EnumerationT

EnumerationT is a generic abstraction used in programming and type theory to describe a parameterized enumeration of values. It represents a potentially finite or infinite sequence of elements of type T, produced on demand. An instance is often written as EnumerationT<T> and embodies the idea of enumerating a domain rather than declaring a fixed set of constants.

A typical EnumerationT provides a small set of operations: hasNext or isEnd to test for completion, next or advance to move to the next element, and current or head to access the current element. Many designs support functional composition, offering map, filter, take, drop, and fold to transform or consume the stream. Implementations usually emphasize laziness, computing elements only when requested, which allows working with large or infinite sequences without upfront allocation.

EnumerationT is distinct from enumerated types (enums) or simple lists: it models a stateful, potentially unbounded sequence, while enums define a finite set of named values. It is also distinct from iterators in some languages, though it often serves a similar role, as a provider of a sequence rather than a container.

Common use cases include enumerating natural numbers, iterating over generated combinations or permutations, streaming data, or mapping a generator function over a domain. When used in a language with strong type or effect systems, EnumerationT can enable static reasoning about termination, memory usage, and purity.

See also: iterator, generator, stream, lazy evaluation, functional programming.