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>From [EMAIL PROTECTED] Tue Feb 6 11:07 MET 1996
Date: Tue, 6 Feb 1996 11:07:26 +0100
From: [EMAIL PROTECTED] (Denis WALLEZ)
To: [EMAIL PROTECTED]
Subject: fully defined type vs. class , as a result of function
Hi,
I was wondering how it is possible to use classes in a project I have
to make symbolic calculus in Haskell. Since I have to do it in
several programming languages, I want to apply quite the same basic design,
an expression is a tree:
a+b => +
/ \
a b
Well, the interest of symbolic calculus is the modification of the
trees WITHOUT evaluation ; for instance
what_s_the_slope ( tree=> a, variable => a) = 1
or simplify(tree=>(a-0)) = (leaf a)
I started a little exemple like this:
>class Derivable a where
> derive :: (Derivable b)=> a -> b
I make the hypothesis that the result of derivation is still derivable,
BUT not necessarily the same kind as the initial upper node value:
(fg)'=(f'g)+(fg') the upper node of tree is first a multiplication,
but the second is an addition... no conservation.
>data Op_bin = Plus (Op_bin) (Op_bin)
> | Times (Op_bin) (Op_bin)
>instance Derivable Op_bin where
> derive (Plus a b) = Plus (derive a) (derive b)
> derive (Times a b) = Plus (Times (derive a) b) (Times a (derive b))
This seem quite coherent. I thought I could then define
data Op_1 = Val_int (Int)
| Val_var [Char]
| Val_float (Float)
instance Derivable Op_1 where
derive (Val_var x) | x=="x" = Val_int 1
| otherwise = Val_int 0
derive _ = Val_int 0
But no way to do this:
(with HUGS, which is declared fully implementing Haskell)
Reading script file "test4.hs":
Type checking
ERROR "test4.hs" (line 8): Declared type too general
*** Expression : derive
*** Declared type : Opbin -> a
*** Inferred type : Opbin -> Opbin
This is not OK. If I make another class with a 'simplify' function,
the result simplify(a+b)=(a+b) with no hypothesis on a and b, but
symplify(1+2)=Val_int 3... so I NEED to make my declarations such as
I can return ANY type in the class With_simplify.
Since the idea I had was to simplify the result of the naive derivation,
before returning it (i.e. Op_bin should be also an instance of
With_simplify), I NEED the 'general' declaration for the derivation.
How can I achieve this ?
Does Haskell need ANYWAY a fully defined type when defining the
type of the result of a function ?
If there's a way to round the difficulty, what is it, or do you have
any pointer ?
Thanks a lot in advance.
Denis.
Denis WALLEZ --- TELECOM BRETAGNE \ 3A-IPR \ technopole Brest-Iroise
(98 00 18 12) --- 29280 PLOUZANE [EMAIL PROTECTED]
fax 98 00 11 90 (preciser: "pour WALLEZ- 3A")
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