On Mon, Feb 2, 2009 at 3:27 PM, David Menendez wrote:
> Does that help at all?
>
I think it does. But ... it gives me crazy ideas. Like: a functor is a
kind of magic non-computing function! That's why they didn't call it a
function? We know it maps A to FA, but we don't know how (maybe we
On Sun, Feb 1, 2009 at 12:36 PM, Gregg Reynolds wrote:
> On Sat, Jan 31, 2009 at 3:14 PM, David Menendez wrote:
>>
>> There's a paper about defining catamorphisms for GADTs and nested
>> recursive types that models type constructors that way.
>
> If you recall a title or author I'll google it.
I
Gregg Reynolds wrote:
On Sat, Jan 31, 2009 at 4:26 PM, wren ng thornton wrote:
> > But a data constructor Dcon a is an /element/ mapping taking elements
> > (values) of one type to elements of another type. So it too can be
> > construed as a functor, if each type itself is construed as a
> > c
On Sat, Jan 31, 2009 at 5:11 PM, Derek Elkins wrote:
>>
>> But a data constructor Dcon a is an /element/ mapping taking elements
>> (values) of one type to elements of another type. So it too can be
>> construed as a functor, if each type itself is construed as a
>> category.
>
> What are "elemen
On Sat, Jan 31, 2009 at 4:26 PM, wren ng thornton wrote:
>> But a data constructor Dcon a is an /element/ mapping taking elements
>> (values) of one type to elements of another type. So it too can be
>> construed as a functor, if each type itself is construed as a
>> category.
>
> Actually no, i
On Sat, Jan 31, 2009 at 3:14 PM, David Menendez wrote:
>
> There's a paper about defining catamorphisms for GADTs and nested
> recursive types that models type constructors that way.
If you recall a title or author I'll google it.
>> So this gives us two functors, but they operate on different t
On Sun, Feb 1, 2009 at 8:26 AM, Ben Moseley wrote:
>
]>
> So, the idea is that any polymorphic Haskell function (including Data
> constructors) can be seen as a natural transformation - so a "function" from
> any object (ie type) to an arrow (ie function). So, take "listToMaybe :: [a]
> -> Maybe a
On 31 Jan 2009, at 20:54, Gregg Reynolds wrote:
On Sat, Jan 31, 2009 at 1:02 PM, Ben Moseley
wrote:
You can view a polymorphic unary type constructor of type ":: a ->
T" as a
polymorphic function.
Shouldn't that be * :: a -> T a ?
Yes, you're right. And when I say "polymorphic unary t
On Sat, 2009-01-31 at 11:00 -0600, Gregg Reynolds wrote:
> Hi,
>
> I think I've finally figured out what a monad is, but there's one
> thing I haven't seen addressed in category theory stuff I've found
> online. That is the relation between type constructors and data
> constructors.
The typical
Gregg Reynolds wrote:
Hi,
I think I've finally figured out what a monad is, but there's one
thing I haven't seen addressed in category theory stuff I've found
online. That is the relation between type constructors and data
constructors.
As I understand it, a type constructor Tcon a is basical
On Sat, Jan 31, 2009 at 12:00 PM, Gregg Reynolds wrote:
> I think I've finally figured out what a monad is, but there's one
> thing I haven't seen addressed in category theory stuff I've found
> online. That is the relation between type constructors and data
> constructors.
What sort of relatio
On Sat, Jan 31, 2009 at 1:02 PM, Ben Moseley wrote:
> You can view a polymorphic unary type constructor of type ":: a -> T" as a
> polymorphic function.
Shouldn't that be * :: a -> T a ?
> In general, polymorphic functions correspond roughly to natural
> transformations (in this case from the i
You can view a polymorphic unary type constructor of type ":: a -> T"
as a polymorphic function.
In general, polymorphic functions correspond roughly to natural
transformations (in this case from the identity functor to T).
--Ben
On 31 Jan 2009, at 17:00, Gregg Reynolds wrote:
Hi,
I thi
Hi,
I think I've finally figured out what a monad is, but there's one
thing I haven't seen addressed in category theory stuff I've found
online. That is the relation between type constructors and data
constructors.
As I understand it, a type constructor Tcon a is basically the object
component
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