Fw: Modification of State Transformer

I 'm sorry,

What I meant was discussion about the state transformer ST s a itself. And how it works. What does mean the second inner forall loop and so on. I can't find explanations of this in the Haskell library.

Regards

Scott ----- Original Message ----- From: "Shawn P. Garbett" To: "Scott J." Cc: Sent: Monday, August 12, 2002 4:19 PM Subject: Re: Modification of State Transformer

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On Sunday 11 August 2002 07:26 pm, Scott J. wrote:

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Hi,

I invite you then to explain what happens with every step.

The use of "forall" is misleading and fast to be misunderstood: I mention here the inner forall's.

Thx

Scott

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This list is great. The implementation in the ST module solves the problem and I understand how it works.

Shawn

Given the level of detailed explanations to date, I don't see the point. But I'll go ahead and do so anyway, by summarizing what I've learned from

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previous posts.

I had read the example in Bird'd book on state transformers. The definition of state however was a fixed type in the examples. Wanting to extend the definition and make it more general I was trying to figure out how to modify the type.

Bird's definition was: newtype St a = MkSt (State -> (a,State)) type State = type

I had attempted to extend the type as follows newtype St a s = MkSt (s -> (a,s))

This died in the compiler when declaring this type as an instance of Monad: instance Monad St where return x = MkSt f where f s = (x,s) p >>= q = MkSt f where f s = apply(q x) s' where (x,s') = apply p s ghc returned the following (referencing the instance line): Couldn't match `*' against `* -> *' Expected kind: (* -> *) -> * Inferred kind: (* -> * -> *) -> * When checking kinds in `Monad St' In the instance declaration for `Monad St'

When a type constructor has an argument it has a type of `* -> *'. When a type constructor has two arguments it has a type of `* -> * -> *'. This construction of the type can be extended to n arguments by having

----- Original Message ----- From: "Scott J." To: "Shawn P. Garbett" Sent: Monday, August 12, 2002 9:04 PM Subject: Re: Modification of State Transformer the the

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number of `->' match the n arguments of type and the `*' be n+1.

The class definition of Monad contains the following: class Monad m where return :: a -> m a (>>=) :: m a -> (a -> m b) -> m b

So the class of St a s needs reduction from `* -> * -> *' to `* -> *' to fit the single argument type constructor of the Monad class. By using (St a) which causes the type constructor to be of type `(* -> *) -> *'. Since `(* -> *)' can be used as `*', by creation of another type. This because equivalent to `* -> *'.

The only thing left is reversing the order so that the result type is of the correct form in the Monad usage. I.e, in my initial ordering the `return' of the Monad would end up returning something of type `s' which is not particularly useful, since type `a' is the desired return type from the transformer.

So the corrected version of State becomes: newtype St s a = MkSt (s -> (a, s))

instance Monad (St s) where ...

Shawn Garbett - -- You're in a maze of twisty little statements, all alike. Public Key available from http://www.garbett.org/public-key -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.0.7 (GNU/Linux)

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