coeffects

Coeffects are a concept in programming language theory that describe the contextual requirements a computation draws from its execution environment. While effects describe how a computation may alter the outside world, coeffects describe what the computation needs from its context to run. Examples include access to a clock, a configuration parameter, or an input stream. Coeffect systems extend type systems by annotating functions with their contextual dependencies, enabling safer composition and reasoning about where code can run and which resources it depends on.

Historically, coeffects have been studied as a formal counterpart to effect systems. They can be modeled using category-theoretic structures such as comonads or indexed coeffect algebras, and they are incorporated into type systems to express context dependencies. A function with no coeffects requires no ambient resources; others require certain capabilities to be available, and the type system can enforce that callers supply them.

Examples of coeffectful computations include a function that reads the current time (requiring a clock), one that looks up configuration from an environment map, or a data stream processor that needs an input source. A function may also declare a dependency on security tokens, permissions, or I/O channels. Note that coeffects describe context requirements, not necessarily whether side effects will occur during execution.

Applications of coeffect systems include safer resource management, modular programming across components with different capabilities, and reasoning about distributed systems where code runs in varying environments. They complement effect systems by offering a fuller picture of program behavior: what a function requires from its context and what it may do to the environment. The topic remains active in theory and language design, with ongoing research into practical implementations.