2 Head - Strictness Is Not Definable

A property P of a language is said to be deenable by abstract interpretation if there is a monotonic map abs from the domain of standard semantics to an abstract domain A of nite height, and a partition of the abstract domain into two parts A P and A non-P , such that any value has property P if and only if abs maps it to an element of A P. Head-strictness is a property of functions over lists which asserts, roughly speaking, that whenever the function looks at some preex of a list, it looks every element in that preex. We prove that head-strictness is not deenable by abstract interpretation.