Abstract Interpretation as a Programming Language

In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters 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 analysis. 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 interpretations. Furthermore, it may be seen as a programming paradigm and be used to write programs in a circular style.