The equivalent verbose Haskell code follows. s1, s2 and s3 are actual states. v1 and v2 are values. pA, pB and pAB are state processors. Note that the wrapping and unwrapping by state/runState is implicit in the diagram.

-- pAB = s1 --> pA --> (v1,s2) --> pB --> (v2,s3)        
pAB = pA >>= f
    = state $ \ s1 -> (v2, s3)
        where
        (v1, s2) = runState pA s1
        pB = f v1
        (v2, s3) = runState pB s2