Program derivation by fixed point computation
Science of Computer Programming
On the shape of mathematical arguments
On the shape of mathematical arguments
Abstract interpretation and application to logic programs
Journal of Logic Programming
Science of Computer Programming - Special issue on mathematics of program construction
Information Processing Letters - Special issue on the calculational method
Algebra of programming
Modern compiler implementation in Java
Modern compiler implementation in Java
Global Data Flow Analysis and Iterative Algorithms
Journal of the ACM (JACM)
SIAM Journal on Computing
A fast algorithm for finding dominators in a flowgraph
ACM Transactions on Programming Languages and Systems (TOPLAS)
Systematic design of program transformation frameworks by abstract interpretation
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Contification using dominators
Proceedings of the sixth ACM SIGPLAN international conference on Functional programming
Checking security of Java bytecode by abstract interpretation
Proceedings of the 2002 ACM symposium on Applied computing
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Constructive design of a hierarchy of semantics of a transition system by abstract interpretation
Theoretical Computer Science
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Introduction to Algorithms
Conservative Fixpoint Functions on a Graph
Proceedings of the Second International Conference on Mathematics of Program Construction
Galois connections and fixed point calculus
Algebraic and coalgebraic methods in the mathematics of program construction
Proceedings of a symposium on Compiler optimization
'Galculator': functional prototype of a Galois-connection based proof assistant
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
A Calculational Approach to Control-Flow Analysis by Abstract Interpretation
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Applications of Boolean matrices to the analysis of flow diagrams
IRE-AIEE-ACM '59 (Eastern) Papers presented at the December 1-3, 1959, eastern joint IRE-AIEE-ACM computer conference
Abstract interpreters for free
SAS'10 Proceedings of the 17th international conference on Static analysis
TOOLS'11 Proceedings of the 49th international conference on Objects, models, components, patterns
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We calculate two iterative, polynomial-time graph algorithms from the literature: a dominance algorithm and an algorithm for the single-source shortest path problem. Both algorithms are calculated directly from the definition of the properties by fixed-point fusion of (1) a least fixed point expressing all finite paths through a directed graph and (2) Galois connections that capture dominance and path length. The approach illustrates that reasoning in the style of fixed-point calculus extends gracefully to the domain of graph algorithms. We thereby bridge common practice from the school of program calculation with common practice from the school of static program analysis, and build a novel view on iterative graph algorithms as instances of abstract interpretation.