Typee

TypeE is a theoretical framework and small practical extension used to study effect-aware type systems in programming languages. It introduces a family of types that are parameterized by an effect set E, where E represents a collection of computational effects such as input/output, state, exceptions, or termination. In TypeE, function types are written as A ->_E B, indicating that the function consumes A, returns B, and may perform effects from the set E. The system supports polymorphic effect variables, enabling effect polymorphism so that a function can be typed with a generic effect set that is instantiated later.

A core feature of TypeE is the enforcement that the effects declared in a function type are a superset of the effects actually used in the function body. This allows static reasoning about side effects and helps ensure safer composition of components in larger systems. TypeE also incorporates basic formalisms for type inference and subtyping, with a focus on how effects interact with traditional type guarantees.

History and usage: TypeE originated in type theory research as part of experiments with effect systems and row polymorphism. It has appeared in academic papers and toy implementations to compare approaches for tracking and handling effects. While not a mainstream programming language, TypeE serves as a reference model for exploring how effect information can be integrated into type systems and how it influences program correctness and modular reasoning.

Limitations: TypeE is primarily a theoretical construct with experimental implementations. Practical adoption requires deeper integration with existing languages, scalable type inference, and robust handling of complex effect interactions. See also effect system, algebraic effects, type system, polymorphism.

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