[Haskell-cafe] Semantic Domain, Function, and denotational model.....

[Daryoush Mehrtash]

ّ I don't follow the "at" and  "type B a".  "Behavior a" itself is a
time function.   At least in the version of the code that was
developed in Pual Hudak's Haskell School of Expression it was defined
as:

> newtype Behavior a
>   = Behavior (([Maybe UserAction],[Time]) -> [a])

In a function like time you can see that the "at" function makes things simpler.

In the original version  time was defined as:

> time :: Behavior Time
> time = Behavior (\(_,ts) -> ts)

In Conal's paper

time :: Behavior Time
at time = id

Comparing the two implementation of the time, it seems to me that "at"
and "type B a" has put the design on a more solid ground.  But I don't
quite understand the thought process, or the principal behind what is
happening.

daryoush


On Mon, Sep 15, 2008 at 10:46 AM, Ryan Ingram <ryani.spam at gmail.com> wrote:
> Here's a quick overview that might help you.
>
> For a reactive behavior, we have two types to think about:
>
> type B a = Time -> a
>    (the semantic domain)
>
> data Behavior a = ?
>    (the library's implementation).
> at :: Behavior a -> B a
>    (observation function)
>
> This is really just classic "information hiding" as you would do with
> any abstract data type.  Consider a simple "stack" data structure that
> supports push and pop.
>
>> data S a = S
>>     { popS :: Maybe (a, S a)
>>     , pushS :: a -> S a
>>     }
>
>> data Stack a = ?
>> observeStack :: Stack a -> S a
>
> As a library user, you don't really care about the implementation of
> Stack, just as a user of Conal's library doesn't really care about the
> implementation of Behavior.  What you *do* care about is that you can
> think about it in the simpler terms of "Time -> a" which is the model
> he has chosen.
>
> The rest of the library design comes from taking that model and
> thinking about what typeclasses and operations "Time -> a" should
> support, and creating typeclass morphisms between Behavior a and B a
> where necessary.  For example:
>
>> -- This makes (r -> a) into a functor over a; it is a generalization of Time -> a
>> instance Functor ((->) r) where
>>    -- fmap :: (a -> b) -> (r -> a) -> (r -> b)
>>    fmap f x = \r -> f (x r)
>>    -- or, "fmap = (.)", if you're golfing :)
>
> In order for the morphism between B and Behavior to make sense, you
> want this law to hold:
>   fmap f (at behavior) = at (fmap f behavior)
> for all behavior :: Behavior a.
>
> The fmap on the left applies to B which is (Time ->); the fmap on the
> right applies to Behavior.
>
> Conal writes this law more elegantly like this:
>> instance(semantic) Functor Behavior where
>>    fmap f . at = at . fmap f
>
> As long as you as the user can think about behaviors generally as
> functions of Time, you can ignore the implementation details, and
> things that you expect to work should work.  This drives the design of
> the entire library, with similar morphisms over many typeclasses
> between Event and E, Reactive and B, etc.
>
>  -- ryan
>
> On Mon, Sep 15, 2008 at 10:13 AM, Daryoush Mehrtash <dmehrtash at gmail.com> wrote:
>> Interestingly, I was trying to read his paper when I realized that I
>> needed to figure out the meaning of denotational model, semantic
>> domain, semantic functions.  Other Haskell books didn't talk about
>> design in those terms, but obviously for him this is how he is driving
>> his design.   I am looking for a simpler tutorial, text book like
>> reference on the topic.
>>
>> Daryoush
>>
>> On Mon, Sep 15, 2008 at 1:33 AM, Ryan Ingram <ryani.spam at gmail.com> wrote:
>>> I recommend reading Conal Elliott's "Efficient Functional Reactivity"
>>> paper for an in-depth real-world example.
>>>
>>> http://www.conal.net/papers/simply-reactive
>>>
>>>  -- ryan
>>>
>>> On Sun, Sep 14, 2008 at 11:31 AM, Daryoush Mehrtash <dmehrtash at gmail.com> wrote:
>>>> I have been told that for a Haskell/Functional programmer the process
>>>> of design starts with defining Semantic Domain, Function, and
>>>> denotational model of the problem.  I have done some googling on the
>>>> topic but haven't found a good reference on it.    I would appreciate
>>>> any good references on the topic.
>>>>
>>>> thanks,
>>>>
>>>> daryoush
>>>>
>>>> ps.  I have found referneces like
>>>> http://en.wikibooks.org/wiki/Haskell/Denotational_semantics  which
>>>> talks about semantic domain for "the Haskell programs 10, 9+1, 2*5"
>>>> which doesn't do any good for me.    I need something with a more real
>>>> examples.
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>>>
>>
>