Mapping to Haskell:

    [a]     <-> newline separate strings
    a       <-> a string
    (a,a)   <-> white space separated strings

    `|' maps to function composition for referentially transparent code
    filenames map to named variables

------------------------------------------------------------------------

Both Functor,Monad IO  and Functor,Monad List hold.

The laws for functor and Monad are:

Monad:

    class  Monad m  where
        (>>=)       :: forall a b. m a -> (a -> m b) -> m b
        (>>)        :: forall a b. m a -> m b -> m b
        return      :: a -> m a

    > return a >>= k           ==  k a
    > m >>= return             ==  m
    > m >>= (\x -> k x >>= h)  ==  (m >>= k) >>= h

Functor:

    class  Functor f  where
        fmap        :: (a -> b) -> f a -> f b

    > fmap id       ==  id
    > fmap (f . g)  ==  fmap f . fmap g

And instances of both also need to obey:

    > fmap f xs  ==  xs >>= return . f

------------------------------------------------------------------------

* The shell as an instance of Functor IO

Following Oleg[ref], we require that named variables correspond to
filenames in our language, and we consider pipes as writing to temporary
files.

The IO instance of Monad is defined as:

    instance  Monad IO  where
        m >> k      =  m >>= \ _ -> k

        m >>= k     = bindIO m k
            where
                bindIO (IO m) k = IO ( \ s ->
                  case m s of 
                    (# new_s, a #) -> unIO (k a) new_s
                  )
        return x	= returnIO x

The IO instance of Functor is defined as:

    m >>= k     = bindIO m k
    fail s	    = failIO s

failIO :: String -> IO a
failIO s = ioError (userError s)

    instance  Functor IO where
       fmap f x = x >>= (return . f)

If we take 
    

* And as Monad IO

------------------------------------------------------------------------

* Shell programming in Functor List


* And the Monad List

------------------------------------------------------------------------

if we take:
    return  == i
    >>=     == |
and filenames as variable names (including temp files in pipes), then (due to Oleg):
    i a | k       == k a
    m | i         == m
    m | (k x | h) == (m | k) | h  

Instances of both 'Monad' and 'Functor' should additionally satisfy the law:

> fmap f xs  ==  xs >>= return . f

i.e.
    map f xs == i xs | ap f | i
which holds.

------------------------------------------------------------------------

Now, lets see if we case use the list monad directly

------------------------------------------------------------------------

Todo, add bind, return for List

    Monad:

instance Monad [] where
    m >>= k             = foldr ((++) . k) [] m
    m >> k              = foldr ((++) . (\ _ -> k)) [] m
    return x            = [x]
    fail _		        = []
\end{code}
        
List monad:

    return x   = words x/ show x/ echo x            or
    m >>= k    = foldr '((++) . k)' m               or  map k m | concat
    m >>  k    = foldr '((++) . (\ _ -> k))' m      or  map 'const k' m | concat

The usual list properties should still apply, for example:
If we treat the unix command 'map' as an implementation of map, and
take:

    instance Functor [] where
        fmap = map

then the usual laws for Functor [String] apply on the command line:

    Functor:
        map id        == i
        map '(f . g)' == map f | map g

So you can either program in the IO or List monads!