Constant applicative form

Also referred to as CAF.

Any super combinator which is not a lambda abstraction. This includes truly constant expressions such as 12, ((+) 1 2), [1,2,3] as well as partially applied functions such as ((+) 4). Note that this last example is equivalent under eta abstraction to \ x -> (+) 4 x which is not a CAF.

Examples and discussions

Since a CAF is a super combinator, it contains no free variables. Moreover, since it is not a lambda abstraction it contains no variables at all. It may however contain identifiers which refer to other CAFs, e.g.

c 3 where c = (*) 2

A CAF can always be lifted to the top level of the program. It can either be compiled to a piece of graph which will be shared by all uses or to some shared code which will overwrite itself with some graph the first time it is evaluated. A CAF such as

ints = from 1  where  from n = n : from (n+1)

can grow without bound but may only be accessible from within the code of one or more functions. In order for the garbage collector to be able to reclaim such structures, we associate with each function a list of the CAFs to which it refers. When garbage collecting a reference to the function we collect the CAFs on its list.

See also

• Simon Peyton Jones' Implementation of Functional Programming Languages for more about this and related terms.
• Memoising constant applicative forms