I'd like to be able to say the end angle has to be less than the start angle, that the unit has to be radians (AKA unit-less :), the unit of radius & that negative values are sensical, and so forth; and have all these properties checked by a compiler.

Which I can do in some modern languages, surprisingly. :)

   data Directionality = Clockwise | Anticlockwise

   data AngularInterval = {
     beginAngle :: Double,
     endAngle :: Double,
     directionality :: Directionality
   }

But we use plenty of literals in our programs all the time. Eg lambdas are function literals. (And definitions of named functions are just a special case folding binding and a lambda.)