There are some terms for these cases, but they are a bit ad hoc. length is what we might call spine-strict; head is head-strict. Projection analysis takes the approach that we can more precisely characterize the strictness only by considering both what is passed to the function as input, as well as how much is demanded by the context (for example, you might return a tuple, one of the values of which causes lots of evaluation, and the other of which doesn't.) Unfortunately, this is not enough precision to consider elem. Edward Excerpts from Yves Parès's message of Fri Jan 27 10:13:54 -0500 2012:
If I consider the functions head, length, elem & sum, each is of them is strict, as: head/length/elem x/sum _|_ are always _|_.
However: head (x:_|_) is never _|_. length [_|_, _|_, _|_ ...] is also never _|_. elem x [4,5,6,8,2,90,_|_,_|_ ...] is *only sometimes *_|_ (depending on x value). In fact, only sum [4,5,6,8,2,90,_|_,_|_ ...] is always _|_.
Which shows they don't have the same level of strictness.
So can you say things like "all these functions are strict, but some are *more *than other", or "sum is *deeply strict*" ...? What terms can you use to compare those functions?