Tom Nielsen tanielsen at gmail.com
Mon Jan 31 11:09:09 CET 2011

```Patrick,

I find Andrew Frank's work on axiomatic specifications of GIS systems
-- which the paper you cite is built on -- very confusing, or indeed,
confused. They have a bunch of example like

data Car = Car Color

class Car a where
carColor :: a -> Color

instance Car Car where
carColor (Car c _) = c

as if there is some kind of special logical interpretation of having a
class Car in addition to the data type Car. As far as I remember, they
interpret type classes as axioms. After reading it, without being an
expert in either GIS or a logician, I came away thinking that they
were mixing some very abstract ideas from object-oriented languages
into Haskell. I find the presentations of type classes by e.g. Mark
Jones, and the links between functional programming and logic from
either the Curry-Howard correspondence or HOL-style reasoning (for
instance, see the HOL light manual), somewhat crisper.

Tom

On Sun, Jan 30, 2011 at 10:27 AM, Patrick Browne <patrick.browne at dit.ie> wrote:
> 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
>
> *A>  unit (LengthInMetres  7)
> Metre
> *A> unit (LengthInCentimetres 7)
> Centimetre
> *A>
>
>
>
>
> ======================================================================
>
> 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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