[Haskell-cafe] Relevance and applicability of category theory

Dan Weston westondan at imageworks.com
Thu Jan 31 12:13:53 EST 2008

Even though you cannot "dive into this matter now", maybe when you get 
time you can update your blog with an explicit embedding of Haskell 
monads and arrows in your Thrist construction. Concrete examples will 
help me (and probably others) more quickly see the novelty, increased 
generality, and usefulness of a Thrist.

Also, although you say that thrists are the moral equivalent of a free 
category, it appears (at least to me) possible that the first Thrist 
argument enables the construction of a restricted domain monad, e.g. (Eq 
a => Set a) monad. Is this so?


Gabor Greif wrote:
> Am 31.01.2008 um 01:23 schrieb aaltman at pdx.edu <mailto:aaltman at pdx.edu>:
>> 3. I believe the documentation stating that Haskell arrows are a 
>> generalization of Haskell monads, but arrows are a categorical thing 
>> too and in that context bear a much more distant relationship to 
>> monads.  Does a Haskell arrow have Hask as domain and codomain?  Or is 
>> one particular element in Hask its domain and possibly another its 
>> codomain?  Those are not at all the same thing.
> Without being able to dive into this matter now,
> I just want to say that both the Haskell monads
> and arrows can be generalized to something
> I call a "thrist", which appears to be the moral
> equivalent of a free category. The underlying
> category is obtained by a two-parameter GADT
> (defining the morphisms) and the domains and
> codomains of its members (which are Haskell types)
> being the objects.
> Here is my blog entry that motivates the concept
> a bit:
> http://heisenbug.blogspot.com/2007/11/trendy-topics.html
> Cheers,
> Gabor
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