An Introduction to Functional Programming Through Lambda Calculus

- 164 -opWe will look at this in more detail when we consider standard functions.9.7. Boolean standard functionsThe boolean negation function:notreturns the negation of its boolean argument, for example:- not true;> false : boolThus, not’s type is:- not;> fn : bool -> boolConjunction and disjunction are provided through the sequential infix operators:andalso orelsein the derived syntax, for example:- true orelse false;> true : bool- true andalso false;> false : boolSML systems may not be able to display these operators’ types but they are effectively:fn : (bool * bool) -> boolas they both take two boolean arguments, which are treated as a:bool * booltuple for infix syntax, and return a boolean result.9.8. Numeric standard functions and operator overloadingSML provides real numbers as well as integers. However, as in many other languages, the same operators are used forboth even though they are distinct types. This use of the same operator with different types is known as operatoroverloading.The addition, subtraction and multiplication infix operators are:+ - *SML systems may not display their types because they are overloaded. SML literature uses the invented type:num