We present a program logic for reasoning about resource consumption of programs written in Grail, an abstract fragment of the Java Virtual Machine Language. Serving as the target logic of a certifying compiler, the logic exploits Grail's dual nature of combining a functional interpretation with object-oriented features and a cost model for the JVM. We present the resource-aware operational semantics of Grail, the program logic, and prove soundness and completeness. All of the work described has been formalised in the theorem prover Isabelle/HOL, which provides us with an implementation of the logic as well as confidence in the results. We conclude with examples of using the logic for proving resource bounds on code resulting from compiling high-level functional programs.

We present a program logic for verifying the heap consumption of programs written in an abstract representation of the Java virtual machine language. The logic is defined by an expansion into the more general program logic presented in [2], but concrete program program verification may be performed purely on the abstract level, without recourse to the base logic. Format and interpretation of assertions closely match the interpretation of [8]'s type system for functional programs where the consumption of heap space is bounded by a linear function on the input size. The derived proof rules enable us to replay typing derivations in a theorem prover, given assertions about individual methods. The resulting verification conditions are of limited complexity, and may be discharged without significant programmer intervention.