Formal proof of a program: Find

Mudiam, Sudhakiran V.; Gannod, Gerald C.; Lindquist, Timothy E.

doi:10.1016/j.scico.2006.10.002

Cited by 8 publications

(3 citation statements)

References 6 publications

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“…However, the correctness of the implementation must be checked, e.g. in the spirit of [13]. Another promising way is the extraction of certified functional programs from our constructive proofs [5].…”

Section: Resultsmentioning

confidence: 99%

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An Intuitionistic Proof of a Discrete Form of the Jordan Curve Theorem Formalized in Coq with Combinatorial Hypermaps

Dufourd

2009

J Autom Reasoning

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This paper presents a completely formalized proof of a discrete form of the Jordan Curve Theorem. It is based on a hypermap model of planar subdivisions, formal specifications and proofs assisted by the Coq system. Fundamental properties are proven by structural or noetherian induction: Genus Theorem, Euler Formula, constructive planarity criteria. A notion of ring of faces is inductively defined and a Jordan Curve Theorem is stated and proven for any planar hypermap.

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Section: Resultsmentioning

confidence: 99%

“…In Fig. 1, the (internal) face of 5 is φ (5) = (5, 1) and the (external) face of 13 is φ (13) = (13,14). Let d, e, v, f and c be the numbers of darts, edges, vertices, faces and components of M.…”

Section: Definition 2 (Orbits and Hypermap Cells)mentioning

confidence: 99%

An Intuitionistic Proof of a Discrete Form of the Jordan Curve Theorem Formalized in Coq with Combinatorial Hypermaps

Dufourd

2009

J Autom Reasoning

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“…• In his paper [Hoa71b] concerned with the correctness of the FIND program, Hoare expressed the desire for computer support in "formulating the lemmas, and perhaps even checking the proofs." Only much later, Filliâtre [Fil07] published a mechanized proof of FIND using the interactive theorem prover Coq and following Hoare's proof from [Hoa71b] as closely as possible. He noticed that Hoare's informal termination proof does not meet the requirements of a termination function in the sense that the additional invariants used by Hoare are not real invariants.…”

Section: Final Remarks: a Summary And An Assessmentmentioning

confidence: 99%