On Fri, Dec 05, 2008 at 04:59:04PM +0100, Thomas Davie wrote:
On 5 Dec 2008, at 16:54, Ross Paterson wrote:
On Fri, Dec 05, 2008 at 04:35:51PM +0100, Martijn van Steenbergen wrote:
How do I implement the following?
instance Applicative f => Applicative (StateT s f)
The implementation of pure is trivial, but I can't figure out an implementation for <*>. Is it possible at all, or do I need to require f to be a monad?
Yes, because you need part of the value generated by the first computation, namely the state (inside the f), to construct the second one. You can do that in a Monad, but not in an Applicative.
I don't think that's true, although I'm yet to decide if Applicative for State is possible.
someState <*> someOtherState should take the value out of the first state, take the value out of the second state, apply one to the other, and return a new stateful value as the result. At no point in that description do I make mention of the previous state of one of these values.
That would be incompatible with the ap of the monad where it exists, but it's worse than that. Which state will you return? If you return one of the states output by one or other of the arguments, you'll break one of the laws: pure id <*> v = v u <*> pure y = pure ($ y) <*> u You're forced to return the input state, so the Applicative would just be an obfuscated Reader.