On Nov 9, 7:45 am, Ralf Hemmecke <r...@hemmecke.de> wrote:
> And even if the above were possible, I don't see how it would help to
> reuse code. My code above is just a category after all with no default
> implementation.
What might (or might not) be useful is to look at how Functor and
Monad are defined as typeclasses and then implemented in the standard
Haskell prelude:
class Functor f where
fmap :: (a -> b) -> f a -> f b
class Monad m where
(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
fail :: String -> m a
-- Minimal complete definition:
-- (>>=), return
m >> k = m >>= \_ -> k
fail s = error s
and then to go on to see how instances of it are used, perhaps the
simplest is the maybe monad:
instance Monad Maybe where
(Just x) >>= k = k x
Nothing >>= k = Nothing
return = Just
fail s = Nothing
The problem is that I think we are trying to do something different
from Haskell. Haskell is using this mostly as a tool to separate the
pure from the impure code but languages like SPAD don't try to do
that, I think we would be more interested in modelling the
mathematical concept of the monad and perhaps exploring its
relationship to T-algebras? (well that what I'm interested in).
So from the mathematical point of view we may need to keep in mind
that:
1) The above Monad typeclass is not built from the Functor in the way
that a mathematical monads is built from an (endo-)Functor (the above
typeclasses are separate).
2) 'return' above corresponds to what we have been calling 'unit' but
'>>=' does not quite correspond to what we have been calling 'mult'.
They have swapped things around a bit to make it easier to simulate
imperative code.
Martin
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