[Haskell-cafe] Newbie: Is‘type’ synonym hiding two much?

[Antti-Juhani Kaijanaho]

On Thu, Mar 22, 2007 at 06:13:00PM +0300, Dmitri O.Kondratiev wrote:
> F :: a -> b -> c
> 
> Is the same as:
> 
> F :: a -> (b -> c)

Correcting the typo (use f, not F), these mean the same thing.

> And means either:
> 
> -    a function 'f' of one argument of type 'a' that returns a function of
> type (b -> c), or it can also be interpreted as:
> -    a function 'f' of two arguments of type 'a' and 'b' returning value of
> type 'c'

Yes.  The essential point to understand that these interpretations *are
the same*.

> Now, in the 17.5 section of a book one may see the following declarations:
> 
> succeed :: b -> Parse a b
> 
> *Before looking at 'succeed' function definition* one may think that
> 'succeed' is a function of *one* argument of type 'b' that returns object of
> type 'Parse a b'.

That's what it is.  However, without looking at the definition of 
Parse a b, you can't tell whether that is a function or not, and
therefore all you can say about succeed is that it takes *at least* one
argument.

> Then I do this substitution *myself as a Haskell runtime* and get in
> the result the following declaration of a * real
> function that Haskell runtime* works with:

I'm not sure why you feel the need to talk about runtime.  This all
happens at compile time.

> 2. Should I search through main and imported modules for treacherous 'type'
> constructs?

They are not treacherous.  But yes, if you want to know what a type
stands for, you need to look it up.

The "treacherous" thing here is that in Haskell, returning a function is
the same as taking one more parameter.  This may feel strange at first,
but it is a very important idiom and you do need to learn to live with
it if you want to use Haskell.

> 3. Where, in this case goes implementation abstraction principle? Why I must
> provide *all* the details about function argument type structure in order to
> understand how this function works?

"type" is just notational convenience.  If you want abstraction, use
"newtype" or "data".