A constraint-based data flow analysis is formalised in the specification language of the Coq proof assistant. This involves defining a dependent type of lattices together with a library of lattice functors for modular construction of complex abstract domains. Constraints are represented in a way that allows for both efficient constraint resolution and correctness proof of the analysis with respect to an operational semantics. The proof of existence of a solution to the constraints is constructive which means that the extraction mechanism of Coq provides a provably correct data flow analyser in Ocaml from the proof. The library of lattices and the representation of constraints are defined in an analysisindependent fashion that provides a basis for a generic framework for proving and extracting static analysers in Coq.

Abstract. We present a certified algorithm for resource usage analysis, applicable to languages in the style of Java byte code. The algorithm verifies that a program executes in bounded memory. The algorithm is destined to be used in the development process of applets and for enhanced byte code verification on embedded devices. We have therefore aimed at a low-complexity algorithm derived from a loop detection algorithm for control flow graphs. The expression of the algorithm as a constraint-based static analysis of the program over simple lattices provides a link with abstract interpretation that allows to state and prove formally the correctness of the analysis with respect to an operational semantics of the program. The certification is based on an abstract interpretation framework implemented in the Coq proof assistant which has been used to provide a complete formalisation and formal verification of all correctness proofs.

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