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Towards Formal Proof Metrics [PDF]
Lecture Notes in Computer Science, 2016 Recent years have seen increasing success in building large formal proof developments using interactive theorem provers (ITPs). Some proofs have involved many authors, years of effort, and resulted in large, complex interdependent sets of proof “source code” files. Developing these in the first place, and maintaining and extending them afterwards, is a
Cezary Kaliszyk
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BIT, 1994
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A Formal Proof Generator from Semi-formal Proof Documents
2017We present the CafeInMaude Proof Assistant (CiMPA) and the CafeInMaude Proof Generator (CiMPG), two complementary extensions of CafeInMaude, a CafeOBJ interpreter implemented in Maude. CiMPA is a proof assistant for inductive properties of CafeOBJ specifications, and CiMPG generates formal proofs that can be fed into CiMPA from semi-formal proof ...
Adrián Riesco, Kazuhiro Ogata
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2012
The goal of the lecture is to present some aspects of formal security proofs of protocols. This is a wide area, and there is another lecture (by B. Banchet) on related topics. The idea is therefore to explain in depth one particular technique, that relies on deducibility constraints. We rely mainly on two introductory documents [8,14].
Comon-Lundh Hubert +1 more
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The goal of the lecture is to present some aspects of formal security proofs of protocols. This is a wide area, and there is another lecture (by B. Banchet) on related topics. The idea is therefore to explain in depth one particular technique, that relies on deducibility constraints. We rely mainly on two introductory documents [8,14].
Comon-Lundh Hubert +1 more
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2008
We address two questions: what is the use of formal proofs? how do we proceed from a formal proof to a computation?
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We address two questions: what is the use of formal proofs? how do we proceed from a formal proof to a computation?
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A Formal Proof of Pick’s Theorem
Mathematical Structures in Computer Science, 2010Pick's Theorem relates the area of a simple polygon with vertices at integer lattice points to the number of lattice points in its inside and boundary. We describe a formal proof of this theorem using the HOL Light theorem prover. As sometimes happens for highly geometrical proofs, the formalisation turned out to be more work than initially expected ...
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2014
Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive ...
Nederpelt, R., Geuvers, H.
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Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive ...
Nederpelt, R., Geuvers, H.
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Formal Proofs and Decidibility
1996In order to demonstrate the consistency of certain axiom systems, Hilbert makes use of a theory of mathematical proof in which the proof must be thought of as rigorously formalized in concrete symbols (see Hilbert [1922], [1923], [1926], Bernays [1922], Ackermann [1924]).
David Booth, Renatus Ziegler
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2008
The need to integrate the processes of programming and program verification requires notations for formal proofs that are easily readable. We discuss this problem in the context of Hoare logic and separation logic. It has long been the custom to describe formal proofs in these logics informally by means of "annotated specifications" or "proof ...
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The need to integrate the processes of programming and program verification requires notations for formal proofs that are easily readable. We discuss this problem in the context of Hoare logic and separation logic. It has long been the custom to describe formal proofs in these logics informally by means of "annotated specifications" or "proof ...
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FORMAL PROOFS OF FUNCTIONAL BSP PROGRAMS
Parallel Processing Letters, 2003The Bulk Synchronous Parallel ML (BSML) is a functional language for BSP programming, a model of computing which allows parallel programs to be ported to a wide range of architectures. It is based on an extension of the ML language by parallel operations on a parallel data structure called parallel vector, which is given by intention. We present a new
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