Is there a strongly typed programming language which allows you to define new operators?

Question

I am currently looking for a programming language to write a math class in. I know that there are lots and lots of them everywhere around, but since I'm going to start studying math next semester, I thought this might be a good way to get a deeper insight in to what I've learned.

Thanks for your replys.

BTW: If you are wondering what I wanted to ask:

"Is there a strongly typed programming language which allows you to define new operators?"

Answer 1

Like EFraim said, Haskell makes this pretty easy:

% ghci
ghci> let a *-* b = (a*a) - (b*b)
ghci> :type (*-*)
(*-*) :: (Num a) => a -> a -> a
ghci> 4 *-* 3
7
ghci> 1.2 *-* 0.9
0.6299999999999999
ghci> (*-*) 5 3
16
ghci> :{
          let gcd a b | a > b     = gcd (a - b) b 
                      | b > a     = gcd a (b - a) 
                      | otherwise = a
      :}
ghci> :type gcd
gcd :: (Ord a, Num a) => a -> a -> a
ghci> gcd 3 6
3
ghci> gcd 12 11
1
ghci> 18 `gcd` 12
6

You can define new infix operators (symbols only) using an infix syntax. You can then use them as infix operators, or enclose them in parens to use them as a normal function.

You can also use normal functions (letters, numbers, underscores and single-quotes) as operators by enclosing them in backticks.

Answer 2

Well, you can redefine a fixed set of operators in many languages, like C++ or C#. Others, like F# or Scala allow you to define even new operators (even as infix ones) which might be even nicer for math-y stuff.