XSLT 2.0 and XPath 2.0 Programmer's Reference, 4th Edition (91 page)

xs:boolean

This is the simplest type defined in XML Schema. It has two values in the value space, referred to as
true
and
false
, and each of these has two permitted lexical representations:
1
and
true
,
0
and
false
.

Although it's so simple, there are some interesting quirks in the way XML Schema and XPath handle this type.

• As far as XML Schema is concerned, the
  xs:boolean
  type has no ordering. But in XPath, there is an ordering:
  false
  is considered to be less than
  true
  . XPath 2.0 has taken this position largely for backward compatibility with XPath 1.0, and also because it can actually be useful; for example, a stylesheet might use the expression
  age < 18
  as a sort key, which will output the adults first, then the children.
  
• There are two ways of converting a string to a boolean. An XML Schema processor interprets
  1
  and
  true
  as true,
  0
  and
  false
  as false. This behavior also occurs when you use the
  xs:boolean()
  constructor (described in Chapter 11). But if you use the
  boolean()
  function (or
  fn:boolean()
  if you want to write it with a namespace prefix), as described in Chapter 13, then a zero-length string translates to
  false
  , and everything else to
  true
  . This is also the result you get if you do an implicit conversion of a string to a boolean by using a string in a context such as
  if (S) then A else B
  , where S is a string.
  

  Again, the difference is partly historic: the XPath 1.0 rules were invented before XML Schema came along. But the convention of equating a zero-length string to
  false
  also has a long history in weakly typed programming languages, and is very convenient in some recursive algorithms that need to terminate when the argument is a zero-length string.