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Program transformation has gained a wide interest since it is used for several purposes: altering semantics of a program, adding features to a program or performing optimizations. In this paper we focus on program transformations at the bytecode level. Because these transformations may introduce errors, our goal is to provide a formal way to verify the update and establish its correctness. The formal framework presented includes a definition of a formal semantics of updates which is the base of a static verification and a scheme based on Hoare triples and weakest precondition calculus to reason about behavioral aspects in bytecode transformation
We present a system called Adelfa that provides mechanized support for reasoning about specifications developed in the Edinburgh Logical Framework or LF. Underlying Adelfa is a new logic named L_LF. Typing judgements in LF are represented by atomic formulas in L_LF and quantification is permitted over contexts and terms that appear in such formulas. Contexts, which constitute type assignments to uniquely named variables that are modelled using the technical device of nominal constants, are characterized in L_LF by context schemas that describe their inductive structure. We present these formulas and an associated semantics before sketching a proof system for constructing arguments that are sound with respect to the semantics. We then outline the realization of this proof system in Adelfa and illustrate its use through a few example proof developments. We conclude the paper by relating Adelfa to existing systems for reasoning about LF specifications.
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursion will become one of the fundamental paradigms of quantum programming. Several program logics have been developed for verification of quantum while-programs. However, there are as yet no general methods for reasoning about (mutual) recursive procedures and ancilla quantum data structure in quantum computing (with measurement). We fill the gap in this paper by proposing a parameterized quantum assertion logic and, based on which, designing a quantum Hoare logic for verifying parameterized recursive quantum programs with ancilla data and probabilistic control. The quantum Hoare logic can be used to prove partial, total, and even probabilistic correctness (by reducing to total correctness) of those quantum programs. In particular, two counterexamples for illustrating incompleteness of non-parameterized assertions in verifying recursive procedures, and, one counterexample for showing the failure of reasoning with exact probabilities based on partial correctness, are constructed. The effectiveness of our logic is shown by three main examples -- recursive quantum Markov chain (with probabilistic control), fixed-point Grovers search, and recursive quantum Fourier sampling.
We present FJ&$lambda$, a new core calculus that extends Featherweight Java (FJ) with interfaces, supporting multiple inheritance in a restricted form, $lambda$-expressions, and intersection types. Our main goal is to formalise how lambdas and intersection types are grafted on Java 8, by studying their properties in a formal setting. We show how intersection types play a significant role in several cases, in particular in the typecast of a $lambda$-expression and in the typing of conditional expressions. We also embody interface emph{default methods} in FJ&$lambda$, since they increase the dynamism of $lambda$-expressions, by allowing these methods to be called on $lambda$-expressions. The crucial point in Java 8 and in our calculus is that $lambda$-expressions can have various types according to the context requirements (target types): indeed, Java code does not compile when $lambda$-expressions come without target types. In particular, in the operational semantics we must record target types by decorating $lambda$-expressions, otherwise they would be lost in the runtime expressions. We prove the subject reduction property and progress for the resulting calculus, and we give a type inference algorithm that returns the type of a given program if it is well typed. The design of FJ&$lambda$ has been driven by the aim of making it a subset of Java 8, while preserving the elegance and compactness of FJ. Indeed, FJ&$lambda$ programs are typed and behave the same as Java programs.
We provide a sound and relatively complete Hoare-like proof system for reasoning about partial correctness of recursive procedures in presence of local variables and the call-by-value parameter mechanism, and in which the correctness proofs are linear in the length of the program. We argue that in spite of the fact that Hoare-like proof systems for recursive procedures were intensively studied, no such proof system has been proposed in the literature.
A common approach to improve software quality is to use programming guidelines to avoid common kinds of errors. In this paper, we consider the problem of enforcing guidelines for Featherweight Java (FJ). We formalize guidelines as sets of finite or infinite execution traces and develop a region-based type and effect system for FJ that can enforce such guidelines. We build on the work by Erbatur, Hofmann and Zu{a}linescu, who presented a type system for verifying the finite event traces of terminating FJ programs. We refine this type system, separating region typing from FJ typing, and use ideas of Hofmann and Chen to extend it to capture also infinite traces produced by non-terminating programs. Our type and effect system can express properties of both finite and infinite traces and can compute information about the possible infinite traces of FJ programs. Specifically, the set of infinite traces of a method is constructed as the greatest fixed point of the operator which calculates the possible traces of method bodies. Our type inference algorithm is realized by working with the finitary abstraction of the system based on Buchi automata.