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Author

The Ambi Calculator and Programming Language was created by David Pratten.

Introduction

Ambi is a programming language generalised from Reverse Polish Notation arithmetic and an extensible RPN Calculator hosted in the browser. Other languages such as Forth and RPL have similar roots and illustrious histories, but have embraced non-RPN elements as they developed. In contrast, Ambi attempts to stick strictly to the RPN approach. Ambi also has similarities to the CAT language.

Why "Ambi"

"Ambi" is named for its ability to be ambidextrous with expressions and programs. Ambi detects and correctly evaluates expressions and programs either in Reverse Polish Notation or in Polish Notation. For example, the following two expressions give the same answer:

3 5 + 2 / .

and

. / + 3 5 2

Documentation

Expressions

Expressions are terminated by semi-colons: ";" Each expression starts with a fresh stack. Variables defined in one expression are available in expressions evaluated later. Expressions can be of arbitary length. Empty expressions ";;" are equivalent to ";true;".

Comments

Comments are a special kind of expression that begins and/or ends with "//".

Operators

Ambi operators are not case sensitive.

• Arithmetic operators include: + - * / sq sqrt abs ln floor ceil min max exp inv pow
• The Unary Minus operator is _.
• Aggregate operators include: sum sumsq product.
• Boolean operators include: == eq != <> neq < lt > gt <= lte >= gte && and || or ! not
• Trigonometry operators (radians) include: sin cos tan asin acos atan
• The stack operators include dup swap drop
• The assignment operator is =
• Compound operators include: += -= /= *= ++ --
• The . or printtop operator will print the number on top of the stack. While the .. or printall operator will print the all the numbers in the stack.

Values

Booleans are represented by numeric values. Non-zero is True, 0 is False.

Constants

true has value 1. false as value 0. The constants pi and e are available.

Variables

Variables are names that start with "$". Examples of valid variable names include: $a, $5, $count Variables defined outside functions are preserved between program executions. Variables define inside functions are local to the function. There are no global variables.

Examples

Simple Calculation

// Simple Calculation ; 
1 2 + 3 + 5 + 7 / .

Monitor Stack

// Show stack values ;
1 . 2 . + .

Variable Assignment

// Variable Assignment and Use ;
1 $a = 2 $b = $a $b + .

Aggregate Function Example

// Area of circle of radius 5 ;
5 $radius = pi $radius sq product . 

Multi-expression programs

Programs may be built up by treating the expressions as lambdas acted on by the: if ifelse whiledo dowhile and function operators.

The if operator executes the second lamda expression on the stack depending on the result of executing the first. And then executes the finalise expression.

// if operator ;
if;
  23.4 $a = $a floor 23 ==;
  $a .;
  ;

Equivalently ...

// if operator ;
  ;
  $a .;
  23.4 $a = $a floor 23 ==;
if;

if;
  <initialise & test expression>;
  <if true expression>;
  <finalise expression>;

  <finalise expression>;
  <if true expression>;
  <initialise & test expression>;
if;

The ifelse operator is similar except that it has an <if false expression> as well.

ifelse;
  <initialise & test expression>;
  <if true expression>;
  <if false expression>;
  <finalise expression>;

  <finalise expression>;
  <if false expression>;
  <if true expression>;
  <initialise & test expression>;
ifelse;

The whiledo operator and dowhile operators differ only in that whiledo evaluates the test expression before executing the repeated expression while dowhile evaluates the repeated expression at least once and then checks the test expression.

The reverse polish variants of these operators are not shown here for brevities sake.

whiledo;
  <initialise expression>;
  <test expression>;
  <repeated expression>;
  <finalise expression>;

dowhile;
  <initialise expression>;
  <repeated expression>;
  <test expression>;
  <finalise expression>;

The for operator mirror's the C style for construct.

The reverse polish variant of this operator is not shown here.

for;
  <initialise expression>;
  <test expression>;
  <increment expression>;
  <repeated expression>;
  <finalise expression>;

// Enumerate the first 10 square numbers;
for;
  1 $i =;
  $i 11 <;
  1 $i +=;
  $i sq .;
  ;

Functions are defined using the function operator, which binds a lambda expression to a name. The only communication between a function and its calling context is via the import and export operators. Within a function body import will pop one item off the calling context's stack and push it onto the local stack. Conversely, export takes one item off the local stack and pushes it onto the calling context's stack.

The reverse polish variant of this operator is not shown here.

function; <name>;
<function body expression>;

// Function to Enumerate N numbers starting with M;
function; generate;
for;
  import $count = import $start = $start $i =;
  $i $start $count + <;
  1 $i +=;
  $i export;
  ;

1 10 generate ..

Further Examples

// Calculate Area Of Circle ;
function; areaofcircle;
  pi import sq product export;

5 areaofcircle . 

Recursive Factorial Function (Prefix version)

function; ! ;
  ifelse;
    import $n = $n 1 eq;
    1 export;
    $n 1 - ! $n * export;
    ;

// Use the function ;
5 ! .

Equivalent Factorial Function (Postfix version)

// Factorial Function (Postfix version);
. ! 6 ;
// Define the function ;

    ;
    $n 1 - ! $n * export;
    1 export;
    import $n = $n 1 eq;
  ifelse;
! ; function 

The following two programs are equivalent:

function;
max;
  ifelse;
    import dup $a = import dup $b = >;
    $a export;
    $b export;
    ;

1 100 max .;

function;
max;
  ifelse;
    > = $a dup import = $b dup import;
    export $a;
    export $b;
    ;

. max 1 100;

Interative Cuberoot Function using X(r+1) = 0.5+ N/(Xr)^2;

function; cuberoot;
  dowhile;
    import dup $n = $guess =;
    $guess $prev = $n $prev sq / $prev + .5 * $guess =;
    $guess $prev - abs .000000001 >;
    $guess export ;
125 cuberoot .

... and a recursive Cuberoot Function

function; inner-root3;
  if;
    import $n = import $prev = $prev $n $prev sq / + .5 * $guess = $guess $prev - abs .000000001 >;
    $guess $n inner-root3 $guess =;
    $guess export;

function; root3;
  import dup inner-root3 export ;

100 root3 .

Implementation

Ambi is currently implemented in javascript that executes completely in your browser.

Version Change Log

0.6

• ADD: drop, pow, exp, and inv operators
• ADD: 9 short lessons on how to use ambi
• CHG: Complete redesign of UI using browser local storage to preserve state across invocations. Added 'My Ambi Functions' which are persistent. UI now auto recalculates as the expression is edited.
• ADD: Added extensive error reporting.
• ADD: Virtual Keyboard.
• CHG: Removal of global variable dependencies from ambi.js
• ADD: Unit tests

0.4.4 Streamlining.

• ADD: The increment and decrment ++ -- operators.
• CHG: Removed the seq operator. It is no longer necessary.
• ADD: Added the pass constant. It does nothing, it is behaves as a synonym for true.
• CHG: The empty expression ";;" is now equivalent to ";pass;" .
• CHG: Added <initialise expression> to the dowhile whiledo and for operators. Added <finalise expression> to the if ifelse dowhile whiledo and for operators. The initialise and finalise expressions must always present but may be pass or simply empty.

0.4.3 Ambi is now Turing complete.

• ADD: Added seq dowhile whiledo for if ifelse operators.
• ADD: Added function import export operators.
• ADD: Added . operator (Synonym for printtop)
• ADD: Added .. operator (Synonym for printall) which prints the whole stack.
• ADD: Added dup swap stack operators.
• ADD: Added min and max binary arithmetic operators.
• ADD: Added // comment operator
• ADD: Added mathematical constant e.
• CHG: The unary minus operator is changed from - to _.
• CHG: The prefix form of the assignment operator is now =

  <val>

• FIX: Variables were not pushed onto stack with immutable value only by mutable reference.

0.4.2 further explands the arithmetic capabilities of Ambi.

• ADD: Added trigonometry operators and constants.
• FIX: Expressions beginning with a constant such as true where not correctly evaluated.
• ADD: Added display of variables.
• FIX: The unary minus operator is changed from un to um.

0.4.1 is aimed at greatly expanding the arithmetic capabilities of Ambi.

• ADD: Added boolean operators.
• ADD: Added aggregate operators.
• ADD: Added many arithmetic operators.

0.4.0 is the first public release.