CODEWITHSUNDEEP
smlml
user2682811
user2682811

Reputation: 195

subtract functions with type real in ml

I'm trying to subtract two functions(both with type real) in moscow ml. It then says "Overloaded - cannot be applied to arguments of type real -> real. So how should I write the function? 

fun CircleArea  x = x*x*Math.pi

fun SquareArea x:real = 4*x*x

fun Area x = SquareArea - CircleArea

Upvotes: 3

Views: 641

Answers (2)

Sebastian Paaske Tørholm
Sebastian Paaske Tørholm

Reputation: 50928

Subtraction of functions like we have in mathematics isn't provided as a built-in operator. You can, however, define your own.

Mathematically speaking, we define

(f - g)(x) = f(x) - g(x)

We can replicate this definition in SML as follows:

infix 5 --
fun f -- g = fn x => f x - g x

What this does is produce an operator, --, such that f -- g produces the function corresponding to fn x => f x - g x, i.e. the function that given an x calculates f x - g x.

Note, due to the type-ambiguity in the - operator, it'll default to let you subtract 'a -> int functions. In your case you'll want to subtract 'a -> real functions, so you'll need a slight modification:

infix 5 --
fun f -- g = fn x => f x - g x : real

If you use this ---operator, you will be able to define your Area function like so:

val area = squareArea -- circleArea;

(I took the liberty of making the first letter of function names lowercase, to match the SML naming conventions.)

Upvotes: 2

sshine
sshine

Reputation: 16145

You probably don't actually want to subtract one function from another, but the return values of those functions once they are applied. You could achieve this in the following way:

fun Area x = (SquareArea x) - (CircleArea x)

The parentheses are not mandatory, since function application (i.e. the space between SquareArea and x) binds tighter than any binary operator, including -.

You should consider using the following naming convention in ML: Regular functions have a lowercase starting symbol, while value constructors for algebraic types have uppercase starting symbols. For example:

fun area x = squareArea x - circleArea x

But:

datatype shape = Square of int * int
               | Circle of int

Upvotes: 5

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