Note that a function
f is said to diverge if it returns : operationally, that would mean that
f either causes abnormal termination of the enclosing program (e.g., failure with an error message) or that it loops infinitely. The notion of "divergence" is significant because a strict function is one that always diverges when given an argument that diverges, whereas a lazy (or non-strict) function is one that may or may not diverge when given such an argument. Strictness analysis attempts to determine the "divergence properties" of functions, which thus identifies some functions that are strict.
The Glasgow Haskell Compiler uses a backward abstract interpretation known as demand analysis to perform strictness analysis as well as other program analyses. In demand analysis, each function is modelled by a function from value demands on the result to value demands on the arguments. A function is strict in an argument if a demand for its result leads to a demand for that argument.
Projection-based strictness analysis, introduced by Philip Wadler and R.J.M. Hughes, uses strictness projections to model more subtle forms of strictness, such as head-strictness in a list argument. (By contrast, GHC's demand analysis can only model strictness within product types, i.e., datatypes that only have a single constructor.) A function is considered head-strict if , where is the projection that head-evaluates its list argument.
There was a large body of research on strictness analysis in the 1980s.