The term lifting is used to depict the process of converting an ordinary operator to a variant that can operate on behaviors. This process is essential for the end user of the language/framework, since it ensures conciseness and composability. In other words, lifting is used to move from the non-reactive world to reactive behaviors.
Lifting a value creates a constant behavior while lifting a function applies the function continuously to the argument behaviors. There is no similar lifting operation for events, since an event would need an occurrence time as well as a value.
Lifting an operation can be formalized by the following definition, assuming functions that only take one parameter (generalising to functions that take multiple arguments is trivial):
The function can now be applied to behaviors that holds values of type . Lifting enables the language or framework to register a dependency graph in the application's dataflow graph.
Starting from the previous definition, the evaluation of a lifted function called with a behavior at the time step can be formalized as follows:
where is the value of the behavior at the time step .
In the literature there are at least three main lifting strategies:
Implicit lifting, that happens when an ordinary language operator is applied on a behaviour and it is automatically lifted. Implicit lifting is often used by dynamically typed languages. Formally:
Explicit lifting, usually used by statically typed languages. In this case the language provides a set of combinators to lift ordinary operators to operate on behaviors. Formally:
Manual lifting, when the language does not provide lifting operators. Formally: