An Introduction to Functional Programming Through Lambda Calculus

- 180 -A datatype constructor may be preceded by a type variable to parameterise the datatype. For example, SML lists mightbe defined by:- datatype ’a list = lnil | cons of ’a * (’a list);> datatype ’a list = lnil | cons of ’a * (’a list)con lnil : ’a listcon cons = fn : (’a * ’a list) -> (’a list)This defines cons as a prefix constructor.Type variables in datatype definitions may be set to other types in subsequent type expressions. For example, in:- type intlist = int list> type intlist = int listthe type variable ’a is set to int to use intlist to name an integer list type.SML systems will also deduce the intended type when the constructor from a parameterised data type is used withconsistent values Thus, the following are all string lists:- cons("ant",lnil);> cons("ant",lnil) : string list- cons("ant",cons("bee",lnil));> cons("ant",cons("bee",lnil)) : string list- cons("ant",cons("bee",cons("caterpiller",lnil)));> cons("ant",cons("bee",cons("caterpiller",lnil))) : string listStructured datatype values may also be used in patterns with typed variables and constructors in the tuple followingthe datatype constructor. It is usual to have separate patterened definitions for base and for structured values.For example, to sum the elements of an intlist:- fun sum intnil = 0 |sum (intcons(x:int,y:intlist)) = x + (sum y);> val sum = fn : intlist -> int- sum (intcons(9,intcons(8,intcons(7,intnil))));> 24 : intFor examples, to join the elements of a string list:- fun join lnil = "" |join (cons(s:string,l:(string list))) = sˆjoin l;> val join = fn : (string list) -> string- join (cons("here",cons("we",cons("go",lnil))));> "herewego" : stringNote that existing types cannot be used as base types directly. For example, we might try to define a general numbertype as:- datatype number = int | real;> datatype number = int | realcon int = int : numbercon real = int : number