[Haskell-cafe] Instantiation problem

[Patrick Browne]

On 29/01/2011 20:56, Henning Thielemann wrote:
> Is there a reason why you use an individual type for every unit?
> The existing implementations of typed physical units only encode the
> physical dimension in types and leave the unit factors to the value
> level. I found this to be the most natural way.

I am studying type classes using examples from the literature [1].
There is no particular intension to implement anything.

I am confused about the unit function in the code below.
My understanding is:
The signature of the unit function is defined in the MetricDescription
class.
Any valid instantce of MetricDescription will respect the functional
dependency (FD):
The FD | description -> unit  is exactly the signature of the unit function.

My confusions
I do not understand the definitions of unit in the instances.
I do not know how the constant 1 can be equated with a *type*, Where did
1 come from?
I do not know how the constant 1 can be equated with *two distinct*
definitions of the function uint and still produce the following correct
results

Ok, modules loaded: A.
*A>  unit (LengthInMetres  7)
Metre
*A> unit (LengthInCentimetres 7)
Centimetre
*A>



[1] http://ifgi.uni-muenster.de/~lutzm/odbase04_schade_et_al.pdf

======================================================================

module A where

-- Each member of the Unit class has one operator convertFactorToBaseUnit
-- that takes a measurement unit (say metre) and returns a conversion
factor for that unit of measurement
class  Unit unit where
  convertFactorToBaseUnit :: unit -> Double



class (Unit unit) => MetricDescription description unit | description ->
unit where
 unit :: description -> unit
 valueInUnit :: description -> Double
 valueInBaseUnit :: description -> Double
 valueInBaseUnit d = (convertFactorToBaseUnit(unit d)) * (valueInUnit d)

data Dog = Dog  deriving Show
data Metre = Metre  deriving Show
data Centimetre = Centimetre deriving Show


-- An instance for metres, where the convert factor is 1.0
instance Unit Metre where
 convertFactorToBaseUnit Metre  = 1.0

-- An instance for centimetres, where the convert factor is 0.1
instance Unit Centimetre where
  convertFactorToBaseUnit Centimetre  = 0.1



data LengthInMetres = LengthInMetres Double  deriving Show
data LengthInCentimetres = LengthInCentimetres Double  deriving Show

instance MetricDescription LengthInMetres Metre where
 valueInUnit (LengthInMetres d) = d
 unit l = Metre



instance MetricDescription LengthInCentimetres Centimetre where
 valueInUnit (LengthInCentimetres d) = d
 unit l = Centimetre


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