A category theoretic formalism for abstract interpretation

W e present a form al theory of abstract interpretation based on a new category theoretic form alism . This form alism allows one to derive a collecting semantics which preserves continuity of lifted functions and for which the lifting functor is itself continuous. The theory of abstract interpretation is then presented as an approxim ation of this collecting semantics. The use of categories rather than com plete partial orders elim inates the need for introducing tw o distinct partial orders and for introducing any closure operation on the allowable elem ents, as is necessary with powerdomains. Furthermore, our construction can be applied to any situation for which the underlying domains are com plete partial orders, sice the domains are not further restricted in any way. This form alism can be applied to first order languages. keywords and phrases: abstract interpretation, category theory, complete partial orders, denotational semantics, indeterm inate functions, quasi-functor, strictness.