Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
A relational framework for abstract interpretation
on Programs as data objects
Two-level semantics and abstract interpretation
Theoretical Computer Science
Generating data flow analysis algorithms from modal specifications
TACS'91 Selected papers of the conference on Theoretical aspects of computer software
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)
Data flow analysis is model checking of abstract interpretations
POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Temporal abstract interpretation
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Making abstract interpretations complete
Journal of the ACM (JACM)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Principles of Program Analysis
Principles of Program Analysis
Dynamic Logic
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Optimality in Abstractions of Model Checking
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Structure-preserving binary relations for program abstraction
The essence of computation
Compiler Optimization Correctness by Temporal Logic
Higher-Order and Symbolic Computation
Higher-Order and Symbolic Computation
The Description Logic Handbook
The Description Logic Handbook
A calculus of logical relations for over- and underapproximating static analyses
Science of Computer Programming
Underapproximating predicate transformers
SAS'06 Proceedings of the 13th international conference on Static Analysis
Strong preservation of temporal fixpoint-based operators by abstract interpretation
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Comparing completeness properties of static analyses and their logics
APLAS'06 Proceedings of the 4th Asian conference on Programming Languages and Systems
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We connect the activity of defining an abstract-interpretation-based static analysis with synthesizing its appropriate programming logic by applying logical relations as demonstrated by Abramsky. We begin with approximation relations of base type, which relate concrete computational values to their approximations, and we lift the relations to function space and upper- and lower-powerset. The resulting family's properties let us synthesize an appropriate logic for reasoning about the outcome of a static analysis. The relations need not generate Galois connections, but when they do, we show that the relational notions of soundness and completeness coincide with the Galois-connection-based notions.