Examples of monad

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Similar remarks apply to each of the monads appearing in this paper.
Satisfaction of the monad laws is, however, not enforced by the compiler.
The type checking monad is just a combination of a state and error monad, and it interacts with a parsing monad.
We can incrementally construct these terms and interpret them as computations in the state monad.
Is there any way of characterising the algebras for this monad?
We note at once that we cannot expect every taut presentation of a shaped monad to be shaped.
Any shapely monad admits a monad map to lists that assigns its list of members.
However, we will see that some examples of collection monad do not have an obvious equational presentation.
The next result establishes constraints for any equational presentation of a zipped monad.
This leads to a theory of divergences from which a notion of (computable) partial function is derived together with a lift monad classifying partial functions.
We can now characterize those monads with commutative strength as follows.
In fact, no exactness is required of the local monads in this case.
In general, operations that work on one specific monad can be lifted into the new, extended monad.
In category theory, non-determinism and probability are represented by suitable monads.
In other words, a classifying monad is effective if it is the partial map classifier for a category of partial maps.
The system of monads should be taken as the metaphysical model of the best of all possible worlds.
We can give explicit criteria of a more elementary sort providing a characterization of morphisms that are lax monads.
The following three equations express the laws required of a monad.

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