Program transformations in a denotational setting
ACM Transactions on Programming Languages and Systems (TOPLAS)
Frontiers and open sets in abstract interpretation
FPCA '89 Proceedings of the fourth international conference on Functional programming languages and computer architecture
Inverse image analysis generalises strictness analysis
Information and Computation
Handbook of theoretical computer science (vol. B)
Two-level functional languages
Two-level functional languages
Semantics of programming languages: structures and techniques
Semantics of programming languages: structures and techniques
Property preserving abstractions for the verification of concurrent systems
Formal Methods in System Design - Special issue on computer-aided verification (based on CAV'92 workshop)
Abstract interpretation: a semantics-based tool for program analysis
Handbook of logic in computer science (vol. 4)
Abstract interpretation of reactive systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
Making abstract interpretations complete
Journal of the ACM (JACM)
Data flow analysis of applicative programs using minimal function graphs
POPL '86 Proceedings of the 13th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Parametric shape analysis via 3-valued logic
ACM Transactions on Programming Languages and Systems (TOPLAS)
Principles of Program Analysis
Principles of Program Analysis
Flow analysis and optimization of LISP-like structures
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Strictness Logic and Polymorphic Invariance
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
Power Domains and Predicate Transformers: A Topological View
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Optimality in Abstractions of Model Checking
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Incompleteness, Counterexamples, and Refinements in Abstract Model-Checking
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
Construction of Abstract State Graphs with PVS
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Higher-Order and Symbolic Computation
3-Valued abstraction: More precision at less cost
Information and Computation
Underapproximating predicate transformers
SAS'06 Proceedings of the 13th international conference on Static Analysis
Comparing completeness properties of static analyses and their logics
APLAS'06 Proceedings of the 4th Asian conference on Programming Languages and Systems
Hi-index | 5.23 |
We develop abstract-interpretation domain construction in terms of the inverse-limit construction of denotational semantics and topological principles: we define an abstract domain as a ''structural approximation'' of a concrete domain if the former exists as a finite approximant in the inverse-limit construction of the latter, and we extract the appropriate Galois connection for sound and complete abstract interpretations. The elements of the abstract domain denote (basic) open sets from the concrete domain's Scott topology, and we hypothesize that every abstract domain, even non-structural approximations, defines a weakened form of topology on its corresponding concrete domain. We implement this observation by relaxing the definitions of topological open set and continuity; key results still hold. We show that families of closed and open sets defined by abstract domains generate post- and pre-condition analyses, respectively, and Giacobazzi's forwards- and backwards-complete functions of abstract-interpretation theory are the topologically closed and continuous maps, respectively. Finally, we show that Smyth's upper and lower topologies for power domains induce the overapproximating and underapproximating transition functions used for abstract-model checking.