Question

I would like to know how to compare two function F(x) & G(x) in SML, which two functions must return the same value that f(x)==g(x), where 1<= x <= 100. For example:

- fun f x = x*x;    
val f = fn : int -> int
- fun g x = x+x;
val g = fn : int -> int
- iden f g;
val it = false : bool
- fun f x = x*x;
val f = fn : int -> int
- fun g x = if x<0 then 0 else x*x;
val g = fn : int -> int
- iden f g;
val it = true : bool

Answer 1

由于对所有投入而言,对两项职能(表格)是否平等进行测试是无法计算的,因此,你的<代码>iden功能可能必须比对其比较的两种功能更具参数。

总的说来,<代码>iden 将:

- fun iden f g elem = f(elem) = g(elem)
val iden = fn : ( a ->   b) -> ( a ->   b) ->  a -> bool

在你的具体情况下,你可能希望这样做:

- fun iden f g = let
=   fun iden_h f g (a, b) =
=     if a > b then iden_h f g (b, a)
=     else if a = b then f(a) = g(a)
=     else f(a) = g(a) andalso iden_h f g (a+1, b)
=  in
=   iden_h f g (1, 100)
=  end
val iden = fn : (int ->   a) -> (int ->   a) -> bool
-
- iden (fn x => x + x) (fn x => 2 * x);
val it = true : bool
- iden (fn x => x + x) (fn x => x * x);
val it = false : bool

友情链接