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seL4: Formal Verification of an OS Kernel
 ACM SYMPOSIUM ON OPERATING SYSTEMS PRINCIPLES
, 2009
"... Complete formal verification is the only known way to guarantee that a system is free of programming errors. We present our experience in performing the formal, machinechecked verification of the seL4 microkernel from an abstract specification down to its C implementation. We assume correctness of ..."
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Cited by 288 (45 self)
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Complete formal verification is the only known way to guarantee that a system is free of programming errors. We present our experience in performing the formal, machinechecked verification of the seL4 microkernel from an abstract specification down to its C implementation. We assume correctness of compiler, assembly code, and hardware, and we used a unique design approach that fuses formal and operating systems techniques. To our knowledge, this is the first formal proof of functional correctness of a complete, generalpurpose operatingsystem kernel. Functional correctness means here that the implementation always strictly follows our highlevel abstract specification of kernel behaviour. This encompasses traditional design and implementation safety properties such as the kernel will never crash, and it will never perform an unsafe operation. It also proves much more: we can predict precisely how the kernel will behave in every possible situation. seL4, a thirdgeneration microkernel of L4 provenance, comprises 8,700 lines of C code and 600 lines of assembler. Its performance is comparable to other highperformance L4 kernels.
Formal verification of a realistic compiler
 Communications of the ACM
"... This paper reports on the development and formal verification (proof of semantic preservation) of CompCert, a compiler from Clight (a large subset of the C programming language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. ..."
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Cited by 173 (19 self)
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This paper reports on the development and formal verification (proof of semantic preservation) of CompCert, a compiler from Clight (a large subset of the C programming 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 critical software and its formal verification: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well. 1.
Engineering formal metatheory
 In ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 2008
"... Machinechecked proofs of properties of programming languages have become a critical need, both for increased confidence in large and complex designs and as a foundation for technologies such as proofcarrying code. However, constructing these proofs remains a black art, involving many choices in th ..."
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Cited by 116 (11 self)
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Machinechecked proofs of properties of programming languages have become a critical need, both for increased confidence in large and complex designs and as a foundation for technologies such as proofcarrying code. However, constructing these proofs remains a black art, involving many choices in the formulation of definitions and theorems that make a huge cumulative difference in the difficulty of carrying out large formal developments. The representation and manipulation of terms with variable binding is a key issue. We propose a novel style for formalizing metatheory, combining locally nameless representation of terms and cofinite quantification of free variable names in inductive definitions of relations on terms (typing, reduction,...). The key technical insight is that our use of cofinite quantification obviates the need for reasoning about equivariance (the fact that free names can be renamed in derivations); in particular, the structural induction principles of relations
Formal verification of a C compiler frontend
, 2006
"... This paper presents the formal verification of a compiler frontend that translates a subset of the C language into the Cminor intermediate language. The semantics of the source and target languages as well as the translation between them have been written in the specification language of the Coq pr ..."
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Cited by 73 (16 self)
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This paper presents the formal verification of a compiler frontend that translates a subset of the C language into the Cminor intermediate language. The semantics of the source and target languages as well as the translation between them have been written in the specification language of the Coq proof assistant. The proof of observational semantic equivalence between the source and generated code has been machinechecked using Coq. An executable compiler was obtained by automatic extraction of executable Caml code from the Coq specification of the translator, combined with a certified compiler backend generating PowerPC assembly code from Cminor, described in previous work.
Oracle semantics for concurrent separation logic
 In Proc. European Symp. on Programming (ESOP 2008
, 2008
"... Abstract. We define (with machinechecked proofs in Coq) a modular operational semantics for Concurrent C minor—a language with shared memory, spawnable threads, and firstclass locks. By modular we mean that one can reason about sequential control and dataflow knowing almost nothing about concurre ..."
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Cited by 73 (12 self)
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Abstract. We define (with machinechecked proofs in Coq) a modular operational semantics for Concurrent C minor—a language with shared memory, spawnable threads, and firstclass locks. By modular we mean that one can reason about sequential control and dataflow knowing almost nothing about concurrency, and one can reason about concurrency knowing almost nothing about sequential control and dataflow constructs. We present a Concurrent Separation Logic with firstclass locks and threads, and prove its soundness with respect to the operational semantics. Using our modularity principle, we proved the sequential C.S.L. rules (those inherited from sequential Separation Logic) simply by adapting Appel & Blazy’s machinechecked soundness proofs. Our Concurrent C minor operational semantics is designed to connect to Leroy’s optimizing (sequential) C minor compiler; we propose our modular semantics as a way to adapt Leroy’s compilercorrectness proofs to the concurrent setting. Thus we will obtain endtoend proofs: the properties you prove in Concurrent Separation Logic will be true of the program that actually executes on the machine. 1
Dependently typed programming in Agda
 In Lecture Notes from the Summer School in Advanced Functional Programming
, 2008
"... In HindleyMilner style languages, such as Haskell and ML, there is a clear separation between types and values. In a dependently typed language the line is more blurry – types can contain (depend on) arbitrary values and appear as arguments and results of ordinary functions. ..."
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Cited by 60 (1 self)
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In HindleyMilner style languages, such as Haskell and ML, there is a clear separation between types and values. In a dependently typed language the line is more blurry – types can contain (depend on) arbitrary values and appear as arguments and results of ordinary functions.
Ynot: Dependent types for imperative programs
 In Proceedings of ICFP 2008
, 2008
"... We describe an axiomatic extension to the Coq proof assistant, that supports writing, reasoning about, and extracting higherorder, dependentlytyped programs with sideeffects. Coq already includes a powerful functional language that supports dependent types, but that language is limited to pure, t ..."
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Cited by 55 (15 self)
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We describe an axiomatic extension to the Coq proof assistant, that supports writing, reasoning about, and extracting higherorder, dependentlytyped programs with sideeffects. Coq already includes a powerful functional language that supports dependent types, but that language is limited to pure, total functions. The key contribution of our extension, which we call Ynot, is the added support for computations that may have effects such as nontermination, accessing a mutable store, and throwing/catching exceptions. The axioms of Ynot form a small trusted computing base which has been formally justified in our previous work on Hoare Type Theory (HTT). We show how these axioms can be combined with the powerful type and abstraction mechanisms of Coq to build higherlevel reasoning mechanisms which in turn can be used to build realistic, verified software components. To substantiate this claim, we describe here a representative series of modules that implement imperative finite maps, including support for a higherorder (effectful) iterator. The implementations range from simple (e.g., association lists) to complex (e.g., hash tables) but share a common interface which abstracts the implementation details and ensures that the modules properly implement the finite map abstraction.
Coinductive bigstep operational semantics
, 2006
"... This paper illustrates the use of coinductive definitions and proofs in bigstep operational semantics, enabling the latter to describe diverging evaluations in addition to terminating evaluations. We show applications to proofs of type soundness and to proofs of semantic preservation for compilers ..."
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Cited by 45 (6 self)
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This paper illustrates the use of coinductive definitions and proofs in bigstep operational semantics, enabling the latter to describe diverging evaluations in addition to terminating evaluations. We show applications to proofs of type soundness and to proofs of semantic preservation for compilers.
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java ..."
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Cited by 44 (21 self)
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This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higherorder logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables
Parametric HigherOrder Abstract Syntax for Mechanized Semantics
, 2008
"... We present parametric higherorder abstract syntax (PHOAS), a new approach to formalizing the syntax of programming languages in computer proof assistants based on type theory. Like higherorder abstract syntax (HOAS), PHOAS uses the meta language’s binding constructs to represent the object language ..."
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Cited by 43 (3 self)
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We present parametric higherorder abstract syntax (PHOAS), a new approach to formalizing the syntax of programming languages in computer proof assistants based on type theory. Like higherorder abstract syntax (HOAS), PHOAS uses the meta language’s binding constructs to represent the object language’s binding constructs. Unlike HOAS, PHOAS types are definable in generalpurpose type theories that support traditional functional programming, like Coq’s Calculus of Inductive Constructions. We walk through how Coq can be used to develop certified, executable program transformations over several staticallytyped functional programming languages formalized with PHOAS; that is, each transformation has a machinechecked proof of type preservation and semantic preservation. Our examples include CPS translation and closure conversion for simplytyped lambda calculus, CPS translation for System F, and translation from a language with MLstyle pattern matching to a simpler language with no variablearity binding constructs. By avoiding the syntactic hassle associated with firstorder representation techniques, we achieve a very high degree of proof automation.