Editing Abstract interpretation (section)

{{Short description|Approach to static program analysis}}
In [[computer science]], '''abstract interpretation''' is a theory of [[soundness|sound approximation]] of the [[semantics of programming languages|semantics of computer programs]], based on [[Monotonic function#Monotonicity in order theory|monotonic function]]s over [[ordered set]]s, especially [[lattice (order)|lattice]]s. It can be viewed as a partial [[Execution (computers)|execution]] of a [[computer program]] which gains information about its semantics (e.g., [[control-flow analysis|control-flow]], [[data-flow analysis|data-flow]]) without performing all the [[calculation]]s.

Its main concrete application is formal [[static code analysis|static analysis]], the automatic [[information extraction|extraction of information]] about the possible executions of computer programs; such analyses have two main usages:
* inside [[compiler]]s, to analyse programs to decide whether certain [[Optimization (computer science)|optimization]]s or [[Program transformation|transformation]]s are applicable;
* for [[debugging]] or even the certification of programs against classes of bugs.

Abstract interpretation was formalized by the French computer scientist working couple [[Patrick Cousot]] and [[Radhia Cousot]] in the late 1970s.<ref>{{cite book |first1=Patrick |last1=Cousot |first2=Radhia |last2=Cousot |chapter-url=https://www.di.ens.fr/~cousot/publications.www/CousotCousot-POPL-77-ACM-p238--252-1977.pdf |chapter=Abstract Interpretation: A Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints |title=Conference Record of the Fourth ACM Symposium on Principles of Programming Languages, Los Angeles, California, USA, January 1977 |publisher=ACM Press |year=1977 |pages=238–252 |doi=10.1145/512950.512973 |s2cid=207614632 }}</ref><ref name="CCPOPL79">{{cite book |first1=Patrick |last1=Cousot |first2=Radhia |last2=Cousot |chapter-url=https://www.di.ens.fr/~cousot/publications.www/CousotCousot-POPL-79-ACM-p269--282-1979.pdf |chapter=Systematic Design of Program Analysis Frameworks  |title=Conference Record of the Sixth Annual ACM Symposium on Principles of Programming Languages, San Antonio, Texas, USA, January 1979 |publisher=ACM Press |year=1979 |pages=269–282 |doi=10.1145/567752.567778|s2cid=1547466 }}</ref>