Abstract Interpretation as a Programming Language

Abstract

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

Staged abstract interpreters: fast and modular whole-program analysis via meta-programming

“…As we mentioned earlier, the ADI approach uses a two-cache mechanism to compute the least fixed-point and prevent non-termination. The caching algorithm is also called a co-inductive caching or truncated depth-first evaluation [Rosendahl 2013]. It has been used in other abstract interpreters or fixed-point computation [Darais et al 2017;Rosendahl 2013;Wei et al 2018].…”

“…The caching algorithm is also called a co-inductive caching or truncated depth-first evaluation [Rosendahl 2013]. It has been used in other abstract interpreters or fixed-point computation [Darais et al 2017;Rosendahl 2013;Wei et al 2018]. The idea is to use an in cache and an out cache during the depth-first evaluation.…”

Verification of high-level transformations with inductive refinement types

“…Partition-driven trace memoization The idea is to detect the paths where execution recursively meets similar input, merging the new recursive node with the similar previous one, thus creating a loop in the execution tree [41,43]. This loop is then resolved by a fixed-point iteration.…”

“…Abstract interpretation and static program analysis in general perform fixed-point calculation for analysing unbounded loops and recursion. In Schmidt-style abstract interpretation, the main technique to handle recursion is trace memoization [41,43]. The core idea of trace memoization is to detect non-structural re-evaluation of the same program element, i.e., when the evaluation of a program element is recursively dependent on itself, like a while-loop or traversal.…”

“…We believe that our interpreter would benefit by being written in such style 5 , which complements our modular domain construction well. To ensure termination they rely on a caching algorithm, similar to ordinary finite input trace memoization [41]. Similarly, Van Horn and Might [28] present a systematic framework to abstract higher-order functional languages with effects and complex control flow.…”