An Introduction to Functional Programming Through Lambda Calculus

- 170 -is used. For example, an integer squaring function may be defined by:- fn (x:int) => x*x;> fn : int -> intFor a tuple of bound variables:( : , : , ... )is used. For example, we might define the sum of squares function as:- fn (x:int,y:int) => x*x+y*y;> fn : (int * int) -> intIt is thought to be ‘good practise’ to make all bound variables’ types explicit. This is supposed to make it easier toread functions and to ensure that types are consistent. However, without care, type expressions can becomeunmanageably long. SML provides ways to name complex types which we will consider in a later section.9.15. DefinitionsGlobal definitions may be established with:val = For example:- val sq = fn (x:int) => x*x;> val sq = fn : int -> int- val sum_sq = fn (x:int,y:int) => x*x+y*y;> val sum_sq = fn : (int * int) -> intNote that the SML system acknowledges the definition by displaying the defined name and the expression’s valueand/or type.Defined names may be used in subsequent expressions, for example:- sq 3;> 9 : intand subsequent definitions, for example:- val sum_sq = fn (x:int,y:int) => (sq x)+(sq y)> val sum_sq = fn : (int * int) -> int9.16. Conditional expressionsThe SML conditional expression has the form:if then else The first expression must return a boolean and the option expressions and must have the same type.