Forward and backward simulations I.: untimed systems
Information and Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Craft of Programming
Separation Logic: A Logic for Shared Mutable Data Structures
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Simple relational correctness proofs for static analyses and program transformations
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Theoretical Computer Science
Secure Microkernels, State Monads and Scalable Refinement
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
A Formally Verified Compiler Back-end
Journal of Automated Reasoning
Verified just-in-time compiler on x86
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Hoare logic for realistically modelled machine code
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
An approach to formal verification of arithmetic functions in assembly
ASIAN'06 Proceedings of the 11th Asian computing science conference on Advances in computer science: secure software and related issues
A kripke logical relation between ML and assembly
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Modern Computer Arithmetic
Flocq: A Unified Library for Proving Floating-Point Algorithms in Coq
ARITH '11 Proceedings of the 2011 IEEE 20th Symposium on Computer Arithmetic
A machine-checked framework for relational separation logic
SEFM'11 Proceedings of the 9th international conference on Software engineering and formal methods
Formal verification of the heap manager of an operating system using separation logic
ICFEM'06 Proceedings of the 8th international conference on Formal Methods and Software Engineering
A compositional logic for control flow
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
On construction of a library of formally verified low-level arithmetic functions
Proceedings of the 27th Annual ACM Symposium on Applied Computing
Certifying assembly with formal security proofs: The case of BBS
Science of Computer Programming
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
Towards formal verification of TLS network packet processing written in C
PLPV '13 Proceedings of the 7th workshop on Programming languages meets program verification
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Arithmetic functions are used in many important computer programs such as computer algebra systems and cryptographic software. The latter are critical applications whose correct implementation deserves to be formally guaranteed. They are also computation-intensive applications, so that programmers often resort to low-level assembly code to implement arithmetic functions. We propose an approach for the construction of a library of formally verified low-level arithmetic functions. To build our library, we first introduce a formalization of data structures for signed multi-precision arithmetic in low-level programs. We use this formalization to verify the implementation of several primitive arithmetic functions using Separation logic, an extension of Hoare logic to deal with pointers. Since this direct style of formal verification leads to technically involved specifications, we also propose for larger functions to show a formal simulation relation between pseudo-code and assembly. This style of verification is illustrated with a concrete implementation of the binary extended gcd algorithm.