This paper reports on the development and formal certification (proof of semantic preservation) of a compiler from Cminor (a C-like imperative language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a certified compiler is useful in the context of formal methods applied to the certification of critical software: the certification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well.

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well. Categories and Subject Descriptors: F.3.1 [Logics and meanings of programs]: Specifying and verifying and reasoning about programs—Mechanical verification; D.2.4 [Software engineering]: Software/program verification—Correctness proofs, formal methods, reliability; D.3.4 [Programming languages]: Processors—Compilers, optimization

Some of the success stories of model based refinement are recalled, as well as some of the annoyances that arise when refinement is deployed in the engineering of large systems. The way that retrenchment attempts to alleviate such inconveniences is briefly reviewed. The Mondex Electronic Purse formal development provides a highly credible testbed for examining how real world refinement difficulties can be treated via retrenchment. The contributions of retrenchment to integrating the real implementation with the formal development are surveyed, and the extraction of commonly occurring `retrenchment patterns' is recalled. One of the Mondex difficulties, the `Balance Enquiry Quandary' is treated in detail, and the way that retrenchment is able to account for the system behaviour is explained. The problem is reconsidered using generalised forward refinement, and the simplicity of the resolution of the quandary, both by retrenchment, and by generalised forward refinement, inspires the creation of a genuine (1; 1) forward refinement for Mondex, something long thought impossible. The forward treatment exhibits a similar balance enquiry quandary to the backward refinement, as it must, given that both are refinements of an atomic action to a non-atomic protocol, and the forward quandary is dealt with as easily by retrenchment as is the backward case.

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... Java Card Virtual Machine Language. We use the instruction set and the program structures proposed in [1]. We define a small-step relation between program con- figurations, including rules for exception handling, arrays and subroutines. We also include the basic structures needed to model object ownership and the Java Card firewall.

The Mondex Electronic Purse is an outstanding example of industrial scale formal refinement, and was the first verification to achieve ITSEC level E6 certification. A formal abstract model and a formal concrete model were developed, and a formal refinement was hand-proved between them. Nevertheless, certain requirements issues were set beyond the scope of the formal development, or handled in an unnatural manner. The retrenchment Tower Pattern is used to address one such issue in detail: the finiteness of the purse log (which records unsuccessful transactions). A retrenchment is constructed from the lowest level model of the purse system to a model in which logs are finite, and is then lifted to create two refinement developments of the purse, working at different levels of detail, and connected via retrenchments, forming the tower. The tower development is appropriately validated, vindicating the design used.

We discuss the formalization of Abadi and Cardelli's imp#, a paradigmatic object-based calculus with types and side e#ects, in (Co)Inductive Type Theories.

The Mondex Electronic Purse is an outstanding example of industrial scale formal refinement, and was the first verification to achieve ITSEC level E6 certification. A formal abstract model and a formal concrete model were developed, and a formal refinement was hand-proved between them. Nevertheless, certain requirements issues were set beyond the scope of the formal development, or handled in an unnatural manner. The retrenchment Tower Pattern is used to address one such issue in detail: the finiteness of the purse log (which records unsuccessful transactions). A retrenchment is constructed from the lowest level model of the purse system to a model in which logs are finite, and is then lifted to create two refinement developments of the purse, working at different levels of detail, and connected via retrenchments, forming the tower. The tower development is appropriately validated, vindicating the design used. 1

Abstract. The goal of this lecture is to show how modern theorem provers—in this case, the Coq proof assistant—can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and over generic program transformations, as typically found in compilers. The topics covered include: operational semantics (small-step, big-step, definitional interpreters); a simple form of denotational semantics; axiomatic semantics and Hoare logic; generation of verification conditions, with application to program proof; compilation to virtual machine code and its proof of correctness; an example of an optimizing program transformation (dead code elimination) and its proof of correctness.