Controlling Effects

Many computational effects, such as exceptions, state, or nondeterminism, can be conveniently specified in terms of monads. We investigate a technique for uniformly adding arbitrary such effects to ML-like languages, without requiring any structural changes to the programs themselves. Instead, we use monadic reflection, a new language construct for explicitly converting back and forth between representations of effects as behavior and as data.

Using monadic reflection to characterize concisely all effects expressible with a given monad, we can give a precise meaning to the notion of simulating one effect by another, more general one. We isolate a simple condition allowing such a simulation, and in particular show that any monadic effect can be simulated by a continuation monad. In other words, under relatively mild assumptions on the base language (allowing formation of a suitably large answer type), control becomes a universal effect.

Concluding the development, we show that this universal effect can itself be explicitly implemented in terms of only standard first-class continuations (call/cc) and a piece of global state. This means that we can specify an effect such as nondeterminism abstractly, in terms of result lists, then directly obtain from this description a nondeterministic-choice operator performing imperatively-implemented backtracking. We include a full realization of the general construction in Standard ML of New Jersey, and give several programming examples.

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