Maple ordinarily uses a three-valued logic using the Boolean values true, false, and FAIL. The Maple type truefalseFAIL describes this set of values.

The expression type(e,'truefalseFAIL') evaluates to true if, and only if, the expression e is of type truefalseFAIL, which is defined as the expressions true, false, and FAIL. No other expression is of type truefalseFAIL.

The type boolean_constant is a synonym for truefalseFAIL and behaves identically.

Note that every expression that is of type truefalseFAIL is also of type boolean, but that the converse is not true.  Expressions of type relation such as x and y where x and y are symbols, are of type boolean but not of truefalseFAIL.

The type truefalse refers to only the two Boolean values true and false and excludes the value FAIL.

type/truefalse

type/boolean, type/symbol

$\mathrm{type}\left(\mathrm{true}\,'\mathrm{truefalseFAIL}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{false}\,'\mathrm{truefalseFAIL}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{FAIL}\,'\mathrm{truefalseFAIL}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(x\mathbf{and}y\,'\mathrm{truefalseFAIL}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(x\le y\,'\mathrm{truefalseFAIL}'\right)$

$\mathrm{false}$

type( proc() true; end proc, 'truefalseFAIL' );

$\mathrm{false}$

$\mathrm{type}\left(x^2-3\,'\mathrm{truefalseFAIL}'\right)$

$\mathrm{false}$

The type/truefalseFAIL and type/boolean_constant commands were introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.