Understanding Haskell accessor functions

Question

I'm reading up on Monad tutorials, and the one I'm working on now is http://www.muitovar.com/monad/moncow.xhtml , but I ran on a problem with the state Monad, or to be more precise the runState accessor function.

The type is defined as

newtype State s a = State { runState :: (s -> (a,s)) } 

and it's called e.g.

runState (chncasewst3 'e' 'd' 'f') False

I don't know how to read the definition for getting to the second line, especially because of the "State s a" part. If it where "State a s", I could deduce that the accessor has been curried 'as far' as the 's'.

So the question is; how to read the type definition so that I could see how to call the accessor function in this situation, and if possible how to read accessor functions per se.

Answer 1

When you have a data type defined as

data T a b = MkT { getA :: a, getB :: b }

read it like

data T a b = MkT a b

with two helper functions defined automatically:

getA :: (T a b) -> a
getA (MkT x _) = x

getB :: (T a b) -> b
getB (MkT _ y) = y

When you apply getA to the value of T, the result is of type a.

Now your State type consists of only one element, which type is a function (:: s -> (a, s)). runState converts a value of type State s a to a function of this type.

ghci> :t runState
runState :: State s a -> s -> (a, s)

Every time you apply runState to the value of type State s a, the result is a function of type s -> (a,s). And the first argument of this function is an initial value of the state variable (of type s).

In the tutorial example,

• chncasewst3 'e' 'd' 'f' has type State Bool String.
• So, runState (chncasewst3 'e' 'd' 'f') has type Bool -> (String, Bool).
• So, runState (chncasewst3 'e' 'd' 'f') False has type (String, Bool).

Further reading:

• Learn You a Haskell: Making Our Own Types and Typeclasses
• RWH: Defining Types, Streamlining Functions