On 7/13/06, Jared Warren <[EMAIL PROTECTED]> wrote:
Haskell's type checking language is a logical programming language.
The canonical logical language is Prolog. However, Idealised Prolog
does not have data structures, and does Peano numbers like:
natural(zero).
natural(x), succ(x,y) :- natural(y)
And I believe (but cannot confirm):
succ(zero,y).
succ(x,y) :- succ(y,z)
That is not a valid encoding of peano numbers in prolog, so I think
that's where your problems stem from. :-)
% defining natural numbers
natural(zero).
natural(s(X)) :- natural(X).
% translate to integers
toInt(zero, 0).
toInt(s(X), N) :- toInt(X, Y), N is Y + 1.
In the same style of reasoning for Haskell, we would define
data Zero
data Succ x
class Natural x
instance Natural Zero
instance (Natural x) => Natural (Succ x)
class Natural x => ToInt x where
toInt :: x -> Int
instance ToInt Zero where
toInt _ = 0
instance (ToInt x) => ToInt (Succ x) where
toInt _ = toInt (undefined :: x) + 1
Or we could add the toInt method directly to the Natural class like
you did above. So yes, we can mimic (some of) prolog in Haskell's type
language. :-)
/Niklas
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