scala - Is the Writer Monad effectively the same as the State Monad? -

there's great tutorial here seems suggest me writer monad special case tuple object operations on behalf of (a,b). writer accumulates values on left (which a) , has corresponding monoid (hence can accumulate or mutate state). if collection, accumulates.

the state monad object deals internal tuple. both can flatmap'd, map'd, etc. , operations seem same me. how different? (please respond scala example, i'm not familiar haskel). thanks!

your intuition these 2 monads closely related right. difference writer more limited, in doesn't allow read accumulated state (until cash out @ end). thing can state in writer tack more stuff onto end.

more concisely, state[s, a] kind of wrapper s => (s, a), while writer[w, a] wrapper (w, a).

consider following usage of writer:

import scalaz._, scalaz._  def addw(x: int, y: int): writer[list[string], int] =   writer(list(s"$x + $y"), x + y)  val w = {   <- addw(1, 2)   b <- addw(3, 4)   c <- addw(a, b) } yield c 

now can run computation:

scala> val (log, res) = w.run log: list[string] = list(1 + 2, 3 + 4, 3 + 7) res: int = 10 

we same thing state:

def adds(x: int, y: int) =   state((log: list[string]) => (log |+| list(s"$x + $y"), x + y))  val s = {   <- adds(1, 2)   b <- adds(3, 4)   c <- adds(a, b) } yield c 

and then:

scala> val (log, res) = s.run(nil) log: list[string] = list(1 + 2, 3 + 4, 3 + 7) res: int = 10 

but little more verbose, , lots of other things state couldn't writer.

so moral of story should use writer whenever can—your solution cleaner, more concise, , you'll satisfaction of having used appropriate abstraction.

very writer won't give power need, though, , in cases state waiting you.