This work is licensed under the Creative Commons Attribution License. Abstract Interpretation as a Programming Language

In David Schmidts PhD work he explored the use of denotational semantics as a programming lan-guage. It was part of an effort to not only treat formal semantics as specifications but also as inter-preters and input to compiler generators. The semantics itself can be seen as a program and one may examine different programming styles and ways to represent states. Abstract interpretation is primarily a technique for derivation and specification of program anal-ysis. As with denotational semantics we may also view abstract interpretations as programs and examine the implementation. The main focus in this paper is to show that results from higher-order strictness analysis may be used more generally as fixpoint operators for higher-order functions over lattices and thus provide a technique for immediate implementation of a large class of abstract inter-pretations. Furthermore, it may be seen as a programming paradigm and be used to write programs in a circular style.