I think the recursive solution of Milan will give you a finite list of all
subtypes. But the list will contain things like Array{T, N}, that is, a
type with a parameter. How do you handle those? Do you want to count them
as abstract or concrete?
On Wednesday, February 10, 2016 at 9:10:16 AM UTC+1, Jeffrey Sarnoff wrote:
>
> Hello Tommy,
>
> OK, putting off inclusion of recursive types ...
> and ignoring all possible values for the parameters of a parameterized
> type unless already explicitly defined (present in memory) ...
>
> allsupertypes(T) should be a short list from T to supertype(T) to
> supertype(supertype(T)) .. to Any
>
> allsubtypes(T) seems obtainable
> I can throw things into a tree until the leaves have no subtypes, then
> traverse it; is there a nice way to do that implicitly within a function?
>
>
>
>
> On Wednesday, February 10, 2016 at 2:32:35 AM UTC-5, Tommy Hofmann wrote:
>>
>> You implicitly assume that a type has only finitely many sub/supertypes,
>> which for arbitrary types is clearly not the case. The simplest example is
>> Any but you can also get this behavior when defining recursive types. More
>> generally, given types TL, TU there is no way of returning all types T with
>> TL <: T <: TU. You can describe this set using TypeVar, but you cannot just
>> write it down.
>>
>> Tommy
>>
>> On Wednesday, February 10, 2016 at 12:50:43 AM UTC+1, Jeffrey Sarnoff
>> wrote:
>>>
>>> I see that your definition pours the subtypes from a pitcher of the
>>> poured subtypes. The note about parametric types is well pointed. --
>>> Jeffrey
>>>
>>> Clearly, the answer is therein. Cloudily, I'm looking.
>>>
>>>
>>> On Tuesday, February 9, 2016 at 3:43:48 PM UTC-5, Milan Bouchet-Valat
>>> wrote:
>>>>
>>>> Le mardi 09 février 2016 à 12:24 -0800, Jeffrey Sarnoff a écrit :
>>>> > Any advice on quick 'n EZ coding of something like these?
>>>> >
>>>> > allsupertypes(Irrational) == ( Real, Number, Any )
>>>> >
>>>> > allsubtypes(Integer) == ( BigInt, Bool, Signed,
>>>> Int128,Int16,Int32,Int64,Int8, Unsigned,
>>>> UInt128,UInt16,UInt32,UInt64,UInt8 )
>>>> > abstractsubtypes(Integer) == ( Signed, Unsigned )
>>>> > concretesubtypes(Integer) == (
>>>> BigInt,Bool,UInt128,UInt16,UInt32,UInt64,UInt8,UInt16,UInt32,UInt64,UInt8)
>>>> Here's a way to get all concretes ubtypes:
>>>> subtypestree(x) = length(subtypes(x)) > 1 ? map(subtypestree,
>>>> subtypes(x)) : x
>>>> [subtypestree(AbstractArray)...;]
>>>>
>>>> You should be able to adapt this to return all abstract types instead
>>>> by using isleaftype() (which would better be called isconcretetype()?).
>>>> But note there's the special case of parametric types, which aren't
>>>> leaf types.
>>>>
>>>>
>>>> Regards
>>>>
>>>
