Groundness analysis for Prolog: implementation and evaluation of domain prop
PEPM '93 Proceedings of the 1993 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Experimental evaluation of a generic abstract interpretation algorithm for PROLOG
ACM Transactions on Programming Languages and Systems (TOPLAS)
Type analysis of Prolog using type graphs
PLDI '94 Proceedings of the ACM SIGPLAN 1994 conference on Programming language design and implementation
Program analysis with partial transfer functions
PEPM '00 Proceedings of the 2000 ACM SIGPLAN workshop on Partial evaluation and semantics-based program manipulation
Propagating differences: an efficient new fixpoint algorithm for distributive constraint systems
Nordic Journal of Computing
Static Monotonicity Analysis for lambda-definable Functions over Lattices
VMCAI '02 Revised Papers from the Third International Workshop on Verification, Model Checking, and Abstract Interpretation
Nordic Journal of Computing
Boolean equation solving as graph traversal
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
Static extensivity analysis for λ-definable functions over lattices
New Generation Computing
A Scalable Inclusion Constraint Solver Using Unification
Logic-Based Program Synthesis and Transformation
Explicit Versus Symbolic Algorithms for Solving ALFP Constraints
Electronic Notes in Theoretical Computer Science (ENTCS)
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Verifying a local generic solver in coq
SAS'10 Proceedings of the 17th international conference on Static analysis
A policy iteration algorithm for computing fixed points in static analysis of programs
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Model checking Is static analysis of modal logic
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
On monadic parametricity of second-order functionals
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
How to combine widening and narrowing for non-monotonic systems of equations
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Boolean equation solving as graph traversal
CATS '06 Proceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 51
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Computing fixpoints and postfixpoints of transformations has numerous applications in computer science. In this paper, we present a universal top-down fixpoint algorithm based on the weak assumption that the transformation is defined by an effective procedure. Given the procedure and a parameter value, the universal algorithm computes the value of the parameter value in the least fixpoint of the transformation has the property of focusing on the subset of elements necessary to compute the result. The total correctness of the algorithm is proven and requires some weak (but rather technical) assumptions. These conditions can be relaxed further if postfixpoints suffice for the application. As a consequence, the algorithm generalizes and abstracts numerous algorithms and provides a versatile alternative to bottom-up algorithms. It has been used to derive specific abstract interpretation algorithms for Prolog, which are practical both in terms of efficiency and accuracy and are, to our knowledge, the fastest algorithms available.