Proof Obligations Sample Clauses

Proof Obligations. For a combination of a flow and machine we would like to be able to demonstrate that the flow is consistent or concrete (the latter requires the former). The general strategy is split an overall proof into a collection of simpler conditions. For flow consistency, a suitable way to do this is to analyse each instance of sequential composition individually as suggested by the condition of Theorem 1 (see Definition 6 for operator cons). For an instance of a sequential composition, from Definition 5 we have the following feasibility condition for a composed event. I(v) ∧ G(p, v) ▶ ∃v' · (S(p, v, v'); (∃q · H(q, v) ∧ R(q, v, v'))) ▶ ∃ · ∧ ∃ · ∧ ' v1 (S(p, v, v1) q H(q, v1) R(q, v1, v ))) The condition is far too complex in the current form. A more compact one could be found. Let us first assume that the composed events are feasible on their own. This gives the following two axioms. axm1 : I(v) ∧ G(p, v) ▶ ∃v' · S(p, v, v') ∧ ▶ ∃ · ' ' axm2 : I(v) H(q, v) v R(q, v, v ) Applying axiom axm1, the feasibility condition for a composed event is sim- plified to the following: I(v) ∧ G(p, v) ∧ S(p, v, v1) ▶ ∃ q · H(q, v1) ∧ R(q, v1, v') With the help of the second axiom we are able to remove R(q, v1, v′) clause from the goal: ∧ ∧ ▶ ∃ · I(v) G(p, v) S(p, v, v1) q H(q, v1) Finally, extending the above with the consideration of model constants and sets, the following proof obligation is formulated. P (c, s) ∧ I(c, s, v) ∧ G(c, s, pe, v) ∧ S(c, s, pe, v, v') ▶ H(c, s, q, v) Here G and S are the guard and before-after predicate (actions) of what is possibly a result of merging several model events. The proof obligation demon- strates that an event characterised by G and S is able to pass control to another (possibly merged) event with guard H for any possible state permitted by G. The axioms we have rely upon are sound since they are a part of model consistency proof obligations that are to be discharge for every Event-B model[3]. With a similar procedure we are able to find a practical form of a proof obli- gation for demonstrating that a flow is concrete. The following proof obligation requires that for a given instance p; q of a sequential composition the choice branches in q, if there any, are mutually exclusive. P (c, s) ∧ I(c, s, v) ∧ G(c, s, p, v) ∧ S(c, s, p, v, v') ▶ {s,t}∈EN(q)∧s/=t ¬(Hs(c, s, qs, v') ∧ Ht(c, s, qt, v')) Here Hs and Ht are the guards of possibly merged events. The goal in this proof obligation may become lengthy in some extreme case when there is a...
Sample 1
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Proof Obligations. For a combination of a flow and machine we would like to be able to demonstrate that the flow is consistent or concrete (the latter requires the former). The general strategy is split an overall proof into a collection of simpler conditions. For flow consistency, a suitable way to do this is to analyse each instance of sequential composition individually as suggested by the condition of Theorem 1 (see Definition 6 for oper- ator cons). For an instance of a sequential composition, from Definition 5 we have the following feasibility condition for a composed event. A ▶ I(v) G(p, v) I · I · A ▶ vr (S(p, v, vr); ( q H(q, v) R(q, v, vr))) I · A I · A v1 (S(p, v, v1) q H(q, v1) R(q, v1, vr))) The condition is far too complex in the current form. A more compact one could be found. Let us first assume that the composed events are feasible on their own. This gives the following two axioms. A ▶ I · axm1 : I(v) G(p, v) vr S(p, v, vr) A ▶ I · axm2 : I(v) H(q, v) vr R(q, v, vr) Applying axiom axm1, the feasibility condition for a composed event is simplified to the following: I(v) AG(p, v) AS(p, v, v1) ▶ I q · H(q, v1) AR(q, v1, vr) With the help of the second axiom we are able to remove R(q, v1, vr) clause from the goal: I(v) AG(p, v) AS(p, v, v1) ▶ I q · H(q, v1) Finally, extending the above with the consideration of model constants and sets, the follow- ing proof obligation is formulated. P(c, s) AI(c, s, v) AG(c, s, pe, v) AS(c, s, pe, v, vr) ▶ H(c, s, q, v) Here G and S are the guard and before-after predicate (actions) of what is possibly a result of merging several model events. The proof obligation demonstrates that an event characterised by G and S is able to pass control to another (possibly merged) event with guard H for any possible state permitted by G. The axioms we have rely upon are sound since they are a part of model consistency proof obligations that are to be discharge for every Event-B model[3]. With a similar procedure we are able to find a practical form of a proof obligation for demon- strating that a flow is concrete. The following proof obligation requires that for a given instance p; q of a sequential composition the choice branches in q, if there any, are mutually exclusive. V r r(H (c s q v ) H (c s q v )) P(c, s) AI(c, s, v) AG(c, s, p, v) AS(c, s, p, v, vr) ▶ {s,t}∈EN(q)As/=t ч s , , s, A t , , t , Here Hs and Ht are the guards of possibly merged events. The goal in this proof obligation may become lengthy in some extreme case when there i...
Sample 1
Proof Obligations. In the second application (start/stop system) we started not with a requirement set, we developed the needed requirements by ourselves. We did not produce a comparable chart to the one for the cruise control system. In the second pilot we were more interested in gathering evidence that the proof obligations, which arise using Event-B, are manageable.
Sample 1
Proof Obligations. Compatible Parallel Composition From components with verified contract compliance, we now compose systems and provide safety guarantees about them, without redoing system proofs. For L
Sample 1

Related to Proof Obligations

  • Payment of Obligations Pay, discharge or otherwise satisfy at or before maturity or before they become delinquent, as the case may be, all its material obligations of whatever nature, except where the amount or validity thereof is currently being contested in good faith by appropriate proceedings and reserves in conformity with GAAP with respect thereto have been provided on the books of the Borrower or its Subsidiaries, as the case may be.

  • Fulfilment of Obligations The Parties shall take any general or specific measures required to fulfil their obligations under this Agreement.

  • Extent of Obligations The Parties shall ensure that all necessary measures are taken in order to give effect to the provisions of this Agreement in their respective territories, including ensuring that their respective regional and local governments and authorities, and non- governmental bodies in the exercise of governmental powers delegated to them by central, regional and local governments or authorities observe all obligations and commitments under this Agreement.

  • Compliance Obligations All GE employees are obligated to comply with the requirements — the “letter”— of the Company’s compliance policies set forth in the Spirit & Letter. These policies implement the GE Code of Conduct and are supplemented by compliance procedures and guidelines adopted by GE components. A summary of some of the key compliance obligations of GE employees follows: IMPROPER PAYMENTS • Always adhere to the highest standards of honesty and integrity in all contacts on behalf of GE. Never offer bribes, kickbacks, illegal political contributions or other improper payments to any customer, government official or third party. Follow the laws of the United States and other countries relating to these matters. • Do not give significant gifts or provide any extravagant entertainment to a customer or supplier without GE management approval. Make sure all business entertainment and gifts are lawful and disclosed to the other party’s employer. • Employ only reputable people and firms as GE representatives and understand and obey any requirements governing the use of third party representatives. INTERNATIONAL TRADE CONTROLS • Understand and follow applicable international trade control and customs laws and regulations, including those relating to licensing, shipping and import documentation and reporting and record retention requirements. • Never participate in boycotts or other restrictive trade practices prohibited or penalized under United States or applicable local laws. • Make sure all transactions are screened in accordance with applicable export/import requirements; and that any apparent conflict between U.S. and applicable local law requirements, such as the laws blocking certain U.S. restrictions adopted by Canada, Mexico and the members of the European Union, is disclosed to GE counsel. MONEY LAUNDERING PREVENTION • Follow all applicable laws that prohibit money laundering and that require the reporting of cash or other suspicious transactions. • Learn to identify warning signs that may indicate money laundering or other illegal activities or violations of GE policies. Raise any concerns to GE counsel and GE management. PRIVACY • Never acquire, use or disclose individual consumer information in ways that are inconsistent with GE privacy policies or with applicable privacy and data protection laws, regulations and treaties. • Maintain secure business records of individual consumer information, including computer-based information. SUPPLIER RELATIONSHIPS • Only do business with suppliers who comply with local and other applicable legal requirements and any additional GE standards relating to labor, environment, health and safety, intellectual property rights and improper payments. • Follow applicable laws and government regulations covering supplier relationships. • Provide a competitive opportunity for suppliers to earn a share of GE’s purchasing volume, including small businesses and businesses owned by the disadvantaged, minorities and women. WORKING WITH GOVERNMENTS • Follow applicable laws and regulations associated with government contracts and transactions. • Require any supplier providing goods or services for GE on a government project or contract to agree to comply with the intent of GE’s Working with Governments policy. • Be truthful and accurate when dealing with government officials and agencies. COMPLYING WITH COMPETITION LAWS • Never propose or enter into any agreement with a GE competitor to fix prices, terms and conditions of sale, costs, profit margins, or other aspects of the competition for sales to third parties. • Do not propose or enter into any agreements or understandings with GE customers restricting resale prices. • Never propose or enter into any agreements or understandings with suppliers which restrict the price or other terms at which GE may resell or lease any product or service to a third party. ENVIRONMENT, HEALTH & SAFETY • Learn how to conduct your activities in compliance with all relevant environmental and worker health and safety laws and regulations and conduct your activities accordingly. • Ensure that all new product designs or changes or services offerings are reviewed for compliance with GE guidelines. • Use care in handling hazardous materials or operating processes or equipment that use hazardous materials to prevent unplanned releases into the workplace or the environment. • Report to GE management all spills of hazardous materials; any concern that GE products are unsafe; and any potential violation of environmental, health or safety laws, regulations or company practices or requests to violate established EHS procedures. FAIR EMPLOYMENT PRACTICES • Extend equal opportunity, fair treatment and a harassment-free work environment to all employees, co-workers, consultants and other business associates without regard to their race, color, religion, national origin, sex (including pregnancy), sexual orientation, age, disability, veteran status or other characteristic protected by law. CONFLICTS OF INTEREST • Financial, business, or other non-work related activities must be lawful and free of conflicts with one’s responsibilities to GE. • Report all personal or family relationships, including those of significant others, with current or prospective suppliers you select, manage or evaluate. • Do not use GE equipment, information or other property (including office equipment, e-mail and computer applications) to conduct personal or non-GE business without prior permission from the appropriate GE manager. CONTROLLERSHIP • Keep and report all GE records, including any time records, in an accurate, timely, complete, and confidential manner. Only release GE records to third parties when authorized by GE. • Follow GE’s General Accounting Procedures (GAP), as well as all generally accepted accounting principles, standards, laws and regulations for accounting and financial reporting of transactions, estimates and forecasts. • Financial statements and reports prepared for or on behalf of GE (including any component) must fairly present the financial position, results of operations, and/or other financial data for the periods and/or the dates specified. XXXXXXX XXXXXXX OR DEALING & STOCK TIPPING • Never buy, sell or suggest to someone else that they should buy or sell stock or other securities of any company (including GE) while you are aware of significant or material non-public information (inside information) about that company. Information is significant or material when it is likely that an ordinary investor would consider the information important in making an investment decision. • Do not pass on or disclose inside information unless necessary for the conduct of GE business — and never pass on or disclose such information if you suspect that the information will be used for an improper trading purpose. INTELLECTUAL PROPERTY • Identify and protect commercially significant GE intellectual property in ways consistent with the law. • Consult with GE counsel in advance of soliciting, accepting or using proprietary information of outsiders, disclosing GE proprietary information to outsiders or permitting third parties to use GE intellectual property. • Respect valid patents, copyrighted materials and other protected intellectual property of others; and consult with GE counsel for licenses or approvals to use such intellectual property.

  • Performance of Obligations The Company shall have performed and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before the Closing.

  • Termination of Obligations Termination of this Agreement pursuant to Section 10.1 hereof shall terminate all obligations of the parties hereunder, except for the obligations under Article IX, Article X, and Sections 11.4, 11.7, 11.14, 11.15 and 11.16 hereof; provided, however, that termination pursuant to paragraphs (b) or (c) of Section 10.1 shall not relieve the defaulting or breaching party or parties from any liability to the other parties hereto.

  • Discharge of Obligations If at any time all such Securities of a particular series not heretofore delivered to the Trustee for cancellation or that have not become due and payable as described in Section 11.01 shall have been paid by the Company by depositing irrevocably with the Trustee as trust funds moneys or an amount of Governmental Obligations sufficient to pay at maturity or upon redemption all such Securities of that series not theretofore delivered to the Trustee for cancellation, including principal (and premium, if any) and interest due or to become due to such date of maturity or date fixed for redemption, as the case may be, and if the Company shall also pay or cause to be paid all other sums payable hereunder by the Company with respect to such series, then after the date such moneys or Governmental Obligations, as the case may be, are deposited with the Trustee the obligations of the Company under this Indenture with respect to such series shall cease to be of further effect except for the provisions of Sections 2.03, 2.05, 2.07, 4,01, 4.02, 4,03, 7.06, 7.10 and 11.05 hereof that shall survive until such Securities shall mature and be paid. Thereafter, Sections 7.06 and 11.05 shall survive.

  • Provider Obligations Provider at all times during the term of this Agreement shall:

  • Duration of Obligations The Manager’s obligation to provide Disentanglement Services will continue during the period commencing on the date that a Termination Notice is delivered and ending on the date on which the Successor Manager or the re-engaged Manager assumes all of the obligations of the Manager hereunder (the “Disentanglement Period”).

  • Client Obligations 3.1 The Client shall:

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