A monad containing an environment of type r , output of type w and an updatable state of type s .

Construct an RWS computation from a function. (The inverse of runRWS .)

Unwrap an RWS computation as a function. (The inverse of rws .)

Evaluate a computation with the given initial state and environment, returning the final value and output, discarding the final state.

Evaluate a computation with the given initial state and environment, returning the final state and output, discarding the final value.

Map the return value, final state and output of a computation using the given function.

• runRWS (mapRWS f m) r s = f (runRWS m r s)

withRWS f m executes action m with an initial environment and state modified by applying f .

• runRWS (withRWS f m) r s = uncurry (runRWS m) (f r s)

A monad transformer adding reading an environment of type r , collecting an output of type w and updating a state of type s to an inner monad m .

Evaluate a computation with the given initial state and environment, returning the final value and output, discarding the final state.

Evaluate a computation with the given initial state and environment, returning the final state and output, discarding the final value.

Map the inner computation using the given function.

• runRWST (mapRWST f m) r s = f (runRWST m r s)

withRWST f m executes action m with an initial environment and state modified by applying f .

• runRWST (withRWST f m) r s = uncurry (runRWST m) (f r s)

Constructor for computations in the reader monad (equivalent to asks ).

Fetch the value of the environment.

Execute a computation in a modified environment

• runRWST (local f m) r s = runRWST m (f r) s

Retrieve a function of the current environment.

• asks f = liftM f ask

Construct a writer computation from a (result, output) pair.

tell w is an action that produces the output w .

listen m is an action that executes the action m and adds its output to the value of the computation.

• runRWST (listen m) r s = liftM (\ (a, w) -> ((a, w), w)) (runRWST m r s)

listens f m is an action that executes the action m and adds the result of applying f to the output to the value of the computation.

• listens f m = liftM (id *** f) (listen m)

• runRWST (listens f m) r s = liftM (\ (a, w) -> ((a, f w), w)) (runRWST m r s)

pass m is an action that executes the action m , which returns a value and a function, and returns the value, applying the function to the output.

• runRWST (pass m) r s = liftM (\ ((a, f), w) -> (a, f w)) (runRWST m r s)

censor f m is an action that executes the action m and applies the function f to its output, leaving the return value unchanged.

• censor f m = pass (liftM (\ x -> (x,f)) m)

• runRWST (censor f m) r s = liftM (\ (a, w) -> (a, f w)) (runRWST m r s)

Construct a state monad computation from a state transformer function.

Fetch the current value of the state within the monad.

put s sets the state within the monad to s .

modify f is an action that updates the state to the result of applying f to the current state.

• modify f = get >>= (put . f)

Get a specific component of the state, using a projection function supplied.

• gets f = liftM f get

Uniform lifting of a callCC operation to the new monad. This version rolls back to the original state on entering the continuation.

In-situ lifting of a callCC operation to the new monad. This version uses the current state on entering the continuation.

Lift a catchE operation to the new monad.