[EMAIL PROTECTED]
Hi,
Alain M. Gaudrault <[EMAIL PROTECTED]> writes
in his letter of 26 Jun 1995 16:55
> 1) let fred x = x in fred fred;
> Haskell complains:
> [55] Ambiguously overloaded tyvar(s) in class(es) Text in
> show (let { fred = \A1_fred -> A1_fred
> } in fred fred)
[...]
> 2) I'm attempting to add another instance to the Num class as a
> test of Haskell's OOP functionality.
> Thus, I create a new type which is a 3-tuple:
> data ThreeSpace = TS (Integer, Integer, Integer);
> Then, for each of the methods required by Num, a function is
> defined for the new type ...
>let addTS (TS (x1,x2,x3)) (TS (y1,y2,y3)) =
TS ((x1+y1),(x2+y2),(x3+y3)) ;;
>let fIntegerTS x = TS ((fromInteger x), 0, 0);;
[...]
>Now, I need to add the ThreeSpace instance to Num:
>instance Num ThreeSpace where
>(+) = addTS
>negate = negTS
>fromInteger = fIntegerTS
[...]
;
> This is where things crap out. I get the following error:
> [56] Not an instance Num ThreeSpace in
> ((DD.Num.$fromInteger{FARITY 1}))::(Integer, Int, Double) -> ThreeSpace
> in $fromInteger
---------------------------------------------------------------------
I had a question similar to 2) dealing with Gofer.
I believe the experts will explain the things.
Here are my impressions.
---------------------------------------------------------------------
Concerning the question 1) :
let f x = x in f f
returns something like {v121} in GOFER, which I guess is the
denotation for the function (lambda (x) x). And it applies all
right:
let f x = x in (f f) 2 --> 2
So indeed, let Haskell explain the subject.
---------------------------------------------------------------------
Question 2.
Similarly, a couple of months ago I tried to define Num for
the type like
data SP = SP Int Int
in GOFER.
First it resisted strongly. Then I studied "standard.prelude".
It declares
class Text a => Num a ...
which means that, for example, before defining Num members for
SP one should define the Text class for it.
So I put cynically:
------------------
intance Text SP -- empty definitions !
instance Num SP where (SP n m)+(SP n1 m1) = SP (n+n1) (m+m1)
-------------------
and it all improved.
------------------------------------------------------------------
------------------------------------------------------------------
I have some problems too.
I had written a hundred of pages of Gofer scripts and found it very
nice.
Still I am a novice in Gofer, Haskell.
I intend to try Haskell hoping for the benefits of modularity and
arbitrary length integers.
Here is my question to Haskell.
What is the substitution for the programming style using
the multiple parameters in classes and instances ?
Example 1.
instance (Num a, Num b) => Num (a,b) where
(x,y)+(x1,y1) = (x+x1,y+y1)
Would Haskell allow this ?
And if the Cartesian product is a special constructor, than how
the similar construction will do for some user type, say
SP a b ?
Example 2.
In mathematics, a Vector Space is defined as a tripple {a,c,cM},
where
a is a commutative additive group of Vectors ((+),(-),zero),
c is the Field of coefficients (+,-,*,zero,unity,inverse),
cM is the multiplication-by-coefficient low :: c -> a -> a
- and these objects should satisfy certain properties ...
So I put in Gofer :
----------------------------------------------------------
class Eq a => AddGroup a where add :: a -> a -> a
zero ...
...
class AddGroup a => Field a where mul :: a -> a -> a
unity :: ...
...
class (AddGroup a, Field c) => VectorSpace a c where
coefMul :: c -> a -> a
----------------------------------------------------------
I wonder how this can be expressed without multiple parameters ?
I had tried to represent an instance of vector space as a type
data VS a c = VS a c (c->a->a)
- it is like a tripple where the third element is a coefficient
multiplication low. Further,
class Field v => VectorSpace V
where
coefMul :: v -> v
...
Here the vectors and coefficients are somehow mixed in a single
type v.
Then I try to define the VectorSpace instances for the instances
of the general type VS.
Let, it be, for example the two-dimension space over rationals :
-------------------------------
type RR = (Rational,Rational)
type VR2 = VS RR Rational mulR2
mulR2 r (r1,r2) = (r*r1,r*r2)
------------------------------
First, the coefficients form a field. Hence we are forced to declare
that VS is a field, and extend (*) to the whole VS while it
actually ignores the parts of (VS vec coef cMul) except coef.
Further, the addition add acts on the whole VS, only it is
defined so that vec and coef parts add each in its own way.
So add serves for both additions simulteneousely.
The Second problem:
we need to operate with the two different equalities "inside" VS:
(==) for the Vector parts vec of (VS vec coef cMul) and
(==) for the coefficient parts coef of it.
This difference it expressed automatically through the use of
multiple parameters.
In other case, the whole VS is declared to be a Field, which
requires one the same (==) for VS.
You see, "vectors u,v are equal" and, say, "pairs (u,c1),(v,c2)
are equal" mean very different things ...
The impression is that something is wrong here.
What is the way out ?
So far I use Gofer and multiple parameters (and often fall into
confusion !) and had not thought long on the subject.
But what the loss may be when I try Haskell ?
I will appreciate any reasonable advice.
Regards,
Sergei.D.Meshveliani
