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32
Some lambda calculus and type theory formalized
 Journal of Automated Reasoning
, 1999
"... Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention ..."
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Cited by 61 (9 self)
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Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point out what we feel has been learned about general issues of formalizing mathematics, emphasizing the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts.
Mobile Resource Guarantees for Smart Devices
 Proceedings of CASSIS’04, LNCS
, 2005
"... Abstract. We present the Mobile Resource Guarantees framework: a system for ensuring that downloaded programs are free from runtime violations of resource bounds. Certificates are attached to code in the form of efficiently checkable proofs of resource bounds; in contrast to cryptographic certifica ..."
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Cited by 55 (6 self)
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Abstract. We present the Mobile Resource Guarantees framework: a system for ensuring that downloaded programs are free from runtime violations of resource bounds. Certificates are attached to code in the form of efficiently checkable proofs of resource bounds; in contrast to cryptographic certificates of code origin, these are independent of trust networks. A novel programming language with resource constraints encoded in function types is used to streamline the generation of proofs of resource usage. 1
Automatic Certification of Heap Consumption
 In LPAR’04, LNAI 3452
, 2005
"... Abstract. We present a program logic for verifying the heap consumption of lowlevel programs. The proof rules employ a uniform assertion format and have been derived from a general purpose program logic [1]. In a proofcarrying code scenario, the inference of invariants is delegated to the code pro ..."
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Cited by 27 (15 self)
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Abstract. We present a program logic for verifying the heap consumption of lowlevel programs. The proof rules employ a uniform assertion format and have been derived from a general purpose program logic [1]. In a proofcarrying code scenario, the inference of invariants is delegated to the code provider, who employs a certifying compiler that generates a certificate from program annotations and analysis. The granularity of the proof rules matches that of the linear type system presented in [6], which enables us to perform verification by replaying typing derivations in a theorem prover, given the specifications of individual methods. The resulting verification conditions are of limited complexity, and are automatically discharged. We also outline a proof system that relaxes the linearity restrictions and relates to the type system of usage aspects presented in [2]. 1
Hoare logic for NanoJava: Auxiliary variables, side effects and virtual methods revisited
 Formal Methods – Getting IT Right (FME’02). LNCS 2391
, 2002
"... 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 ..."
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Cited by 21 (2 self)
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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 sideeffecting 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.
Hoare Logics in Isabelle/HOL
 PROOF AND SYSTEMRELIABILITY
, 2002
"... This paper describes Hoare logics for a number of imperative language constructs, from whileloops 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 ..."
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Cited by 21 (2 self)
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This paper describes Hoare logics for a number of imperative language constructs, from whileloops 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.
A Program Logic for Resource Verification
 In Proceedings of the 17th International Conference on Theorem Proving in HigherOrder Logics, (TPHOLs 2004), volume 3223 of LNCS
, 2004
"... We present a program logic for reasoning about resource consumption of programs written in Grail, an abstract fragment of the Java Virtual Machine Language. Serving as the target logic of a certifying compiler, the logic exploits Grail's dual nature of combining a functional interpretation w ..."
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Cited by 19 (9 self)
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We present a program logic for reasoning about resource consumption of programs written in Grail, an abstract fragment of the Java Virtual Machine Language. Serving as the target logic of a certifying compiler, the logic exploits Grail's dual nature of combining a functional interpretation with objectoriented features and a cost model for the JVM. We present the resourceaware operational semantics of Grail, the program logic, and prove soundness and completeness. All of the work described has been formalised in the theorem prover Isabelle/HOL, which provides us with an implementation of the logic as well as confidence in the results. We conclude with examples of using the logic for proving resource bounds on code resulting from compiling highlevel functional programs.
Secure information flow and program logics
 In IEEE Computer Security Foundations Symposium
, 2007
"... We present interpretations of type systems for secure information flow in Hoare logic, complementing previous encodings in binary (e.g. relational) program logics. Treating baseline noninterference, multilevel security and flow sensitivity for a while language, we show how typing derivations may ..."
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Cited by 18 (6 self)
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We present interpretations of type systems for secure information flow in Hoare logic, complementing previous encodings in binary (e.g. relational) program logics. Treating baseline noninterference, multilevel security and flow sensitivity for a while language, we show how typing derivations may be used to automatically generate proofs in the program logic that certify the absence of illicit flows. In addition, we present proof rules for baseline noninterference for objectmanipulating instructions, As a consequence, standard verification technology may be used for verifying that a concrete program satisfies the noninterference property. Our development is based on a formalisation of the encodings in Isabelle/HOL. 1
Hoare Logic for Mutual Recursion and Local Variables
 Foundations of Software Technology and Theoretical Computer Science, volume 1738 of LNCS
, 1999
"... We present a (the first?) sound and relatively complete Hoare logic for a simple imperative programming language including mutually recursive procedures with callbyvalue parameters as well as global and local variables. For such a language we formalize an operational and an axiomatic semantics ..."
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Cited by 15 (1 self)
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We present a (the first?) sound and relatively complete Hoare logic for a simple imperative programming language including mutually recursive procedures with callbyvalue parameters as well as global and local variables. For such a language we formalize an operational and an axiomatic semantics of partial correctness and prove their equivalence.
Weakest Precondition for General Recursive Programs Formalized in Coq
, 2002
"... This paper describes a formalization of the weakest precondition, wp, for general recursive programs using the typetheoretical proof assistant Coq. The formalization is a deep embedding using the computational power intrinsic to type theory. Since Coq accepts only structural recursive functions, th ..."
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Cited by 4 (1 self)
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This paper describes a formalization of the weakest precondition, wp, for general recursive programs using the typetheoretical proof assistant Coq. The formalization is a deep embedding using the computational power intrinsic to type theory. Since Coq accepts only structural recursive functions, the computational embedding of general recursive programs is nontrivial. To justify the embedding, an operational semantics is defined and the equivalence between wp and the operational semantics is proved. Three major healthiness conditions, namely: Strictness, Monotonicity and Conjunctivity are proved as well.
Relational decomposition
 In 2nd ITP, volume 6898 of LNCS
, 2011
"... Abstract. We introduce relational decomposition, a technique for formally reducing terminationinsensitive relational program logics to unary logics, that is program logics for oneexecution properties. Generalizing the approach of selfcomposition, we develop a notion of interpolants that decompose ..."
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Cited by 3 (1 self)
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Abstract. We introduce relational decomposition, a technique for formally reducing terminationinsensitive relational program logics to unary logics, that is program logics for oneexecution properties. Generalizing the approach of selfcomposition, we develop a notion of interpolants that decompose along the phrase structure, and relate these interpolants to unary and relational predicate transformers. In contrast to previous formalisms, relational decomposition is applicable across heterogeneous pairs of transition systems. We apply our approach to justify variants of Benton’s Relational Hoare Logic (RHL) for a language with objects, and present novel rules for relating loops that fail to proceed in lockstep. We also outline applications to noninterference and separation logic. 1