[Haskell-cafe] How to define a Monad instance

[Ryan Ingram]

To take this a step further, if what you really want is the syntax sugar
for do-notation (and I understand that, I love sweet, sweet syntactical
sugar), you are probably implementing a Writer monad over some monoid.

Here's two data structures that can encode this type;

data Replacer1 k a = Replacer1 (k -> Maybe k) a
data Replacer2 k a = Replacer2 [(k,k)] a

instance Monad Replacer1 where
    return x = Replacer1 (\_ -> Nothing) x
    Replacer1 ka a >>= f = result where
        Replacer1 kb b = f a
        result = Replacer1 (\x -> ka x `mplus` kb x) b

(!>) :: Eq k => k -> k -> Replacer1 k ()
x !> y = Replacer1 (\k -> if k == x then Just y else Nothing) ()

replace1 :: Replacer1 k () -> [k] -> [k]    -- look ma, no Eq requirement!
replace1 (Replacer k ()) = map (\x -> fromMaybe x $ k x) -- from Data.Maybe

table1 :: Replacer1 Char ()
table1 = do
    'a' !> 'b'
    'A' !> 'B'

test = replace1 table1 "All I want"

-- Exercise: what changes if we switch ka and kb in the result of (>>=)?
When does it matter?

-- Exercises for you to implement:
instance Monad Replacer2 k where
replacer :: Eq k => Replacer2 k -> [k] -> [k]
($>) :: k -> k -> Replacer2 k

-- Exercise: Lets make use of the fact that we're a monad!
--
-- What if the operator !> had a different type?
-- (!>) :: Eq k => k -> k -> Replacer k Integer
-- which returns the count of replacements done.
--
-- table3 = do
--     count <- 'a' !> 'b'
--     when (count > 3) ('A' !> 'B')
--     return ()
--
-- Do any of the data structures I've given work?  Why or why not?
-- Can you come up with a way to implement this?

  -- ryan

On Sat, Jul 28, 2012 at 10:07 AM, Steffen Schuldenzucker <
sschuldenzucker at uni-bonn.de> wrote:

> On 07/28/2012 03:35 PM, Thiago Negri wrote:
> > [...]
>
>  As Monads are used for sequencing, first thing I did was to define the
>> following data type:
>>
>> data TableDefinition a = Match a a (TableDefinition a) | Restart
>>
>
> So TableDefinition a is like [(a, a)].
>
>  [...]
>>
> >
>
>> So, to create a replacement table:
>>
>> table' :: TableDefinition Char
>> table' =
>>          Match 'a' 'b'
>>          (Match 'A' 'B'
>>           Restart)
>>
>> It look like a Monad (for me), as I can sequence any number of
>> replacement values:
>>
>> table'' :: TableDefinition Char
>> table'' = Match 'a' 'c'
>>           (Match 'c' 'a'
>>           (Match 'b' 'e'
>>           (Match 'e' 'b'
>>            Restart)))
>>
>
> Yes, but monads aren't just about sequencing. I like to see a monad as a
> generalized computation (e.g. nondeterministic, involving IO, involving
> state etc). Therefore, you should ask yourself if TableDefinition can be
> seen as some kind of abstract "computation". In particular, can you
> "execute" a computation and "extract" its result? as in
>
>   do
>     r <- Match 'a' 'c' Restart
>     if r == 'y' then Restart else Match 2 3 (Match 3 4 Restart)
>
> Doesn't immediately make sense to me. In particular think about the
> different possible result types of a TableDefinition computation.
>
> If all you want is sequencing, you might be looking for a Monoid instance
> instead, corresponding to the Monoid instance of [b], where b=(a,a) here.
>
>   [...]
>>
> >
>
>> I'd like to define the same data structure as:
>>
>> newTable :: TableDefinition Char
>> newTable = do
>>          'a' :>  'b'
>>          'A' :>  'B'
>>
>> But I can't figure a way to define a Monad instance for that. :(
>>
>
> The desugaring of the example looks like this:
>
>   ('a' :> 'b') >> ('A' :> 'B')
>
> Only (>>) is used, but not (>>=) (i.e. results are always discarded). If
> this is the only case that makes sense, you're probably looking for a
> Monoid instead (see above)
>
> -- Steffen
>
>
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