Daryoush Mehrtash wrote:
Thanks this was helpful.
In many of Conal Elliot's writings I see that he shows that his semantic
function is a natural transformation. Is that just basically showing the
polymorphic nature of his semantic functions, or are there other benifits
you get by showing a
Thanks for this example I get the point now. (at least i think i do :) )
One more question This all being on the same category then the functor
transformation can also be view as a simple morphism too. In this example
the listToMaybe can be viewed as morphism between list and Maybe types
On Thursday 23 April 2009 2:44:48 pm Daryoush Mehrtash wrote:
Thanks for this example I get the point now. (at least i think i do :) )
One more question This all being on the same category then the functor
transformation can also be view as a simple morphism too. In this example
the
Thanks this was helpful.
In many of Conal Elliot's writings I see that he shows that his semantic
function is a natural transformation. Is that just basically showing the
polymorphic nature of his semantic functions, or are there other benifits
you get by showing a particular function is a
Daryoush Mehrtash-2 wrote:
I am not sure I follow how the endofunctor gave me the 2nd functor.
As I read the transformation there are two catagories C and D and two
functors F and G between the same two catagories. My problem is that I
only
have one functor between the Hask and List
Here F is the identity functor, and G is the list functor. And yes, C=D=
category of (a subset of) Haskell types.
Are you saying the function that goes from list functor to singleton funtor
is a natural transformation?
But aren't they functors to different subset of Haskell Types?
The Haskell
On Wed, Apr 22, 2009 at 03:14:03PM -0700, Daryoush Mehrtash wrote:
The Haskell Wikibooks also says the same thing:
Functors in Haskell are from Hask to func, where func is the
subcategory of Hask defined on just that functor's types. E.g. the
list functor goes from Hask to Lst,
Daryoush Mehrtash-2 wrote:
singleton :: a - [a]
singleton x = [x]
Here F is the identity functor, and G is the list functor. And yes, C=D=
category of (a subset of) Haskell types.
Are you saying the function that goes from list functor to singleton
funtor
is a natural
In category theory functors are defined between two category of C and D
where every object and morphism from C is mapped to D.
I am trying to make sense of the above definition with functor class in
Haskell. Let say I am dealing with List type. When I define List to be a
instance of a functor
You are on the right track. The usual construction is that Hask is the
category (with types as objects and functions as morphisms).
Functor F is then an endofunctor taking Hask to itself:
a - F a
f - fmap f
So, for F = []:
a - [a]
f - map f
Natural transformations are then any fully
I am not sure I follow how the endofunctor gave me the 2nd functor.
As I read the transformation there are two catagories C and D and two
functors F and G between the same two catagories. My problem is that I only
have one functor between the Hask and List catagories. So where does the
2nd
List is not a full subcategory of Hask, so it's a bad choice. Namely,
types of functions on a list (e.g. [a] - [a]) are not themselves lists
of type [b] for some b, and so are not objects of List (though they are
morphisms in it). In Hask, ([a] - [a]) is both an object and a morphism
(in fact,
Daryoush Mehrtash wrote:
I am not sure I follow how the endofunctor gave me the 2nd functor.
As I read the transformation there are two catagories C and D and two
functors F and G between the same two catagories. My problem is that I only
have one functor between the Hask and List catagories.
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