Locales are a means to define local scopes for the interactive proving process of the theorem prover Isabelle. They delimit a range in which fixed assumption are made, and theorems are proved that depend on these assumptions. A locale may also contain constants defined locally and associated with pretty printing syntax. Locales can be seen as a simple form of modules. They are similar to reasoning and similar applications of theorem provers. This paper motivates the concept of locales by examples from abstract algebraic reasoning. It also discusses some implementation issues.

Isabelle/HOL has recently acquired new versions of definitional packages for inductive datatypes and primitive recursive functions. In contrast to its predecessors and most other implementations, Isabelle/HOL datatypes may be mutually and indirect recursive, even infinitely branching. We also support inverted datatype definitions for characterizing existing types as being inductive ones later. All our constructions are fully definitional according to established HOL tradition. Stepping back from the logical details, we also see this work as a typical example of what could be called "Formal-Logic Engineering". We observe that building realistic theorem proving environments involves further issues rather than pure logic only. 1

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We present a formal semantics as a conservative shallow embedding of the Object Constraint Language (OCL). OCL is currently under development within an open standardization process within the OMG; our work is an attempt to accompany this process by a proposal solving open questions in a consistent way and exploring alternatives of the language design. Moreover, our encoding gives the foundation for tool supported reasoning over OCL specifications, for example as basis for test case generation.

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 describe aspects of the formalisation and verification of the L4 µ-kernel. Starting from an abstract model of the virtual memory subsystem in L4, we prove safety properties about this model, and then refine the page table abstraction, one part of the model, towards C source code. All formalisations and proofs have been carried out in the theorem prover Isabelle. 1

We have previously introduced role logic as a notation for describing properties of relational structures in shape analysis, databases and knowledge bases. A natural fragment of role logic corresponds to two-variable logic with counting and is therefore decidable.

We present a new proof environment for the specification language Z. The basis is a semantic representation of Z in a structure-preserving, shallow embedding in Isabelle/HOL. On top of the embedding, new proof support for the Z schema calculus and for proof structuring are developed. Thus, we integrate Z into a well-known and trusted theorem prover with advanced deduction technology such as higher-order rewriting, tableaux-based provers and arithmetic decision procedures. A further achievement of this work is the integration of our embedding into a new toolchain providing a Z-oriented type checker, documentation facilities and macro support for refinement proofs; as a result, the gap has been closed between a logical embedding proven correct and a tool suited for applications of non-trivial size.

with an Application to IMP++

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