An Introduction to Functional Programming Through Lambda Calculus

- 169 -Functions have the form:fn => A bound variable is known as an alphabetic identifier and consists of one or more letters, digits and _s starting with aletter, for example:oxymoron Home_on_the_range Highway61A function’s bound variable may be a single bound variable or a tuple of bound variable elements.For example:- fn x => x+1;> fn : int -> intincrements its argument.Note that SML deduces that the domain and range are int because + is used with the int argument 1.For example:- fn x => fn y => not (x orelse y);> fn : bool -> (bool -> bool)is the boolean implication function.Note that orelse has a boolean tuple domain so x and y must both be boolean. Similarly, not returns a boolean sothe inner function:has type:fn y => not (x orelse y)bool -> boolHence, the whole function has type:fn : bool -> (bool -> bool)This might have been written with a tuple domain:- fn (x,y) => not (x orelse y);> fn : (bool * bool) -> bool9.14. Making bound variables’ types explicitSuppose we try to define a squaring function:fn x => x*xBecause * is overloaded, SML cannot deduce x’s type and will reject this function.Domain types may be made explicit by following each bound variable with its type. Thus for a single bound variable:( : )