sml-examples/basics/functions/example.org

Function definitions

(need to import the infinitely large integer structure to avoid overflows for big numbers)

open IntInf;

(in one function) fun fib_naive (n) = if n < 2 then 1 else fib_naive (n - 1) + fib_naive (n - 2);

(using pattern matching) fun fib_naive_2 (0) = 1 | fib_naive_2 (1) = 1 | fib_naive_2 (n) = fib_naive (n - 1) + fib_naive (n - 2);

(avoiding stack overflow by using tail recursion) fun fib_tail_recursive 0 = 1 | fib_tail_recursive 1 = 1 | fib_tail_recursive n let val init_1 1; val init_2 = 1; fun iter (prev_prev, prev, ind) if ind n then prev_prev + prev else iter (prev, prev_prev + prev, ind + 1) in (* starting at 2 because 0 and 1 are already handled in pattern matching ,*) iter (init_1, init_2, 2) end;

fib_naive 10; fib_naive_2 10; fib_tail_recursive 100;

:results: val fib_naive = fn : int -> int :end:

Function type

• expressed using the operator ->
• right-associative: T1 -> T2 -> T3 is the same as ~T1 -> (T2 -> T3)~x

Example functions

fun upper (character) = chr(ord(character) - 32);

fun square (x: real) = x * x;

:results: val upper = fn : char -> char :end: