I think I did understand Monads and Arrows. So I put it to the test: I tried to write my own State Monad and an State Arrow without looking at the real implementation. This is what I got: http://lpaste.net/93801 Please take a look on line 146 where I try to define a State Monad that is represented with a full function (state+result -to- state+result -- like my Arrow implementation). Things got hairy with the bind operator (line 153) and I just hit the keyboard until I hit the correct types and got it to compile. Yet, I can't fully understand my own bind implementation. Using the result "a" twice seems to be wrong, but I couldn't write a test to prove it.