A [2+2]-cycloaddition is a 4 electron process that brings together two components.  Thus, by the above general WH rules, it is only allowed if the reaction is antarafacial with respect to exactly one component.  This is the same conclusion reached with correlation diagrams in the section above.
A rare but stereochemically unambiguous example of a [2 + 2]-cycloaddition is shown on the right.  The strain and steric properties of the trans double bond enables this generally kinetically unfavorable process.  cis, trans-1,5-Cyclooctadiene is also believed to undergo dimerization via this mode.  Ketenes are a large class of reactants favoring [2 + 2] cycloaddition with olefins.  The MO analysis of ketene cycloaddition is rendered complicated and ambiguous by the simultaneous but independent interaction of the orthogonal orbitals of the ketene but may involve a [2 + 2] interaction as well.