Industrial Standards, Computer Algebra,                               and Formal Verification                    Dominik Di...
The Flange  A CAD design of a flange-bolt-gasket system.Industrial Standards, and Formal Verification    German Research Cen...
The Industrial Standard EN 1591  A standard for gasketed circular  flange connections  The standard consists of    Applicab...
The Industrial Standard EN 1591  A standard for gasketed circular  flange connections  The standard consists of    Applicab...
The Industrial Standard EN 1591  A standard for gasketed circular  flange connections  The standard consists of    Applicab...
The Industrial Standard EN 1591  A standard for gasketed circular  flange connections  The standard consists of    Applicab...
The Industrial Standard EN 1591    cont.  The input parameters to the calculation method      Flange data, e.g., dimension...
The Industrial Standard EN 1591    cont.  The input parameters to the calculation method      Flange data, e.g., dimension...
The Industrial Standard EN 1591    cont.  The input parameters to the calculation method      Flange data, e.g., dimension...
Calculation Method and IterationIndustrial Standards, and Formal Verification   German Research CenterD. Dietrich, L. Schr¨...
Calculation Method and IterationIndustrial Standards, and Formal Verification   German Research CenterD. Dietrich, L. Schr¨...
Calculation Method and IterationIndustrial Standards, and Formal Verification   German Research CenterD. Dietrich, L. Schr¨...
Calculation Method and IterationIndustrial Standards, and Formal Verification   German Research CenterD. Dietrich, L. Schr¨...
Calculation Method and MaximizeIndustrial Standards, and Formal Verification   German Research CenterD. Dietrich, L. Schr¨d...
Calculation Method and MaximizeIndustrial Standards, and Formal Verification   German Research CenterD. Dietrich, L. Schr¨d...
Calculation Method and MaximizeIndustrial Standards, and Formal Verification   German Research CenterD. Dietrich, L. Schr¨d...
Calculation Method and MaximizeIndustrial Standards, and Formal Verification   German Research CenterD. Dietrich, L. Schr¨d...
Calculation Method    and Computer Algebra  The formulas occurring in the standard can be calculated using      Standard r...
Calculation Method    and Computer Algebra  The formulas occurring in the standard can be calculated using      Standard r...
Calculation Method    and Computer Algebra  The formulas occurring in the standard can be calculated using      Standard r...
Calculation Method    and Computer Algebra  The formulas occurring in the standard can be calculated using      Standard r...
Calculation Method    and Computer Algebra  The formulas occurring in the standard can be calculated using      Standard r...
Formal Verification  Correctness of calculations crucial for application to safety critical  environments      CASs do not ...
Formal Verification  Correctness of calculations crucial for application to safety critical  environments      CASs do not ...
Formal Verification  Correctness of calculations crucial for application to safety critical  environments      CASs do not ...
Formal Verification  Correctness of calculations crucial for application to safety critical  environments      CASs do not ...
Hets- the Heterogeneous Tool SetIndustrial Standards, and Formal Verification   German Research CenterD. Dietrich, L. Schr¨...
Specification Language CSL  Design goals of CSL      Formal specification of the calculation method      Specification of ass...
Specification Language CSL  Design goals of CSL      Formal specification of the calculation method      Specification of ass...
Specification Language CSL  Design goals of CSL      Formal specification of the calculation method      Specification of ass...
Specification Language CSL  Design goals of CSL      Formal specification of the calculation method      Specification of ass...
Specification Language CSL  Design goals of CSL      Formal specification of the calculation method      Specification of ass...
Specification Language CSL  Design goals of CSL      Formal specification of the calculation method      Specification of ass...
A Little CSL Example  Calculating a root of cos using Newton’s Method     The CSL specification       y := cos(x) %(A)%    ...
A Little CSL Example  Calculating a root of cos using Newton’s Method     The CSL specification                      Buildi...
A Little CSL Example  Calculating a root of cos using Newton’s Method     The CSL specification                      Buildi...
A Little CSL Example  Calculating a root of cos using Newton’s Method     The CSL specification                      Buildi...
A Little CSL Example  Calculating a root of cos using Newton’s Method     The CSL specification                      Buildi...
A Little CSL Example  Calculating a root of cos using Newton’s Method     The CSL specification                      Buildi...
Verified CAS  Verification Points in CSL      are positions of subterms of CSL statements      Evaluating a such marked term...
Verified CAS  Verification Points in CSL      are positions of subterms of CSL statements      Evaluating a such marked term...
Verified CAS  Verification Points in CSL      are positions of subterms of CSL statements      Evaluating a such marked term...
Verified CAS  Verification Points in CSL      are positions of subterms of CSL statements      Evaluating a such marked term...
Verified CAS  Verification Points in CSL      are positions of subterms of CSL statements      Evaluating a such marked term...
Verified CAS  Verification Points in CSL      are positions of subterms of CSL statements      Evaluating a such marked term...
Example  Verifying a result from the CAS   A CAS program                               We set verification point at maximiz...
Example  Verifying a result from the CAS   A CAS program                               We set verification point at maximiz...
Example  Verifying a result from the CAS   A CAS program                               We set verification point at maximiz...
Example  Verifying a result from the CAS   A CAS program                               We set verification point at maximiz...
Example  Verifying a result from the CAS   A CAS program                               We set verification point at maximiz...
Example  Verifying a result from the CAS   A CAS program                               We set verification point at maximiz...
CSL, CAS and Hets  CSL and the Hets Logic Graph                                                   Logic Graph   Isabelle P...
CSL, CAS and Hets  CSL and the Hets Logic Graph                                                   Logic Graph   Isabelle P...
CSL, CAS and Hets  CSL and the Hets Logic Graph                                                   Logic Graph   Isabelle P...
CSL, CAS and Hets  CSL and the Hets Logic Graph                                                   Logic Graph   Isabelle P...
CSL, CAS and Hets cont.  The CSL institution      Signatures are collections of real constants and functions over the real...
CSL, CAS and Hets cont.  The CSL institution      Signatures are collections of real constants and functions over the real...
CSL, CAS and Hets cont.  The CSL institution      Signatures are collections of real constants and functions over the real...
CSL, CAS and Hets cont.  The CSL institution      Signatures are collections of real constants and functions over the real...
CSL, CAS and Hets cont.  The CSL institution      Signatures are collections of real constants and functions over the real...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
Summary and Outlook      Specification language CSL for industrial standards      Synthesis of programs for generic CAS int...
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Industrial Standards, Computer Algebra, and Formal Veri cation

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We develop a language for specification of engineering calculations (EnCL, previously CSL) and apply it to formalize the industrial standard EN1591 concerning gasketed circular flange connections. We furthermore present a methodology how to carry out such specified calculations using a computer algebra system. The results are verified using theorem provers connected to the Hets system. In order to do so we define an institution for EnCL.

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Industrial Standards, Computer Algebra, and Formal Veri cation

  1. 1. Industrial Standards, Computer Algebra, and Formal Verification Dominik Dietrich Lutz Schr¨der o Ewaryst Schulz DFKI Bremen, Germany ewaryst.schulz@dfki.de 20th International Workshop on Algebraic Development Techniques Schloss Etelsen, Germany 4th July 2010Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  2. 2. The Flange A CAD design of a flange-bolt-gasket system.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  3. 3. The Industrial Standard EN 1591 A standard for gasketed circular flange connections The standard consists of Applicability and basic assumptions Nomenclature Calculation method The calculation method assures the impermeability and mechanical strength of the flange-bolt-gasket system.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  4. 4. The Industrial Standard EN 1591 A standard for gasketed circular flange connections The standard consists of Applicability and basic assumptions Nomenclature Calculation method The calculation method assures the impermeability and mechanical strength of the flange-bolt-gasket system.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  5. 5. The Industrial Standard EN 1591 A standard for gasketed circular flange connections The standard consists of Applicability and basic assumptions Nomenclature Calculation method The calculation method assures the impermeability and mechanical strength of the flange-bolt-gasket system.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  6. 6. The Industrial Standard EN 1591 A standard for gasketed circular flange connections The standard consists of Applicability and basic assumptions Nomenclature Calculation method The calculation method assures the impermeability and mechanical strength of the flange-bolt-gasket system.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  7. 7. The Industrial Standard EN 1591 cont. The input parameters to the calculation method Flange data, e.g., dimensions and material constants Mounting data such as screw tightening method Data for operating states such as pressure and temperatureIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  8. 8. The Industrial Standard EN 1591 cont. The input parameters to the calculation method Flange data, e.g., dimensions and material constants Mounting data such as screw tightening method Data for operating states such as pressure and temperatureIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  9. 9. The Industrial Standard EN 1591 cont. The input parameters to the calculation method Flange data, e.g., dimensions and material constants Mounting data such as screw tightening method Data for operating states such as pressure and temperatureIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  10. 10. Calculation Method and IterationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  11. 11. Calculation Method and IterationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  12. 12. Calculation Method and IterationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  13. 13. Calculation Method and IterationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  14. 14. Calculation Method and MaximizeIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  15. 15. Calculation Method and MaximizeIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  16. 16. Calculation Method and MaximizeIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  17. 17. Calculation Method and MaximizeIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  18. 18. Calculation Method and Computer Algebra The formulas occurring in the standard can be calculated using Standard real arithmetic √ Real functions such as cos, n , etc. Special functions such as maximize Control structures such as conditional statements and iteration Use a computer algebra system for the calculations.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  19. 19. Calculation Method and Computer Algebra The formulas occurring in the standard can be calculated using Standard real arithmetic √ Real functions such as cos, n , etc. Special functions such as maximize Control structures such as conditional statements and iteration Use a computer algebra system for the calculations.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  20. 20. Calculation Method and Computer Algebra The formulas occurring in the standard can be calculated using Standard real arithmetic √ Real functions such as cos, n , etc. Special functions such as maximize Control structures such as conditional statements and iteration Use a computer algebra system for the calculations.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  21. 21. Calculation Method and Computer Algebra The formulas occurring in the standard can be calculated using Standard real arithmetic √ Real functions such as cos, n , etc. Special functions such as maximize Control structures such as conditional statements and iteration Use a computer algebra system for the calculations.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  22. 22. Calculation Method and Computer Algebra The formulas occurring in the standard can be calculated using Standard real arithmetic √ Real functions such as cos, n , etc. Special functions such as maximize Control structures such as conditional statements and iteration Use a computer algebra system for the calculations.Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  23. 23. Formal Verification Correctness of calculations crucial for application to safety critical environments CASs do not provide justifications of calculations x x simplifies to 1 in the Reduce CAS Results of the CAS can be formally verified One can generate lemmas from CAS result to be proved Checking is easier than findingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  24. 24. Formal Verification Correctness of calculations crucial for application to safety critical environments CASs do not provide justifications of calculations x x simplifies to 1 in the Reduce CAS Results of the CAS can be formally verified One can generate lemmas from CAS result to be proved Checking is easier than findingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  25. 25. Formal Verification Correctness of calculations crucial for application to safety critical environments CASs do not provide justifications of calculations x x simplifies to 1 in the Reduce CAS Results of the CAS can be formally verified One can generate lemmas from CAS result to be proved Checking is easier than findingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  26. 26. Formal Verification Correctness of calculations crucial for application to safety critical environments CASs do not provide justifications of calculations x x simplifies to 1 in the Reduce CAS Results of the CAS can be formally verified One can generate lemmas from CAS result to be proved Checking is easier than findingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  27. 27. Hets- the Heterogeneous Tool SetIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  28. 28. Specification Language CSL Design goals of CSL Formal specification of the calculation method Specification of assignments in an arbitrary order, but: We require assignments to be unique and sortable w.r.t. the dependency order Generic interface to CAS Translation to CAS Suitably ordered assignments together with control structures form an imperative program Constants depending on constants which were modified are recomputed Executing the program using CAS yields a symbolic valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  29. 29. Specification Language CSL Design goals of CSL Formal specification of the calculation method Specification of assignments in an arbitrary order, but: We require assignments to be unique and sortable w.r.t. the dependency order Generic interface to CAS Translation to CAS Suitably ordered assignments together with control structures form an imperative program Constants depending on constants which were modified are recomputed Executing the program using CAS yields a symbolic valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  30. 30. Specification Language CSL Design goals of CSL Formal specification of the calculation method Specification of assignments in an arbitrary order, but: We require assignments to be unique and sortable w.r.t. the dependency order Generic interface to CAS Translation to CAS Suitably ordered assignments together with control structures form an imperative program Constants depending on constants which were modified are recomputed Executing the program using CAS yields a symbolic valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  31. 31. Specification Language CSL Design goals of CSL Formal specification of the calculation method Specification of assignments in an arbitrary order, but: We require assignments to be unique and sortable w.r.t. the dependency order Generic interface to CAS Translation to CAS Suitably ordered assignments together with control structures form an imperative program Constants depending on constants which were modified are recomputed Executing the program using CAS yields a symbolic valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  32. 32. Specification Language CSL Design goals of CSL Formal specification of the calculation method Specification of assignments in an arbitrary order, but: We require assignments to be unique and sortable w.r.t. the dependency order Generic interface to CAS Translation to CAS Suitably ordered assignments together with control structures form an imperative program Constants depending on constants which were modified are recomputed Executing the program using CAS yields a symbolic valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  33. 33. Specification Language CSL Design goals of CSL Formal specification of the calculation method Specification of assignments in an arbitrary order, but: We require assignments to be unique and sortable w.r.t. the dependency order Generic interface to CAS Translation to CAS Suitably ordered assignments together with control structures form an imperative program Constants depending on constants which were modified are recomputed Executing the program using CAS yields a symbolic valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  34. 34. A Little CSL Example Calculating a root of cos using Newton’s Method The CSL specification y := cos(x) %(A)% z := sin(x) %(B)% x := 10 %(C)% repeat x := x + y/z %(D)% until abs(y) < 0.001 The translation yields this program: C;A;B;repeat D;A;B; until abs(y) < 0.001Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  35. 35. A Little CSL Example Calculating a root of cos using Newton’s Method The CSL specification Building the Dependency Graph y := cos(x) %(A)% z := sin(x) %(B)% x := 10 %(C)% x repeat A x := x + y/z %(D)% y until abs(y) < 0.001 The translation yields this program: C;A;B;repeat D;A;B; until abs(y) < 0.001Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  36. 36. A Little CSL Example Calculating a root of cos using Newton’s Method The CSL specification Building the Dependency Graph y := cos(x) %(A)% z := sin(x) %(B)% x := 10 %(C)% x repeat A B x := x + y/z %(D)% y z until abs(y) < 0.001 The translation yields this program: C;A;B;repeat D;A;B; until abs(y) < 0.001Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  37. 37. A Little CSL Example Calculating a root of cos using Newton’s Method The CSL specification Building the Dependency Graph y := cos(x) %(A)% z := sin(x) %(B)% C x := 10 %(C)% x repeat A B x := x + y/z %(D)% y z until abs(y) < 0.001 The translation yields this program: C;A;B;repeat D;A;B; until abs(y) < 0.001Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  38. 38. A Little CSL Example Calculating a root of cos using Newton’s Method The CSL specification Building the Dependency Graph y := cos(x) %(A)% z := sin(x) %(B)% C x := 10 %(C)% x repeat A B x := x + y/z %(D)% y z until abs(y) < 0.001 D The translation yields this program: C;A;B;repeat D;A;B; until abs(y) < 0.001Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  39. 39. A Little CSL Example Calculating a root of cos using Newton’s Method The CSL specification Building the Dependency Graph y := cos(x) %(A)% z := sin(x) %(B)% C x := 10 %(C)% x repeat A B x := x + y/z %(D)% y z until abs(y) < 0.001 D The translation yields this program: C;A;B;repeat D;A;B; until abs(y) < 0.001Industrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  40. 40. Verified CAS Verification Points in CSL are positions of subterms of CSL statements Evaluating a such marked term produces a verification condition The CAS result is extended by a list of verification conditions Use Hets to prove verification conditions Specifying CAS program semantics in HasCASL Standard interpretation of programs as state transformers Properties of algorithms specified in CSL can be verifiedIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  41. 41. Verified CAS Verification Points in CSL are positions of subterms of CSL statements Evaluating a such marked term produces a verification condition The CAS result is extended by a list of verification conditions Use Hets to prove verification conditions Specifying CAS program semantics in HasCASL Standard interpretation of programs as state transformers Properties of algorithms specified in CSL can be verifiedIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  42. 42. Verified CAS Verification Points in CSL are positions of subterms of CSL statements Evaluating a such marked term produces a verification condition The CAS result is extended by a list of verification conditions Use Hets to prove verification conditions Specifying CAS program semantics in HasCASL Standard interpretation of programs as state transformers Properties of algorithms specified in CSL can be verifiedIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  43. 43. Verified CAS Verification Points in CSL are positions of subterms of CSL statements Evaluating a such marked term produces a verification condition The CAS result is extended by a list of verification conditions Use Hets to prove verification conditions Specifying CAS program semantics in HasCASL Standard interpretation of programs as state transformers Properties of algorithms specified in CSL can be verifiedIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  44. 44. Verified CAS Verification Points in CSL are positions of subterms of CSL statements Evaluating a such marked term produces a verification condition The CAS result is extended by a list of verification conditions Use Hets to prove verification conditions Specifying CAS program semantics in HasCASL Standard interpretation of programs as state transformers Properties of algorithms specified in CSL can be verifiedIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  45. 45. Verified CAS Verification Points in CSL are positions of subterms of CSL statements Evaluating a such marked term produces a verification condition The CAS result is extended by a list of verification conditions Use Hets to prove verification conditions Specifying CAS program semantics in HasCASL Standard interpretation of programs as state transformers Properties of algorithms specified in CSL can be verifiedIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  46. 46. Example Verifying a result from the CAS A CAS program We set verification point at maximize position → maximize(t, x) is marked . . Environment = σ . CAS computes this expression in context σ y := maximize(t, x) and retuns result r . . . Apply substitution σ to t and obtain t We produce the verification condition maximize(t , x) = r Translate this equality to HasCASL for provingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  47. 47. Example Verifying a result from the CAS A CAS program We set verification point at maximize position → maximize(t, x) is marked . . Environment = σ . CAS computes this expression in context σ y := maximize(t, x) and retuns result r . . . Apply substitution σ to t and obtain t We produce the verification condition maximize(t , x) = r Translate this equality to HasCASL for provingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  48. 48. Example Verifying a result from the CAS A CAS program We set verification point at maximize position → maximize(t, x) is marked . . Environment = σ . CAS computes this expression in context σ y := maximize(t, x) and retuns result r . . . Apply substitution σ to t and obtain t We produce the verification condition maximize(t , x) = r Translate this equality to HasCASL for provingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  49. 49. Example Verifying a result from the CAS A CAS program We set verification point at maximize position → maximize(t, x) is marked . . Environment = σ . CAS computes this expression in context σ y := maximize(t, x) and retuns result r . . . Apply substitution σ to t and obtain t We produce the verification condition maximize(t , x) = r Translate this equality to HasCASL for provingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  50. 50. Example Verifying a result from the CAS A CAS program We set verification point at maximize position → maximize(t, x) is marked . . Environment = σ . CAS computes this expression in context σ y := maximize(t, x) and retuns result r . . . Apply substitution σ to t and obtain t We produce the verification condition maximize(t , x) = r Translate this equality to HasCASL for provingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  51. 51. Example Verifying a result from the CAS A CAS program We set verification point at maximize position → maximize(t, x) is marked . . Environment = σ . CAS computes this expression in context σ y := maximize(t, x) and retuns result r . . . Apply substitution σ to t and obtain t We produce the verification condition maximize(t , x) = r Translate this equality to HasCASL for provingIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  52. 52. CSL, CAS and Hets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASLIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  53. 53. CSL, CAS and Hets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL CSLIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  54. 54. CSL, CAS and Hets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL Reduce CSL Maxima Mathematica CAS InterfaceIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  55. 55. CSL, CAS and Hets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL Reduce CSL Maxima Mathematica CAS InterfaceIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  56. 56. CSL, CAS and Hets cont. The CSL institution Signatures are collections of real constants and functions over the reals Sentences are program statements or first order formulas in an extended theory of the reals augmented by the signature Models are program states, i.e., symbolic valuations A state satisfies a program if it terminates successfully A state satisfies a formula φ if φ holds under this valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  57. 57. CSL, CAS and Hets cont. The CSL institution Signatures are collections of real constants and functions over the reals Sentences are program statements or first order formulas in an extended theory of the reals augmented by the signature Models are program states, i.e., symbolic valuations A state satisfies a program if it terminates successfully A state satisfies a formula φ if φ holds under this valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  58. 58. CSL, CAS and Hets cont. The CSL institution Signatures are collections of real constants and functions over the reals Sentences are program statements or first order formulas in an extended theory of the reals augmented by the signature Models are program states, i.e., symbolic valuations A state satisfies a program if it terminates successfully A state satisfies a formula φ if φ holds under this valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  59. 59. CSL, CAS and Hets cont. The CSL institution Signatures are collections of real constants and functions over the reals Sentences are program statements or first order formulas in an extended theory of the reals augmented by the signature Models are program states, i.e., symbolic valuations A state satisfies a program if it terminates successfully A state satisfies a formula φ if φ holds under this valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  60. 60. CSL, CAS and Hets cont. The CSL institution Signatures are collections of real constants and functions over the reals Sentences are program statements or first order formulas in an extended theory of the reals augmented by the signature Models are program states, i.e., symbolic valuations A state satisfies a program if it terminates successfully A state satisfies a formula φ if φ holds under this valuationIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  61. 61. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  62. 62. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  63. 63. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  64. 64. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  65. 65. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  66. 66. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  67. 67. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  68. 68. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  69. 69. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  70. 70. Summary and Outlook Specification language CSL for industrial standards Synthesis of programs for generic CAS interface Verification Points for local verification of CAS result Integration of CSL and CAS interface in Hets Specification of CSL semantics in HasCASL Relating CSL to HasCASL by theoroidal comorphism Benefit from symbolic character of CAS computations Using CAS to simplify CSL specifications for partial instantiations or given set of additional assumptions Replace special functions by closed solutions found by the CAS Finding instantiations for underspecified specifications, e.g., number of bolts needed for flange to satisfy standardIndustrial Standards, and Formal Verification German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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