Lexical Conventions

Whitespace may separate any two lexical tokens. Whitespace is a sequence of space, tab and newline characters.

IBAL uses the following keywords:

Keyword	Use
Bool	Boolean type
Int	Integer type
Symbol	String type
case	Case expression: conditional choice by pattern matching
data	Algebraic data type (ADT) definition
decide	Decision expression or declaration
discount	Discount utility in expression
dist	Dist expression: stochastic choice
else	Else clause of if expression
error	Expression signalling error condition
fix	Fix expression: defines recursive function
flip	Flip expression: binary stochastic choice
forall	Forall type quantifier
from	Choices clause of decision
fun	Lambda expression: defines non-recursive function
given	Information clause of decision
if	If expression
in	Connective in various expressions
let	Let expression: defines variable
letdata	ADT definition in expression
lettype	Type definition in expression
obs	Observation declaration or expression
observe	Observation declaration or expression
of	Connective in case expression
op	Operator value
param	Parameter definition
params	Parameter definitions in expression
pdist	PDist expression: stochastic choice with parameter
pragma	Execution strategy declaration
private	Private label on declaration
retract	Retract an observation at the command line
reward	Utility declaration or expression
then	Then clause of if expression
type	Type definition
uniform	Uniform expression: stochastic choice

The keywords obs and observe are synonymous. From now on, only obs will be used in this manual.

IBAL uses the following punctuation characters. Many have multiple uses:

Character	Name	Use
(	Left parenthesis	Function arguments, and expression grouping
)	Right parenthesis	Ditto
{	Left brace	Block delimeter, and string sets
}	Right brace	Ditto
[	Left square	Dist clauses, and type arguments
]	Right square	Ditto
<	Left tuple	Tuple delimiter
>	Right tuple	Ditto
,	Comma	Argument and tuple element separator
;	Semicolon	Optional declaration separator
"	Double-quote	String delimiter
'	Single-quote	String initiator
=	Equals	Definitions and observations
.	Dot	Component access, and forall type definitions
:	Colon	Type assertions, and dist and case consequences
#	Hash	Case clauses
_	Underscore	Wildcard pattern
~	Not	Boolean negation
|	Or	Boolean disjunction
&	And	Boolean conjunction
+	Plus	Integer addition
-	Minus	Integer subtraction and unary negation
*	Times	Integer multiplication
/	Div	Integer division
%	Mod	Integer remainder
^	Concat	String concatentation

IBAL uses the following multi-character tokens:

Token	Name	Use
->	MapsTo	Function definition connective
==	EqualsEquals	Comparison
++	PlusPlus	Integer increment
--	MinusMinus	Integer decrement
..	DotDot	Integer range

true and false, in all case combinations, are Boolean literals, standing for the Boolean constants.

An identifier is a non-empty sequence of letters, digits or the underscore character, that is not a keyword, a Boolean literal, or a single underscore. Identifiers are divided into two groups, depending on their initial character: an lident begins with a lower case character or underscore, while a uident begins with an upper case character. A longvar is a sequence of identifiers, ending with an lident, each separated by a dot. A ulongvar is similar, except that the final identifier is a uident instead of an lident.

A string literal is a sequence of characters between two double-quote characters, or an identifier following a single-quote character. The quotation marks are not considered part of the string, so ``xyz'' and 'xyz define the same string.

A natural is a sequence of digits. An integer literal is either a natural, or a minus sign followed by a natural.

A posfloat consists of zero or more digits, followed by a decimal point, followed by one or more digits. Exponent-mantissa notation is not currently supported. A float is either a posfloat, or a minus sign followed by a float.