I recently implemented some new Haskell numeric types that, instead of performing calculations, can generate a rendering of the requested calculation or store units with it.

Here you see a transcript of my session with a Haskell interpreter. The mathematical statements I am entering after the “>” are standard Haskell expressions, and, as I demonstrate, normally evaluate to a single result.

Once I get a more powerful simplifier, I will probably write a LaTeX exporting function as well.

The entire implementation of this, BTW, is less than 200 lines.

NumTest> 5 + 1 * 3
8
NumTest> prettyShow $ 5 + 1 * 3
"5+(1*3)"
NumTest> rpnShow $ 5 + 1 * 3
"5 1 3 * +"
NumTest> prettyShow $ 5 + 1 * 3
"5+(1*3)"
NumTest> prettyShow $ simplify $ 5 + 1 * 3
"5+3"
NumTest> prettyShow $ 5 * (Symbol "x") + 3
"(5*x)+3"
NumTest> 5 / 2
2.5
NumTest> (units 5 "m") / (units 2 "s")
2.5_m/s
NumTest> (units 5 "m") / 2
2.5_m
NumTest> 10 * (units 5 "m") / (units 2 "s")
25.0_m/s
NumTest> sin (pi/2)
1.0
NumTest> sin (units (pi/2) "rad")
1.0_1.0
NumTest> sin (units 90 "deg")
1.0_1.0
NumTest> (units 50 "m") * sin (units 90 "deg")
50.0_m
NumTest> ((units 50 "m") * sin (units 90 "deg")) :: Units (SymbolicManip Double)
50.0*sin(((2.0*pi)*90.0)/360.0)_m
NumTest> rpnShow $ dropUnits $ ((units 50 "m") * sin (units 90 "deg"))
"50.0 2.0 pi * 90.0 * 360.0 / sin *"
NumTest> (units (Symbol "x") "m") * sin (units 90 "deg")
x*sin(((2.0*pi)*90.0)/360.0)_m

Also, I defined this in my source file:

test :: forall a. (Num a) => a
test = 2 * 5 + 3

Now, it can be used:

NumTest> test
13
NumTest> rpnShow test
"2 5 * 3 +"
NumTest> prettyShow test
"(2*5)+3"
NumTest> test + 5
18
NumTest> prettyShow (test + 5)
"((2*5)+3)+5"
NumTest> rpnShow $ test + 5
"2 5 * 3 + 5 +"

You can grab the very early experimental code with darcs get http://darcs.complete.org/num.

Haskell has no built-in support for numeric types with units, arbitrary symbols carried through computations, etc. But it was trivial to add it. This kind of extensibility is a key part of why Haskell is so amazing.