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ArrowLISP Reference

Copyright (C) 2006 Nils M Holm. All rights reserved.
See the file LICENSE for conditions of use.

0 Contents

1   . . . . . . . . . . . . . .  Forms
1.1 . . . . . . . . . .  Abbreviations
1.2 . . . . . . . . . . . . . Comments
1.3 . . . . . . . . . Unreadable Forms
2   . . . . . . . . . . .  Expressions
2.1 . . . . . . . . . . . . .  Symbols
2.2 . . . . . . . . . . . .  Functions
3   . . . . . . . . . . .  Some Theory
3.1 . . . . . . . . . Lambda Functions
3.2 . . . . . . . Function Application
4   . . . . . . .  Primitive Functions
4.1 . .  Composition and Decomposition
4.2 . . . . . . .  Binding Constructcs
4.3 . . . . . . . . . . . . Predicates
4.4 . . . . . . . . . . . Control Flow
4.5 . . . . . . . . . . REPL Functions
4.6 . . . . . . . . . . Meta Functions
5   . . . . . . . .  Utility Functions
5.1 . . . . . . . . . . List Functions
5.2 . . . . . . . . . . . . Predicates
5.3 . . . . . . . . . . . Control Flow
5.4 . . . . . . . . . . . . . Packages
6   . . . . . . . . . . Math Functions
6.1 . . . . . . . . . . . . .  Summary
7   . . . . . . . . . . .  Miscellanea
7.1 . . . . . . . .  Naming Convention
7.2 . . . . . . . . Evaluation History
7.3 . . . . . . . . . . .  Source Path

1 Forms

A Symbol is any combination of these characters:

a b c d e f g h i j k l m n o p q r s t u v w x y z
0 1 2 3 4 5 6 7 8 9 0
* + - / < = >

An Atom is either a symbol or () (pronounced NIL).

A Pair is a concatenation of two forms:

(car-part . cdr-part)

A pair may contain other pairs:

((a . b) . c)
(a . (b . c))
((a . b) (c . d))

Each Form is either an atom or a pair.

1.1 Abbreviations

Some pairs may be abbreviated:

     (a . ())  =  (a)
    (a . (b))  =  (a b)
(a . (b . c))  =  (a b . c)

A List is a pair whose innermost cdr part is ():

List = () or (form . list).

These are Lists:

(foo bar baz)
((a . b) foo (nested list))

A list whose innermost cdr part is a symbol is called
a Dotted List. These are dotted lists:

(a b . c)
((foo bar) . baz)

Lists of single-character symbols can be condensed:

      (a)  =  '#a
  (a b c)  =  '#abc
(- 2 5 7)  =  '#-257


A comment may be inserted anywhere (even inside of a form)
by including a semicolon (;). Comments extend to the end of
the current line.


(define (f x)  ; this is a comment
  (cons x x))

1.3 Unreadable Forms

A form that is delimited by curly braces is unreadable:

{no matter what} => undefined

Unreadable forms are used to represent data that have no
unambiguous textual representation.

2 Expressions

An Expression is a form with a meaning.

x => y  denotes that x reduces to y;
        y is the normal form of x.
bottom  denotes an undefined value.

2.1 Symbols

Each symbol reduces to the value bound to it:

Symbol => value of symbol

Undefined-Symbol => bottom

A symbol that is bound to itself is called a Constant,
symbols bound to other values are called Variables.

2.2 Functions

(F x) denotes the application of f to x. F is called a
Function. X is called an Argument.

         (function) => normal form
    (function form) => normal form
(function form ...) => normal form

Function applications are reduced by first reducing arguments
to their normal forms and then applying the Function to the
resulting normal forms.

Pseudo Functions are constructs that are applied in the same
was as functions but do not reduce their arguments.

3 Some Theory

3.1 Lambda Functions

(Lambda (x) e) is a Lambda Function.

X is a variable of that function and E is the Term of that
function. Lambda functions are anonymous.

If X does not occur in E, the function is constant.

X may occur multiple times in E.

X is bound in an expression E, if

- E is a lambda function
- X is a variable of E.


X is bound in (lambda (x) x).
Y is bound in (lambda (y) (lambda (x) (x y)))
Y is not bound in (lambda (x) (x y))

When a variable X is not bound in an expression E,
X is free in E; X is a free variable of E.

3.2 Function Application

A lambda function is applied to an expression using
Beta Reduction.

e[x/v] means: replace each X that is free in E for V.

Beta reduction:
((lambda (x) e) v) => e[x/v]


a --> b  denotes a partial reduction; b is not the normal
         form of a, because it can be reduced further.

    ((lambda (x) x) t) --> t       ; identity
((lambda (x) (x x)) t) --> (t t)   ; self-application
((lambda (x) (f x)) t) --> (f t)   ; f is free
   ((lambda (x) ()) t) --> ()      ; constant function

Functions of multiple variables bind arguments by position:

((lambda (x y z) (list x y z)) 'first 'second 'third)
  => '(first second third)

4 Primitive Functions

The following definitions apply:

symbol   denotes a variable.
'symbol  denotes a constant.
eval[x]  denotes the normal form of x.
x ...    denotes zero or more appearances of x.
x | y    denotes either x or y.

Variables become constants when passed as arguments to pseudo

A list of pairs is called an Association List (or Alist).
The car part of each pair of an alist is called its key and
its cdr part is called its value.

4.1 Composition and Decomposition

4.1.1 CAR

(car pair) => form

Extract the car part of a pair.


    (car '(a.b) => 'a
     (car '(a)) => 'a
   (car '#abc)) => 'a
(car '((ab) c)) => '(ab)
      (car 'a)  => bottom
      (car '()) => bottom

4.1.2 CDR

(cdr pair) => form

Extract the cdr part of a pair.


    (cdr '(a.b) => 'b
     (cdr '(a)) => '()
   (cdr '#abc)) => '#bc
(cdr '((ab) c)) => '(c)
      (cdr 'a)  => bottom
      (cdr '()) => bottom

4.1.3 CONS

(cons form form) => pair

Construct a fresh pair.


    (cons 'foo 'bar) => '(foo . bar)
      (cons 'foo ()) => '(foo)
  (cons 'foo '(bar)) => '(foo bar)
   (cons 'a '(b . c) => '(a b . c)
         (cons () () => (())
(cons '(foo) '(bar)) => '((foo) bar)


(explode symbol) => list

Explode a symbol to a list of single-character symbols. If
the argument is (), return ().


  (explode 'foo) => '(f o o) = '#foo
    (explode 'x) => '(x)     = '#x
    (explode ()) => ()
(explode '(a.b)) => bottom


(implode list) => symbol

Implode a list of single-character symbols to a symbol. If
the argument is (), return ().


  (implode '(f o o)) => 'foo
     (implode '#foo) => 'foo
      (implode '(x)) => 'x
       (implode '()) => ()
(implode '(a (b.c))) => bottom  ; non-atom in list
   (implode '(a bc)) => bottom  ; symbol BC too long

4.1.6 QUOTE

(quote form) => 'form

Indicate normal form.


               foo => eval[foo]
       (quote foo) => 'foo
        (cons t t) => '(t . t)
(quote (cons t t)) => '(cons t t)

Note: 'foo is just an abbreviation of (quote foo).

4.2 Binding Constructcs

4.2.1 DEFINE (pseudo function)

(define symbol form) => 'symbol

Bind eval[form] to symbol.


        (define foo 'bar) => 'foo ; bind foo to 'bar
(define f (lambda (x) x)) => 'f   ; bind f to (lambda (x) x)
         (define (f x) x) => 'f   ; bind f to (lambda (x) x)
     (define (f x . y) y) => 'f   ; bind f to (lambda (x . y) y)
       (define (f . x) x) => 'f   ; bind f to (lambda x x)

4.2.2 LAMBDA (pseudo function)

(lambda (symbol ...) form) => (closure (symbol ...) form env)

Create a closure from a lambda expression.

A Closure is a snapshot of a lambda function at a given time.
In fact, only closures are valid function in ArrowLISP while
lambda expressions merely create closures.

The snapshot is taken by capturing the names and values of
all free variables of the term of the lambda function and
storing them in an alist. This alist is attached to the
closure as the ENV argument.

When a closure is applied, the captured bindings be will
re-established during the application.

Lambda may have zero arguments or more thenthan a single

              ((lambda () t)) => t
((lambda (x y z) z) 'a 'b 'c) => 'c

Variadic arguments are implemented using dotted argument

      ((lambda (x . y) y) 'a) => ()
   ((lambda (x . y) y) 'a 'b) => '(b)
((lambda (x . y) y) 'a 'b 'c) => '(b c)

When the argument list is atomic, all arguments are bound
to that atom:

       ((lambda x x)) => ()
    ((lambda x x) 'a) => '(a)
((lambda x x) 'a b c) => '(a b v)


(lambda (x) x) => (closure (x) x ())
(lambda (x) (lambda (y) (cons x y)))
  => (closure (x) (lambda (y) (cons x y)) ())
((lambda (x) (lambda (y) (x y))) 'foo)
  => (closure (y) (x y) ((x . foo)))

4.2.3 LET (pseudo function)

(let ((symbol form) ...) term) => eval[term]

LET is an alternative syntax for the application of a
lambda function:

(let ((f1 a1) ... (fN aN)) expr)


((lambda (f1 ... fN) expr) a1 ... aN)

The first argument of LET us called its environment. It is
a list of two-element lists valled bindings. The first
element of each binding holds the name of the symbol to
bond and the second element holds the value to be bound.

The term of LET is reduced in the local context created by
establishing the bindings of the environment. The context
ceases to exist after reducing the term to its normal form.

The purpose of LET is to name intermediate results in

(let ((f (lambda (x) (cons x x)))
      (v 'foo))
  (f v))
=> '(foo . foo)

LET first reduces all values of the environment before
it binds any symbols. Therefore,

(let ((v :F))
  (let ((v t)
        (u v))  ; U is bound to the outer value of V
=> :F

4.2.4 LETREC (pseudo function)

(letrec ((symbol form) ...) term) => eval[term]

LETREC works like LET, but in addition it fixes recursive
bindings using RECURSIVE-BIND (see below).

Therefore LETREC can be used to bind recursive functions
(even mutually recursive ones) to symbols.


(recursive-bind '((symbol . form) ...))

RECURSIVE-BIND fixes recursive references in environments.
Its argument is an environment represented by an alist.

A recursive reference occurs when a closure closes over
the symbol it is bound to:

((f . (closure (x) (f x) ((f . void)))))

Because F is closed over before it is bound to the closure,
F cannot recurse. Passing above environment to RECURSIVE-BIND
yields the following recursive structure:

((f . (closure (x) (f x)
  ((f . (closure (x) (f x)
    ((f . (closure (x) (f x)
      ((f . ...

4.3 Predicates

4.3.1 ATOM

(atom form) => t | :F

Reduce to T, if the given form is atomic and otherwise to :F.


    (atom ()) => 't
     (atom t) => 't
  (atom 'foo) => t
(atom '(a.b)) => :F
(atom '(a b)) => :F
 (atom '#foo) => :F


(defined 'symbol) => t | :F

Reduce to T, if the given symbol is bound in any active
context (ie by DEFINE or in a surrounding LET or LETREC).
Otherwise reduce to :F.


(defined 'undefined) => :F
  (defined 'defined) => 't
    (defined '(a.b)) => bottom
     (defined '#foo) => bottom

4.3.3 EQ

(eq form1 form2) => t | :F

Reduce to T, if the given forms are identical and otherwise
to :F.

Two forms are identical, if they are the same symbol, bound
to the same symbol, or if they are both ().


    (eq 'foo 'foo) => 't
      (eq foo foo) => 't
        (eq :F :F) => 't
    (eq 'foo 'bar) => :F
   (eq 'foo '#foo) => :F
    (eq 'a '(a.b)) => :F
  (eq '#foo '#foo) => bottom
(eq '(a.b) '(a.b)) => bottom

4.4 Control Flow

4.4.1 AND (pseudo function)

(and expr ...) => form

Reduce the given expressions in sequence until one of them
reduces to :F. If one of the expressions reduces to :F,
return :F, otherwise return the normal form of the last
expression. If no expression is given, return T.


            (and) => 't
       (and 'foo) => 'foo
         (and :F) => :F
    (and :F 'foo) => :F
    (and 'foo :F) => :F
  (and 'foo 'bar) => 'bar
(and 'a 'b 'c :F) => :F

4.4.2 APPLY

(apply fun list) => form

Apply the function fun to the given argument list, returning
the normal form of the application.

Note: APPLY is called by value, but fun is applied to list
using call-by-name.


        (apply cons '(a b)) => '(a . b)
      (apply cons '('a 'b)) => '('a . 'b)
(apply (lambda () 'foo) ()) => 'foo

4.4.3 BOTTOM

(bottom form ...) => bottom

Reduce to bottom, thereby stopping the reduction in progress.

The given forms print in the resulting error message.


               (bottom) => bottom
          (bottom 'foo) => bottom
(bottom 'foo 'bar 'baz) => bottom

4.4.4 COND (pseudo function)

(cond (pred expr) (pred expr) ...) => form

Reduce expressions conditionally.

Each argument of COND is a called a clause. It consists of
two expressions:

(predicate expression)

COND reduces the predicate of the first clause, and if it
has a true normal form (anything but :F), the entire
application of COND reduces to the normal form  of the
associated expression.

COND keeps evaluating clauses util it finds one with a
true predicate. At least one predicate must be true.


(cond ('foo 'bar)) => 'bar
(cond (:F 'foo) (t 'bar)) => 'bar
(cond ((atom ()) (cons 'foo 'bar))) => '(foo . bar)
(cond (:F 'oops)) => bottom

4.4.5 OR (pseudo function)

(or expr ...) => form

Reduce the given expressions in sequence until one of them
reduces to T. If one of the expressions reduces to T,
return T, otherwise return the normal form of the last
expression. If no expression is given, return :F.


            (or) => :F
       (or 'foo) => 'foo
         (or :F) => :F
    (or :F 'foo) => 'foo
    (or 'foo :F) => 'foo
  (or 'foo 'bar) => 'foo
(or :F :F :F 'a) => 'a

4.5 REPL Functions

These functions provide access to internal procedures of
the interpreter. They can be used to create a bare bones

(define (repl expr) (repl (write (eval (read)))))

REPL is short for Read Eval Print Loop.

4.5.1 EVAL

(eval expr) => form

Reduce expr and return its normal form.


(eval '(cons 'a 'b)) => '(a . b)
 (eval (cons 'a 'b)) => bottom  ; = (eval '(a . b))

4.5.2 READ

(read) form => form

Read an expression from the input stream, parse it,
and return it.


     (read) foo => 'foo
   (read) (a.b) => '(a . b)
(read) '(f o o) => '#foo
   (read) '#foo => '#foo
   (read) x ; y => 'x
  (read) (read) => '(read)

4.5.3 WRITE

(write expr) => form

Write the normal form of the given expression to the output
stream and return it.


        (write 'foo) writes 'foo
      (write '(a.b)) writes '(a . b)
    (write '(f o o)) writes '#foo
       (write '#foo) writes '#foo
(write '(write foo)) writes '(write foo)

4.6 Meta Functions

These functions are designed to be applied at the REPL.
They are not intended for use in programs.

4.6.1 CLOSURE-FORM (pseudo function)

(closure-form args | body | env) => argument | :F

Preset the amount of information to be disclosed when
printing a closure.

(closure-form args) ; this is the default

(lambda (foo) bar) => {closure (foo)}

(closure-form body) ; also print the body

(lambda (foo) bar) => {closure (foo) bar}

(closure-form env) ; also print the environment

; given that BAR is bound to BAZ
(lambda (foo) bar) => (closure (foo) bar ((bar . baz)))

NOTE: (closure-form env) may cause the interpreter to emit
*a lot* of information. Printing recursive closures (created
using LETREC or RECURSIVE-BIND) may take forever.

Incomplete closures are unreadable because their textual
representation is ambiguous.

4.6.2 DUMP-IMAGE (pseudo function)

(dump-image file-name) => t

Dump an image of the interpreter workspace to the given file.
Reduce to T on success and bottom in case of failure.

An image dump may be re-loaded by passing its file name to
the interpreter.

4.6.3 GC (pseudo function)

(gc) => (free-nodes max-use)

Perform a garbage collection and return some information.

Free-nodes is the amount of free nodes in the workspace.

Max-use is the maximum number of live nodes since the the
last application of GC.

4.6.4 LOAD (pseudo function)

(load file-name) => t

Read the content of the given file as if typed in at the
interpreter prompt. A .l suffix will be attached to the
given file name, so

(load foo)

will in fact load the file "foo.l".

4.6.5 PACKAGE (pseudo function)

(package name) => 'name
     (package) => ()

Open or close a package. Used for information hiding in the


To be documented.

4.6.6 QUIT

(quit) =>

Terminate the interpreter.

4.6.7 STATS (pseudo function)

(stats expr) => '(normal-form steps nodes gcs)

Reduce the given expression to its normal form. Return that
normal form plus some additional information.

STEPS is the number of reduction steps performed before
the normal form was found.

NODES is the total number of nodes allocated during the

GCS is the number of garbage collections performed during
the reduction.

The information delivered by STATS may be used to compare


(symbols) => list

Print all symbols of the current package.

4.6.9 TRACE (pseudo function)

(trace function-name) => T

Tell the interpreter to print applications of the given
function before applying it.

Use (trace) to turn off tracing.


(verify-arrows T|:F) => T|:F

Turn verification of reduction operators on or off.

When verification is off, arrow operators (=>) at the top
level act as comments:

(verify-arrows :f)
(cons 'a 'b) => this is a comment
=> '(a . b)

When verification is on, ArrowLISP will make sure that
the normal form of the expression on the lefthand side of
=> is equal to the form on its righthand side:

(verify-arrows t)
(cons 'a 'b) => '(a . b)
=> '(a . b)

When the verification succeeds, nothing special happens.
When the verification fails, an error message is issued:

(cons 'a 'b) => 'foo
=> '(a . b)
* 1: REPL: Verification failed; expected: foo

5 Utility Functions

5.1 List Functions

5.1.1 APPEND

(append list ...) => list

Concatenate lists. Appending () to a list yields the
original list. Appending an atom to a list yields a
dotted list.


(append '(foo bar) '(baz)) => '(foo bar baz)
(append '#abc '#def '#xyz) => '#abcdefxyz
         (append () '#foo) => '#foo
         (append '#foo ()) => '#foo
    (append '(a) '(b . c)) => '(a b . c)
         (append '#abc 'd) => '(a b c . d)
            (append () ()) => ()
               (append ()) => ()
                  (append) => ()

5.1.2 ASSOC / ASSQ

(assoc form alist) => pair

Retrieve a pair with a given key from an association list.
Return :F if no pair has a matching key.


    (assoc 'b '((a.1) (b.2))) => '(b . 2)
    (assoc 'x '((x.1) (x.2))) => '(x . 1)
    (assoc 'q '((x.1) (x.2))) => :F
(assoc '#foo '((#foo . bar))) => '(#foo . bar)

ASSQ is similar to ASSOC, but its first argument is limited
to symbols:

    (assq 'b '((a.1) (b.2))) => '(b . 2)
(assq '#foo '((#foo . bar))) => :F

5.1.3 CAAR ... CDDDDR

  (caar list) = (car (car list))
  (cadr list) = (car (cdr list))
  (cdar list) = (cdr (car list))
  (cddr list) = (cdr (cdr list))
(cddddr list) = (cdr (cdr (cdr (cdr list))))

Extract elements of nested lists:


(caar '((key . value)) => 'key
(cdar '((key . value)) => 'value
(cadr '(first second)) => 'second
        (caddr '#1234) => '3
       (cadddr '#1234) => '4

5.1.4 ID

(id form) => form

Map a value to itself (identity function).

(OK, not really a list function.)


      (id 'foo) => 'foo
(id (id '#foo)) => '#foo

5.1.5 LIST

(list expr ...) => list

Form a list from arguments. Unlike members of quoted (constant)
lists, the arguments of LIST are reduced before inserting them
in the list.


             (list) => ()
        (list 'foo) => '(foo)
    (list 'a 'b 'c) => '#abc
    '((cons 'a 'b)) => '((cons 'a 'b))
(list (cons 'a 'b)) => '((a . b))


(member expr list) => list
(memq symbol list) => list

Find a member of a list.


  (member 'bar '(foo bar baz)) => '(bar baz)
(member '(b.2) '((a.1) (b.2))) => '((b . 2))
  (member 'foo '(a b c d e f)) => :F

MEMQ is like MEMBER, but its first atgument is limited to

  (memq 'bar '(foo bar baz)) => '(bar baz)
(memq '(b.2) '((a.1) (b.2))) => :F


(reverse list) => list

Create a reverse copy of a list:


    (reverse '(foo bar)) => '(bar foo)
(reverse '(a b c d e f)) => '#fedcba
            (reverse ()) => ()
      (reverse '(a . b)) => bottom
  (reverse '(a b c . d)) => bottom

5.2 Predicates

5.2.1 EQUAL

(equal form form) => t | :F

Return T if the two given forms are equal and otherwise :F.

Two forms are equal, if they are both the same symbol or if
they are pairs containing equal car and cdr parts.


                        (equal () ()) => 't
                (equal '(a.b) '(a.b)) => 't
(equal '(f (f x y) z) '(f (f x y) z)) => 't
            (equal '#abcdef '#abcdef) => 't
                    (equal 'foo 'bar) => :F
        (equal '(x (y) z) '(x (q) z)) => :F
                  (equal '#xxx '#xxy) => :F

5.2.2 LISTP

(listp form) => t | :F

Return T if the given form is a (non-dotted) list and
otherwise :F.


        (listp ()) => 't
  (listp '(a b c)) => 't
  (listp '#abcdef) => 't
  (listp '(a . b)) => :F
(listp '(a b . c)) => :F
      (listp 'foo) => :F

5.2.3 NEQ

(neq form form) => t | :F

Return T if the given forms are not identical and otherwise :F.


    (neq 'foo 'bar) => 't
   (neq 'foo '#foo) => 't
    (neq 'a '(a.b)) => 't
    (neq 'foo 'foo) => :F
      (neq foo foo) => :F
        (neq () ()) => :F
  (neq '#foo '#foo) => bottom
(neq '(a.b) '(a.b)) => bottom

5.2.4 NOT

(not form) => t | :F

Check whether the given form is :F (logical negation).


       (not :F) => t
       (not ()) => :F
        (not t) => :F
     (not 'foo) => :F
 (not '(a b c)) => :F

5.2.5 NULL

(not form) => t | :F
(null form) => t | ()

Check whether the given form is ().


      (null ()) => 't
      (null :F) => :F
      (null 'x) => :F
(null '(a b c)) => :F

5.3 Control Flow

5.3.1 MAP

(map fun list list ...) => list

Map the given function over the given list(s). The function
must take the same number of arguments as there are lists.

The N'th member of the resulting list is the result of
applying FUN to the N'th members of all input list.


       (map car '((a) (b) (c))) => '#abc
       (map cdr '((a) (b) (c))) => '(() () ())
   (map cons '(a b c) '(d e f)) => '((a . d) (b . e) (c . f))
(map list '(a b) '(c d) '(e f)) => '(#ace #bdf))

5.3.2 REDUCE

(reduce fun list form) => form

Reduce the given list by combining its first and second
element using the binary function FUN. Combine the result
with the third member, etc:

(REDUCE f (a b c d) ())  =  (f (f (f a b) c) d)

If only one member is given, return it.

If no member is given, return a default, specified in the
third argument.


    (reduce cons '(a b) 'foo) => '(a . b)
(reduce cons '(a b c d) 'foo) => '(((a . b) . c) . d)
      (reduce cons '(a) 'foo) => 'a
        (reduce cons () 'foo) => 'foo

5.3.3 REDUCE-R

(reduce-r fun list form) => form

Reduce the given list by combining its head with its reduced
tail using the binary function FUN.

While REDUCE combines its arguments left-associatively,
REDUCE-R combines them right-associatively:

(REDUCE-R f (a b c d) ())  =  (f a (f b (f c d)))

If only one member is given, return it.

If no member is given, return a default, specified in the
third argument.


    (reduce-r cons '(a b) 'foo) => '(a . b)
(reduce-r cons '(a b c d) 'foo) => '(a b c . d)
      (reduce-r cons '(a) 'foo) => 'a
        (reduce-r cons () 'foo) => 'foo

5.4 Packages

5.4.1 EXPORT

(export symbol ...) => t

Declare symbols for use outside of a package.


To be documented.


(require 'package-name) => t | :F

Load a package (using LOAD) if it is not already present.

REQUIRE checks the presence of a package by testing whether
the given package name is defined. Packages are required to
define that name.


(require 'nmath) => 't  ; load natural math functions
(require 'nmath) => :F  ; already loaded

6 Math Functions

ArrowLISP implements math numbers as lists of digits:

123 is written as '(1 2 3) or '#123.

Rational numbers are lists of numbers with a leading slash:

-5/4 is written as '(/ #-5 #4).

Math functions are not part of the default image. To load
them use

(load nmath) ; load natural math functions
(load imath) ; load integer math functions (includes nmath)
(load rmath) ; load rational math functions (includes rmath)

To create an image with all math functions, type

(load rmath)
(dump-image math-image)

and run ArrowLISP using

alisp math-image.

6.1 Summary

... indicates repetition.
[x] indicates that x is optional.
x|y indicates x or y.
x = number;
n = natural;
i = integer;
r = rational.

Function                   Returns...
(* [x ...]) => x           product
*epsilon* => n             log10 of precision of SQRT
(+ [x ...]) => x           sum
(- x1 x2 [...]) => x       difference
(- x) => x                 negative number
(/ x1 x2) => x             ratio
(< x1 x2 [...]) => t|:f    t for strict ascending order
(<= x1 x2 [...]) => t|:f   t for strict non-descending order
(= x1 x2 [...]) => t|:f    t for equivalence
(> x1 x2 [...]) => t|:f    t for strict descending order
(>= x1 x2 [...]) => t|:f   t for strict non-ascending order
(abs x) => x               absolute value
(denominator r) => i       denominator
(divide i1 i2) => (i3 i4)  quotient i3 and remainder i4
(even i) => t|:f           t, if i is even
(expt x i) => x            x to the power of i
(gcd [i1 ...]) => n        greatest common divisor
(integer x) => i           an integer with the value x
(integer-p x) => t|:f      t, if x is integer
(lcm [i1 ...]) => n        least common multiple
(length list) => n         length of a list
(max x1 [x2 ...]) => x     maximum value
(min x1 [x2 ...]) => x     minimum value
(modulo i1 i2) => i3       modulus
(natural x) => n           a natural with the value x
(natural-p x) => t|:f      t, if x is natural
(negate i|r) => i|r        negative value
(negative x) => t|:f       t, if x is negative
(number-p expr) => t|:f    t, if expr represents a number
(numerator r) => i         numerator
(odd i) => t|:f            t, if i is not even
(one x) => t|:f            t, if x equals one
(quotient i1 i2) => i      quotient
(rational x) => r          a rational with the value x
(rational-p x) => t|:f     t, if x is rational
(remainder i1 i2) => i     division remainder
(sqrt n) => x              square root, see also *espilon*
(zero x) => t|:f           t, if x equals zero

[*] The result of SQRT depends on the library in use.
    The natural and integer versions return the greatest
    natural number whose square is not larger than the
    The rational version returns a number that differs
    from the actual square root of the argument by no
    more than (/ '#1 (expt '#10 *epsilon*)), where
    *epsilon* is a global variable.

7 Miscellanea

7.1 Naming convention

Symbols starting and ending with an asterisk are reserved
for the code implementing ArrowLISP. They must be avoided
in user-level code.

7.2 Evaluation History

The normal form most recently produced by the interpreter
is bound to the symbol **:

(car '(first second))
=> 'first
(cons ** **)
=> '(first . first)

7.3 Source Path

When loading code using LOAD or REQUIRE, the following
abbreviations may be used:

(load ~/foo)

load the file "foo.l" from the user's home directory.

(require '=nmath)

conditionally loads the file "nmath.l" from the directory
specified in the environment variable ALISPSRC.

Copyright (C) 2006 Nils M Holm < nmh @ t3x . org >