISP Manual 3/6/76


   Mapping is a type of iteration in which a function is successively applied to
pieces of a list.  There are several options for the way in which the  pieces of
the  list are  chosen and  for what  is done  with the  results returned  by the
applications of the function.

   For example, mapcar operates on successive elements of the list.  As  it goes
down the list, it calls the function giving it an element of the list as its one
argument:  first the car, then the cadr, then the caddr, etc.,  continuing until
the end of the list is reached.   The value returned by mapcar is a list  of the
results of  the successive  calls to  the function.   An example  of the  use of
mapcar would  be mapcar'ing the  function abs  over the list  (1 -2  -4.5 6.0e15
-4.2).  The result is (1 2 4.5 6.0e15 4.2).

   The form of a call to mapcar is

                                  (mapcar f x)

where f is the function  to be mapped and x is  the list over which it is  to be
mapped.  Thus the example given above would be written as

               (mapcar 'abs
                       '(1 -2 -4.5 6.0e15 -4.2))

This has been generalized to allow a form such as

                            (mapcar f x1 x2 ... xn)

In this case f must be a function of n arguments.  mapcar will proceed  down the
lists x1, x2, ..., xn in parallel.   The first argument to f will come  from x1,
the second from  x2, etc.  The iteration  stops as soon as  any of the  lists is
exhausted.

   There  are five  other  mapping functions  besides mapcar.   maplist  is like
mapcar except that the function is  applied to the list and successive  cdr's of
that list rather than to successive elements of the list.  map and mapc are like
maplist and mapcar respectively except  that the return value is the  first list
being  mapped over  and the  results of  the function  are ignored.   mapcan and
mapcon are  like mapcar and  maplist respectively except  that they  combine the
results of the function using nconc instead of list.  That is,

      (defun mapcon (f x y)
          (apply 'nconc (maplist f x y)))

Of course, this definition is far less general than the real one.

   Sometimes a do or a straight  recursion is preferable to a map;  however, the
mapping  functions should  be used  wherever they  naturally apply  because this
increases the clarity of the code.

   Often f will be a  lambda-type functional form rather than  the atomic-symbol
name of a function.  For example,

              (mapcar '(lambda (x) (cons x something)) some-list)

   The functional argument to a  mapping function must be acceptable to  apply -
it cannot be a macro.  A fexpr or an fsubr may be acceptable however the results
will be bizarre.  For instance, mapping set works better than mapping  setq, and
mapping cond is unlikely to be useful.

   It is permissible (and often  useful) to break out of  a map by use of  a go,
return, or throw in a  lambda-type function being mapped.  This is  a relaxation
of the usual prohibition against "non-local" go's and return's.  If go or return
is used  the program may  have to  be compiled with  the (mapex  t) declaration,
depending on the implementation, so watch out!  Consider this function  which is
similar  to  and,  except that  it  works  on a  list,  instead  of  on separate
arguments.

     (defun andl (x)
      (catch
       (progn
        (mapc (function (lambda (y)
                          (or y (throw nil the-answer)) ))
              x)
        t)
       the-answer))

   Admittedly this could be better expressed as a do:



     (defun andl (x)
       (do ((y x (cdr y)))
           ((null y) t)
        (or (car y) (return nil))
      ))


      Here is a table showing the relations between the six map functions.

                                    applies function to

                               |  successive  |   successive  |
                               |   sublists   |    elements   |
                ---------------+--------------+---------------+
                    its own    |              |               |
                    second     |     map      |     mapc      |
                   argument    |              |               |
                ---------------+--------------+---------------+
                  list of the  |              |               |
      returns      function    |    maplist   |    mapcar     |
                    results    |              |               |
                ---------------+--------------+---------------+
                  nconc of the |              |               |
                    function   |    mapcon    |    mapcan     |
                    results    |              |               |
                ---------------+--------------+---------------+


mapatoms            LSUBR 1 or 2 args

   (mapatoms  fn obarray)  applies the  function fn  to all  the symbols  on the
specified obarray.  If  the second argument is  omitted, the current  obarray is
used.  Note  that the obarray  argument must be  an array-pointer, not  a symbol
which names an array.  The symbol  obarray is bound to the obarray  being mapped
over during the execution of mapatoms.

   This function exists because some of the cells in an obarray contain lists of
symbols and others contain single  symbols, and user programs shouldn't  have to
know this.
Example:


      (mapatoms
        (function
          (lambda (x)
            (and (sysp x)
                 (print (list x (sysp x) (args x))) ))))

file: LISP, node: Indices, up: Top,
Source: MACLISP Manual 3/6/76

    Function Index
    Atom Index
    Concept Index

                                 Function Index


*. . . . . . . . . . . . . . 2-69  LSUBR 0 or more args
*$ . . . . . . . . . . . . . 2-72  LSUBR 0 or more args
*array . . . . . . . . . . . 2-90  LSUBR 3 or more args
*function. . . . . . . . . . 2-6   FSUBR
*rearray . . . . . . . . . . 2-90  LSUBR 1 or more args
+. . . . . . . . . . . . . . 2-69  LSUBR 0 or more args
+$ . . . . . . . . . . . . . 2-72  LSUBR 0 or more args
-. . . . . . . . . . . . . . 2-69  LSUBR 0 or more args
-$ . . . . . . . . . . . . . 2-72  LSUBR 0 or more args
/. . . . . . . . . . . . . . 2-69  LSUBR 0 or more args
/$ . . . . . . . . . . . . . 2-72  LSUBR 0 or more args
1+ . . . . . . . . . . . . . 2-70  SUBR 1 arg
1+$. . . . . . . . . . . . . 2-73  SUBR 1 arg
1- . . . . . . . . . . . . . 2-70  SUBR 1 arg
1-$. . . . . . . . . . . . . 2-73  SUBR 1 arg
<. . . . . . . . . . . . . . 2-63  SUBR 2 args
=. . . . . . . . . . . . . . 2-63  SUBR 2 args
>. . . . . . . . . . . . . . 2-63  SUBR 2 args
abs. . . . . . . . . . . . . 2-65  SUBR 1 arg
add1 . . . . . . . . . . . . 2-68  SUBR 1 arg
alphalessp . . . . . . . . . 2-52  SUBR 2 args
and. . . . . . . . . . . . . 2-32  FSUBR
append . . . . . . . . . . . 2-17  LSUBR 0 or more args
apply. . . . . . . . . . . . 2-5   LSUBR 2 or 3 args
arg. . . . . . . . . . . . . 2-10  SUBR 1 arg
args . . . . . . . . . . . . 2-59  LSUBR 1 or 2 args
array. . . . . . . . . . . . 2-90  FSUBR
arraycall. . . . . . . . . . 2-12  FSUBR
arraydims. . . . . . . . . . 2-91  SUBR 1 arg
ascii. . . . . . . . . . . . 2-81  SUBR 1 arg
assoc. . . . . . . . . . . . 2-26  SUBR 2 args
assq . . . . . . . . . . . . 2-27  SUBR 2 args
atan . . . . . . . . . . . . 2-75  SUBR 2 args
atom . . . . . . . . . . . . 2-1   SUBR 1 arg
bigp . . . . . . . . . . . . 2-1   SUBR 1 arg
boole. . . . . . . . . . . . 2-77  LSUBR 3 or more args
boundp . . . . . . . . . . . 2-46  SUBR 1 arg
caaaar . . . . . . . . . . . 2-14  SUBR 1 arg
caaadr . . . . . . . . . . . 2-14  SUBR 1 arg
caadar . . . . . . . . . . . 2-14  SUBR 1 arg
caaddr . . . . . . . . . . . 2-14  SUBR 1 arg
caadr. . . . . . . . . . . . 2-14  SUBR 1 arg
caar . . . . . . . . . . . . 2-14  SUBR 1 arg
cadaar . . . . . . . . . . . 2-14  SUBR 1 arg
cadadr . . . . . . . . . . . 2-14  SUBR 1 arg
cadar. . . . . . . . . . . . 2-14  SUBR 1 arg
caddar . . . . . . . . . . . 2-14  SUBR 1 arg
cadddr . . . . . . . . . . . 2-14  SUBR 1 arg
caddr. . . . . . . . . . . . 2-14  SUBR 1 arg
cadr . . . . . . . . . . . . 2-14  SUBR 1 arg
car. . . . . . . . . . . . . 2-13  SUBR 1 arg
catch. . . . . . . . . . . . 2-40  FSUBR
catenate . . . . . . . . . . 2-85  LSUBR 0 or more args
cdaaar . . . . . . . . . . . 2-14  SUBR 1 arg
cdaadr . . . . . . . . . . . 2-14  SUBR 1 arg
cdaar. . . . . . . . . . . . 2-14  SUBR 1 arg
cdadar . . . . . . . . . . . 2-14  SUBR 1 arg
cdaddr . . . . . . . . . . . 2-14  SUBR 1 arg
cdadr. . . . . . . . . . . . 2-14  SUBR 1 arg
cdar . . . . . . . . . . . . 2-14  SUBR 1 arg
cddaar . . . . . . . . . . . 2-14  SUBR 1 arg
cddadr . . . . . . . . . . . 2-14  SUBR 1 arg
cddar. . . . . . . . . . . . 2-14  SUBR 1 arg
cdddar . . . . . . . . . . . 2-14  SUBR 1 arg
cddddr . . . . . . . . . . . 2-14  SUBR 1 arg
cdddr. . . . . . . . . . . . 2-14  SUBR 1 arg
cddr . . . . . . . . . . . . 2-14  SUBR 1 arg
cdr. . . . . . . . . . . . . 2-13  SUBR 1 arg
comment. . . . . . . . . . . 2-8   FSUBR
cond . . . . . . . . . . . . 2-32  FSUBR
cons . . . . . . . . . . . . 2-14  SUBR 2 args
copysymbol . . . . . . . . . 2-55  SUBR 2 args
cos. . . . . . . . . . . . . 2-75  SUBR 1 arg
defprop. . . . . . . . . . . 2-50  FSUBR
defun. . . . . . . . . . . . 2-57  FSUBR
delete . . . . . . . . . . . 2-24  LSUBR 2 or 3 args
delq . . . . . . . . . . . . 2-25  LSUBR 2 or 3 args
difference . . . . . . . . . 2-67  LSUBR 1 or more args
dumparrays . . . . . . . . . 2-93  SUBR 2 args
eq . . . . . . . . . . . . . 2-2   SUBR 2 args
equal. . . . . . . . . . . . 2-3   SUBR 2 args
err. . . . . . . . . . . . . 2-43  FSUBR
error. . . . . . . . . . . . 2-42  LSUBR 0 to 3 args
errset . . . . . . . . . . . 2-42  FSUBR
eval . . . . . . . . . . . . 2-5   LSUBR 1 or 2 args
exp. . . . . . . . . . . . . 2-74  SUBR 1 arg
explode. . . . . . . . . . . 2-82  SUBR 1 arg
explodec . . . . . . . . . . 2-83  SUBR 1 arg
exploden . . . . . . . . . . 2-83  SUBR 1 arg
expt . . . . . . . . . . . . 2-68  SUBR 2 args
fillarray. . . . . . . . . . 2-92  SUBR 2 args
fix. . . . . . . . . . . . . 2-65  SUBR 1 arg
fixp . . . . . . . . . . . . 2-1   SUBR 1 arg
flatc. . . . . . . . . . . . 2-83  SUBR 1 arg
flatsize . . . . . . . . . . 2-83  SUBR 1 arg
float. . . . . . . . . . . . 2-65  SUBR 1 arg
floatp . . . . . . . . . . . 2-1   SUBR 1 arg
fsc. . . . . . . . . . . . . 2-78  SUBR 2 args
funcall. . . . . . . . . . . 2-11  LSUBR 1 or more args
function . . . . . . . . . . 2-6   FSUBR
gcd. . . . . . . . . . . . . 2-68  SUBR 2 args
gensym . . . . . . . . . . . 2-55  LSUBR 0 or 1 args
get. . . . . . . . . . . . . 2-49  SUBR 2 args
getchar. . . . . . . . . . . 2-81  SUBR 2 args
getcharn . . . . . . . . . . 2-81  SUBR 2 args
getl . . . . . . . . . . . . 2-49  SUBR 2 args
get_pname. . . . . . . . . . 2-86  SUBR 1 arg
go . . . . . . . . . . . . . 2-38  FSUBR
greaterp . . . . . . . . . . 2-63  LSUBR 2 or more args
haipart. . . . . . . . . . . 2-65  SUBR 2 args
haulong. . . . . . . . . . . 2-62  SUBR 1 arg
implode. . . . . . . . . . . 2-82  SUBR 1 arg
index. . . . . . . . . . . . 2-85  SUBR 2 args
intern . . . . . . . . . . . 2-54  SUBR 1 arg
last . . . . . . . . . . . . 2-16  SUBR 1 arg
length . . . . . . . . . . . 2-16  SUBR 1 arg
lessp. . . . . . . . . . . . 2-63  LSUBR 2 or more args
listarray. . . . . . . . . . 2-92  LSUBR 1 or 2 args
listify. . . . . . . . . . . 2-10  SUBR 1 arg
loadarrays . . . . . . . . . 2-93  SUBR 1 arg
log. . . . . . . . . . . . . 2-74  SUBR 1 arg
lsh. . . . . . . . . . . . . 2-78  SUBR 2 args
lsubrcall. . . . . . . . . . 2-12  FSUBR
make_atom. . . . . . . . . . 2-86  SUBR 1 arg
maknam . . . . . . . . . . . 2-82  SUBR 1 arg
maknum . . . . . . . . . . . 2-28  SUBR 1 arg
makunbound . . . . . . . . . 2-47  SUBR 1 arg
map. . . . . . . . . . . . . 2-95  LSUBR 2 or more args
mapatoms . . . . . . . . . . 2-97  LSUBR 1 or 2 args
mapc . . . . . . . . . . . . 2-95  LSUBR 2 or more args
mapcan . . . . . . . . . . . 2-95  LSUBR 2 or more args
mapcar . . . . . . . . . . . 2-95  LSUBR 2 or more args
mapcon . . . . . . . . . . . 2-95  LSUBR 2 or more args
maplist. . . . . . . . . . . 2-95  LSUBR 2 or more args
max. . . . . . . . . . . . . 2-64  LSUBR 1 or more args
member . . . . . . . . . . . 2-23  SUBR 2 args
memq . . . . . . . . . . . . 2-24  SUBR 2 args
min. . . . . . . . . . . . . 2-64  LSUBR 1 or more args
minus. . . . . . . . . . . . 2-65  SUBR 1 arg
minusp . . . . . . . . . . . 2-61  SUBR 1 arg
munkam . . . . . . . . . . . 2-28  SUBR 1 arg
nconc. . . . . . . . . . . . 2-18  LSUBR 0 or more args
ncons. . . . . . . . . . . . 2-15  SUBR 1 arg
not. . . . . . . . . . . . . 2-4   SUBR 1 arg
nreconc. . . . . . . . . . . 2-19  SUBR 2 args
nreverse . . . . . . . . . . 2-19  SUBR 1 arg
null . . . . . . . . . . . . 2-4   SUBR 1 arg
numberp. . . . . . . . . . . 2-1   SUBR 1 arg
oddp . . . . . . . . . . . . 2-61  SUBR 1 arg
or . . . . . . . . . . . . . 2-32  FSUBR
plist. . . . . . . . . . . . 2-51  SUBR 1 arg
plus . . . . . . . . . . . . 2-67  LSUBR 0 or more args
plusp. . . . . . . . . . . . 2-61  SUBR 1 arg
pnget. . . . . . . . . . . . 2-52  SUBR 2 args
pnput. . . . . . . . . . . . 2-53  SUBR 2 args
prog . . . . . . . . . . . . 2-34  FSUBR
progn. . . . . . . . . . . . 2-8   LSUBR 1 or more args
progv. . . . . . . . . . . . 2-9   FSUBR
putprop. . . . . . . . . . . 2-50  SUBR 3 args
quote. . . . . . . . . . . . 2-5   FSUBR
quotient . . . . . . . . . . 2-67  LSUBR 1 or more args
random . . . . . . . . . . . 2-76  LSUBR 0 to 2 args
readlist . . . . . . . . . . 2-82  SUBR 1 arg
remainder. . . . . . . . . . 2-68  SUBR 2 args
remob. . . . . . . . . . . . 2-55  SUBR 1 arg
remprop. . . . . . . . . . . 2-51  SUBR 2 args
return . . . . . . . . . . . 2-39  SUBR 1 arg
reverse. . . . . . . . . . . 2-18  SUBR 1 arg
rot. . . . . . . . . . . . . 2-78  SUBR 2 args
rplaca . . . . . . . . . . . 2-21  SUBR 2 args
rplacd . . . . . . . . . . . 2-21  SUBR 2 args
samepnamep . . . . . . . . . 2-52  SUBR 2 args
sassoc . . . . . . . . . . . 2-27  SUBR 3 args
sassq. . . . . . . . . . . . 2-28  SUBR 3 args
set. . . . . . . . . . . . . 2-46  SUBR 2 args
setarg . . . . . . . . . . . 2-10  SUBR 2 args
setplist . . . . . . . . . . 2-51  SUBR 2 args
setq . . . . . . . . . . . . 2-45  FSUBR
signp. . . . . . . . . . . . 2-61  FSUBR
sin. . . . . . . . . . . . . 2-75  SUBR 1 arg
sort . . . . . . . . . . . . 2-29  SUBR 2 args
sortcar. . . . . . . . . . . 2-30  SUBR 2 args
sqrt . . . . . . . . . . . . 2-74  SUBR 1 arg
store. . . . . . . . . . . . 2-91  FSUBR
stringlength . . . . . . . . 2-85  SUBR 1 arg
stringp. . . . . . . . . . . 2-2   SUBR 1 arg
sub1 . . . . . . . . . . . . 2-68  SUBR 1 arg
sublis . . . . . . . . . . . 2-22  SUBR 2 args
subrcall . . . . . . . . . . 2-11  FSUBR
subrp. . . . . . . . . . . . 2-2   SUBR 1 arg
subst. . . . . . . . . . . . 2-21  SUBR 3 args
substr . . . . . . . . . . . 2-85  LSUBR 2 or 3 args
sxhash . . . . . . . . . . . 2-25  SUBR 1 arg
symeval. . . . . . . . . . . 2-12  SUBR 1 arg
symeval. . . . . . . . . . . 2-46  SUBR 1 arg
throw. . . . . . . . . . . . 2-40  FSUBR
times. . . . . . . . . . . . 2-67  LSUBR 0 or more args
typep. . . . . . . . . . . . 2-2   SUBR 1 arg
xcons. . . . . . . . . . . . 2-15  SUBR 2 args
zerop. . . . . . . . . . . . 2-61  SUBR 1 arg
\. . . . . . . . . . . . . . 2-70  SUBR 2 args
\\ . . . . . . . . . . . . . 2-70  SUBR 2 args
^. . . . . . . . . . . . . . 2-70  SUBR 2 args
^$ . . . . . . . . . . . . . 2-73  SUBR 2 args
.bp
                                   Atom Index
Source: MACLISP Manual 3/6/76


array. . . . . . . . . . . . 2-2
bignum . . . . . . . . . . . 2-2
car. . . . . . . . . . . . . 2-13
cdr. . . . . . . . . . . . . 2-13
defun. . . . . . . . . . . . 2-58
fixnum . . . . . . . . . . . 2-2
flonum . . . . . . . . . . . 2-2
funarg . . . . . . . . . . . 2-7
list . . . . . . . . . . . . 2-2
nil. . . . . . . . . . . . . 1-10
random . . . . . . . . . . . 2-2
string . . . . . . . . . . . 2-2
symbol . . . . . . . . . . . 2-2
zunderflow . . . . . . . . . 2-76
.bp
                                 Concept Index
Source: MACLISP Manual 3/6/76


application. . . . . . . . . 1-17        lambda . . . . . . . . . . . 1-17
argument . . . . . . . . . . 1-16        lambda variable. . . . . . . 1-17
arithmetic . . . . . . . . . 2-61        lexpr. . . . . . . . . . . . 1-17
array. . . . . . . . . . . . 1-9         list . . . . . . . . . . . . 1-10
association list . . . . . . 2-26        looping. . . . . . . . . . . 2-31
atom . . . . . . . . . . . . 1-7         lsubr. . . . . . . . . . . . 1-17
atomic symbol. . . . . . . . 1-8         macro. . . . . . . . . . . . 1-17
bignum . . . . . . . . . . . 1-7         mapping. . . . . . . . . . . 2-95
binding. . . . . . . . . . . 1-13        mathematical functions . . . 2-74
binding context pointer. . . 1-24        nil. . . . . . . . . . . . . 1-8
boolean operations . . . . . 2-77        non-local exit . . . . . . . 2-31
car. . . . . . . . . . . . . 1-9         number . . . . . . . . . . . 1-7
cdr. . . . . . . . . . . . . 1-9         obarray. . . . . . . . . . . 2-54
character manipulation . . . 2-81        object . . . . . . . . . . . 1-7
character object . . . . . . 1-8         pname. . . . . . . . . . . . 2-52
comment. . . . . . . . . . . 2-8         predicate. . . . . . . . . . 2-1
cons . . . . . . . . . . . . 1-9         property . . . . . . . . . . 2-48
defining functions . . . . . 2-57        property list. . . . . . . . 2-48
dot. . . . . . . . . . . . . 1-10        quote. . . . . . . . . . . . 2-5
dotted pair. . . . . . . . . 1-10        recursion. . . . . . . . . . 2-31
eq versus equal. . . . . . . 2-2         S-expression . . . . . . . . 1-7
errors . . . . . . . . . . . 2-31        sorting. . . . . . . . . . . 2-29
evaluation . . . . . . . . . 1-16        special forms. . . . . . . . 1-21
expr . . . . . . . . . . . . 1-17        string . . . . . . . . . . . 1-9
fexpr. . . . . . . . . . . . 1-17        subr . . . . . . . . . . . . 1-17
fixnum . . . . . . . . . . . 1-7         subr-object. . . . . . . . . 1-9
flonum . . . . . . . . . . . 1-7         substitution . . . . . . . . 2-21
flow of control. . . . . . . 2-31        symbol . . . . . . . . . . . 1-8
form . . . . . . . . . . . . 1-15        t. . . . . . . . . . . . . . 1-8
fsubr. . . . . . . . . . . . 1-17        value cell . . . . . . . . . 2-45
funarg . . . . . . . . . . . 1-20
funarg problem . . . . . . . 2-6
function . . . . . . . . . . 1-15
functional property. . . . . 1-17
gensym . . . . . . . . . . . 2-55
hash table . . . . . . . . . 2-25
indicator. . . . . . . . . . 2-48
intern . . . . . . . . . . . 2-54
iteration. . . . . . . . . . 2-31