SequenceT

SequenceT is a generic data type used in functional programming to model computations that can yield a sequence of results. It is commonly described as a transformer that lifts a base effect M into a sequence-producing context, enabling a uniform way to compose nondeterministic or streaming computations.

In many formulations SequenceT M A is isomorphic to M [A], where M is a fixed type constructor that represents a computational effect such as a Promise, an IO action, or an option. This means the value of type SequenceT M A represents a computation that, when executed, yields a (possibly empty) list of As inside the effect M.

SequenceT supports the standard type-class interfaces when M provides them. Functor allows mapping a function over each element of the produced sequence; Applicative enables combining independent sequences; Monad enables chaining computations that produce sequences, by feeding each element to a subsequent computation. Most implementations provide constructors such as of (or return) to lift a single value into a singleton sequence, and empty to represent no results.

When used, SequenceT often helps express nondeterministic search, multivalued computations, or streaming pipelines where each step may produce multiple outputs. For example, with M as a Promise, a SequenceT Promise A corresponds to a Promise of a list of As; chaining operations preserves the list structure at each step.

Caveats include potential performance overhead from layering effects and the need to manage the inner list structure carefully to avoid combinatorial explosion. See also ListT, Stream, and the broader concept of monad transformers.