This paper describes a compositional shape analysis, where each procedure is analyzed independently of its callers. The analysis uses an abstract domain based on a restricted fragment of separation logic, and assigns a collection of Hoare triples to each procedure; the triples provide an over-approximation of data structure usage. Compositionality brings its usual benefits – increased potential to scale, ability to deal with unknown calling contexts, graceful way to deal with imprecision – to shape analysis, for the first time. The analysis rests on a generalized form of abduction (inference of explanatory hypotheses) which we call bi-abduction. Biabduction displays abduction as a kind of inverse to the frame problem: it jointly infers anti-frames (missing portions of state) and frames (portions of state not touched by an operation), and is the basis of a new interprocedural analysis algorithm. We have implemented

Abstract. We propose a simple compositional program logic for an imperative extension of call-by-value PCF, built on Hoare logic and our preceding work on program logics for pure higher-order functions. A systematic use of names and operations on them allows precise and general description of complex higher-order imperative behaviour. The proof rules of the logic exactly follow the syntax of the language and can cleanly embed, justify and extend the standard proof rules for total correctness of Hoare logic. The logic offers a foundation for general treatment of aliasing and local state on its basis, with minimal extensions. After establishing soundness, we prove that valid assertions for programs completely characterise their behaviour up to observational congruence, which is proved using a variant of finite canonical forms. The use of the logic is illustrated through reasoning examples which are hard to assert and infer using existing program logics.

We present a compositional program logic for call-by-value imperative higherorder functions with general forms of aliasing, which can arise from the use of reference names as function parameters, return values, content of references and part of data structures. The program logic

Abstract not found

This paper presents sound and complete Hoare logics for partial and total correctness of recursive parameterless procedures in the context of unbounded nondeterminism. For total correctness, the literature so far has either restricted recursive procedures to be deterministic or has studied unbounded nondeterminism only in conjunction with loops rather than procedures. We consider both single procedures and systems of mutually recursive procedures. All proofs have been checked with the theorem prover Isabelle/HOL.

Abstract. We define a compositional program logic in the style of Floyd and Hoare for a simple, typed, stack-based abstract machine with unstructured control flow, global variables and mutually recursive procedure calls. Notable features of the logic include a careful treatment of auxiliary variables and quantification and the use of substructural typing to permit local, modular reasoning about program fragments. Semantic soundness is established using an interpretation of types and assertions defined by orthogonality with respect to sets of contexts. 1

Abstract. We develop a general language model for sequential imperative programs together with a Hoare logic. We instantiate the framework with common programming language constructs and integrate it into Isabelle/HOL, to gain a usable and sound verification environment. 1

Abstract. We define NanoJava, a kernel of Java tailored to the investigation of Hoare logics. We then introduce a Hoare logic for this language featuring an elegant approach for expressing auxiliary variables: by universal quantification on the outer logical level. Furthermore, we give simple means of handling side-effecting expressions and dynamic binding within method calls. The logic is proved sound and (relatively) complete using Isabelle/HOL. Keywords: Hoare logic, Java, Isabelle/HOL, auxiliary variables, side effects, dynamic binding.

This paper describes Hoare logics for a number of imperative language constructs, from while-loops via exceptions to mutually recursive procedures. Both partial and total correctness are treated. In particular a proof system for total correctness of recursive procedures in the presence of unbounded nondeterminism is presented. All systems are formalized and shown to be sound and complete in the theorem prover Isabelle/HOL.

Introduction For reasoning about total correctness of while-programs, the rules proposed by Hoare [10] have stood the test of time. But for procedure calls, a number of dierent rules have appeared (e.g, [11,9,2,1,5,12]). There appears to be no consensus on the \right" rule, and some proposals even turn out to be unsound. The results reported in this note were found in an attempt to derive an adaptation rule |rather than pulling it from a magician's hat| using tools from renement calculus. This sheds new light on the subject, explaining and extending the applicability of recent proposals, and it brings to light a new form of specication statement. Adaptation rules. For the moment, let us take for granted a semantics for commands and predicates. Say a triple f pre g S f post g is valid if every computation of command S from a state satisfying pre terminates in