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.