Thoughts about Units of Measurement

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Units of Measurements

Features:
 - Computations: 4s + 5s == 9s
 - Conversions
    between dimensions: 5m + 10cm == ...
    between metric systems: 5ft + 10cm = ...
 - Dimensions: 5m * 5m == 25m² || 10m/s * 1s == 10m || 10m² / 5m == 5m
 - Everything above combined!

Requirements:
 - Static type safety of computations and conversions
 - Verification at compile-time
 - No performance penalty at runtime
 - No restriction on numeric types

Problems:
 - How to express this in an extendable, user-friendly way?
    - Large signatures
    - Heavy boilerplate definitions
    -  ...

Questions:
 - Is this possible without language extensions?
 - Are there any sacrifices possible without substantially reducing the usefulness?
 - If this is implemented via some compile-time-only construct (like Phantom Types), how will it compare to specialization?
 - If it is not possible without runtime wrapping, how much performance penalty will we get with something like Measurement[Length[Meter[Numeric[T]]]]?
 - Code generation necessary?

Discussion:
 - Hard problem, with many uncompromisable requirements
 - Currently no support in Java's or Scala's Development Kit
 - Having core classes covering common ground is always desirable
    - consider Date&Time libraries as a potential consumer
    - consider Groups, Semigroups, Monoids as another area not covered in the SDK
 - Java failed twice (JSR-108/JSR-275) with a "library-only" approach
    - Scala's type system is much more powerful, but is it enough?
 - F# has special support build into the language, but is this approach acceptable for general-purpose language like Scala?
 - IMHO some more generic support benefiting other areas would be desirable, e. g. Numeric[T]
 - Is it possible to ship with a feature set covering 99,9% of all user's requirements, making the issue of extendability much less pressing?
    - If the ugliness is only at the declaration site it is much more acceptable

References:
 - ScalaU and earlier work, especially the old units compiler plugin
 - F#: Language support for Units of Measurement
 - Frink: Special purpose language for unit calculations
 - Java: Failed standardization requests JSR-108/JSR-275