An accumulation monad parameterized by the type w of output to accumulate.

This monad is a more complex extension of both the reader and writer monads. The return function produces the output mempty, while m >>= k uses the output of m both to extend the initial environment of k and to combine with the output of k:

In applications requiring only the ability to accumulate an output and to inspect the output so far, it would be considerably more efficient to use a state monad.

Construct an accumulation computation from a (result, output) pair. (The inverse of runAccum.)

Unwrap an accumulation computation as a (result, output) pair. (The inverse of accum.)

Extract the output from an accumulation computation.

• execAccum m w = snd (runAccum m w)

Evaluate an accumulation computation with the given initial output history and return the final value, discarding the final output.

• evalAccum m w = fst (runAccum m w)

Map both the return value and output of a computation using the given function.

• runAccum (mapAccum f m) = f . runAccum m

An accumulation monad parameterized by:

• w - the output to accumulate.
• m - The inner monad.

This monad transformer is a more complex extension of both the reader and writer monad transformers. The return function produces the output mempty, while m >>= k uses the output of m both to extend the initial environment of k and to combine with the output of k:

In applications requiring only the ability to accumulate an output and to inspect the output so far, it would be considerably more efficient to use a state monad transformer.

Unwrap an accumulation computation. For example, in the call

    (value, locals) <- runAccumT action globals

the action is fed an initial environment globals, and locals is the sum of all arguments to calls of add executed by the action.

Extract the output from an accumulation computation.

• execAccumT m w = liftM snd (runAccumT m w)

Evaluate an accumulation computation with the given initial output history and return the final value, discarding the final output.

• evalAccumT m w = liftM fst (runAccumT m w)

Map both the return value and output of a computation using the given function.

• runAccumT (mapAccumT f m) = f . runAccumT m

look is an action that fetches all the previously accumulated output.

look is an action that retrieves a function of the previously accumulated output.

add w is an action that produces the output w.

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

In-situ lifting of a callCC operation to the new monad. This version uses the current output history on entering the continuation. It does not satisfy the uniformity property (see Control.Monad.Signatures).

Lift a catchE operation to the new monad. The uniformity property (see Control.Monad.Signatures) implies that the lifted catchE discards any output from the body on entering the handler.

Lift a listen operation to the new monad.

Lift a pass operation to the new monad.

Convert a read-only computation into an accumulation computation.

Convert a writer computation into an accumulation computation.

Convert an accumulation (append-only) computation into a fully stateful computation.