Data.Random.Internal.Classification

Description

"Classification systems" - for a motivating example, see the implementation of the Uniform distribution. Basically, I would like to make instances like:

 instance RealFloat a => Distribution Uniform a where ...
 instance Integral a =>  Distribution Uniform a where ...

and so on. However, this is not sound - what happens if someone comes along and makes a type that's an instance of both Integral and RealFloat?

So, we introduce a classification system based on phantom types, so that each type can be unambiguously declared to be "intensionally" Integral, Floating, or whatever.

Now, obviously it'd be nice not to clutter the Distribution typeclass with extra phantom types that the end user shouldn't care about. Hence the pattern of introducing typeclasses such as UniformByClassification

Now, if a new type comes along that is Integral, a single declaration of the following form suffices to attach it to all such Distribution instances:

 instance Classification NumericType t IntegralType

Not quite as automagic as the Integral a => Distribution foo case, but a bit closer. Not only that, it leaves open the possibility that a user may bring in a type that is "mostly" integral, and has an Integral instance, but should be handled differently for purposes of uniform random number generation. In such a case, the user may introduce a new classification of their own and provide the required instances for that classification.

All in all, although it is not yet well-tested, it has the "feel" of a good compromise.

Synopsis

class Classification c t tc | c t -> tc

data NumericType

data IntegralType

data FractionalType

data EnumType

Documentation

class Classification c t tc | c t -> tc

Source

classificiation system, experimental

c (a phantom type) is the classification system
t is the type to be classified
tc (a phantom type) is the classification of t according to c

The functional dependency, aside from being important because the relation is functional, allows the classification system to be "discharged" in cases such as the following:

 class Classification SomeCS t c => FooByClassification t c where ...
 instance FooByClassification t c => Foo t where ...

Thus the class of interest to the end user need not display anything at all about the classification system, except in the superclasses of the classes in the contexts of some of its instances.

Instances

Classification NumericType Bool EnumType

Classification NumericType Char EnumType

Classification NumericType Double FractionalType

Classification NumericType Float FractionalType

Classification NumericType Int IntegralType

Classification NumericType Int8 IntegralType

Classification NumericType Int16 IntegralType

Classification NumericType Int32 IntegralType

Classification NumericType Int64 IntegralType

Classification NumericType Integer IntegralType

Classification NumericType Ordering EnumType

Classification NumericType Word8 IntegralType

Classification NumericType Word16 IntegralType

Classification NumericType Word32 IntegralType

Classification NumericType Word64 IntegralType

Classification NumericType () EnumType

Classification NumericType (Ratio a) FractionalType

data NumericType

Source

A simple classification system covering the cases we care about when sampling distributions. Loosely, these are the reasons we care:

distributions over Fractional types are handled as if the type were continuous.
distributions over Integral types are handled discretely.
distributions over Enum types (which are not Num instances) are handled like Integral types, but require use of fromEnum and/or toEnum to work with them.

Instances