datatype si_prefix
= QUETTA | RONNA | YOTTA | ZETTA | EXA | PETA | TERA | GIGA | MEGA
| KILO | HECTO | DEKA | DECI | CENTI | MILLI | MICRO | NANO
| PICO | FEMTO | ATTO | ZEPTO | YOCTO | RONTO | QUECTO;

datatype si_function
= DIVISION | MULT;

datatype si_unit
= UNIT of string
| PREFIX of si_prefix * si_unit
| ALGEBRA of si_function * si_unit list
;

fun factor_of_prefix QUETTA = 1e30
  | factor_of_prefix RONNA = 1e27
  | factor_of_prefix YOTTA = 1e24
  | factor_of_prefix ZETTA = 1e21
  | factor_of_prefix EXA = 1e18
  | factor_of_prefix PETA = 1e15
  | factor_of_prefix TERA = 1e12
  | factor_of_prefix GIGA = 1e9
  | factor_of_prefix MEGA = 1e6
  | factor_of_prefix KILO = 1e3
  | factor_of_prefix HECTO = 1e2
  | factor_of_prefix DEKA = 1e1
  | factor_of_prefix DECI = 1e~1
  | factor_of_prefix CENTI = 1e~2
  | factor_of_prefix MILLI = 1e~3
  | factor_of_prefix MICRO = 1e~6
  | factor_of_prefix NANO = 1e~9
  | factor_of_prefix PICO = 1e~12
  | factor_of_prefix FEMTO = 1e~15
  | factor_of_prefix ATTO = 1e~18
  | factor_of_prefix ZEPTO = 1e~21
  | factor_of_prefix YOCTO = 1e~24
  | factor_of_prefix RONTO = 1e~27
  | factor_of_prefix QUECTO = 1e~30
  ;

fun apply_function DIVISION (head::[]) = head
  | apply_function DIVISION [] = raise Match
  | apply_function DIVISION (x::y::rest)
    = apply_function DIVISION (x/y::rest)
  | apply_function MULT [] = 1.0
  | apply_function MULT (head::[]) = head
  | apply_function MULT (x::y::rest)
    = apply_function MULT (x*y::rest)
  ;

fun car (x,y) = x;
fun cdr (x,y) = y;

fun remove_prefixes (UNIT x) = (1e0, UNIT x)
  | remove_prefixes (PREFIX (prefix, the_unit))
    = let val (factor, sub_unit) = remove_prefixes the_unit
      in (factor * (factor_of_prefix prefix), sub_unit)
      end
  | remove_prefixes (ALGEBRA (function, units))
   = let val returned = map remove_prefixes units;
         val factors = map car returned;
         val units = map cdr returned;
     in
        (apply_function function factors, (ALGEBRA (function, units)))
     end
  ;