An Introduction to Functional Programming Through Lambda Calculus

- 177 -- fun length [] = 0 |length (h::t) = 1+(length t);> val length = fn : (’a list) -> intThere are no explicit types in the pattern:(h::t)and this pattern is consistent if h is ’a and t is ’a list as (h::t) is then ’a list. This is also consistent withthe use of t as the argument in the recursive call to length. Here again, the element types are irrelevant for purelystructural manipulations.This approach can also be used to define type independent functions which are later made type specific.For example, we might try and define a general purpose list insertion function as:- fun insert i [] = [i] |insert i (h::t) =if i bool) -> (’a -> ((’a list) -> (’a list)))Here, comp needs an (’a * ’a) argument to be consistent in insert and must return a bool to satisfy its use inthe if.Now, different typed comparison functions may be used to construct different typed insertion functions. For example,we could construct a string insertion function through partial application by passing a string comparison function:fn (s1:string,s2:string) => s1 s1 val sinsert = fn : string -> ((string list) -> (string list))Here, the comparison function is:(string * string) -> boolso ’a must be string in the rest of the function’s type.For example, we could also construct a integer insertion function through partial application by passing an integercomparison function:fn (i1:integer,i2:integer) => i1