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Industrial Standards, Computer Algebra, and Formal Veri cation

The document discusses the industrial standard EN 1591 related to gasketed circular flange connections, detailing its calculation method which ensures impermeability and mechanical strength. It emphasizes the importance of formal verification for safety-critical environments, utilizing computer algebra systems for calculations and correctness checks. The paper also introduces a specification language, CSL, for formalizing these calculations and the verification process using various methodologies.

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Formal Methods in Computing•

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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 2010 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
The Flange A CAD design of a flange-bolt-gasket system. Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 temperature Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 temperature Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 temperature Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
Calculation Method and Iteration Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
Calculation Method and Iteration Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
Calculation Method and Iteration Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
Calculation Method and Iteration Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
Calculation Method and Maximize Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
Calculation Method and Maximize Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
Calculation Method and Maximize Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
Calculation Method and Maximize Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 finding Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 finding Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 finding Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 finding Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
Hets- the Heterogeneous Tool Set Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
CSL, CAS and Hets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
CSL, CAS and Hets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL CSL Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
CSL, CAS and Hets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL Reduce CSL Maxima Mathematica CAS Interface Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
CSL, CAS and Hets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL Reduce CSL Maxima Mathematica CAS Interface Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

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Industrial Standards, Computer Algebra, and Formal Veri cation

  • 1.
    Industrial Standards, ComputerAlgebra, 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 2010 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 2.
    The Flange A CAD design of a flange-bolt-gasket system. Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 3.
    The Industrial StandardEN 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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 4.
    The Industrial StandardEN 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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 5.
    The Industrial StandardEN 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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 6.
    The Industrial StandardEN 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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 7.
    The Industrial StandardEN 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 temperature Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 8.
    The Industrial StandardEN 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 temperature Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 9.
    The Industrial StandardEN 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 temperature Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 10.
    Calculation Method andIteration Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 11.
    Calculation Method andIteration Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 12.
    Calculation Method andIteration Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 13.
    Calculation Method andIteration Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 14.
    Calculation Method andMaximize Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 15.
    Calculation Method andMaximize Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 16.
    Calculation Method andMaximize Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 17.
    Calculation Method andMaximize Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 finding Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 finding Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 finding Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 finding Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 27.
    Hets- the HeterogeneousTool Set Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 34.
    A Little CSLExample 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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 35.
    A Little CSLExample 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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 36.
    A Little CSLExample 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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 37.
    A Little CSLExample 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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 38.
    A Little CSLExample 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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 39.
    A Little CSLExample 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) < 0.001 Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 verified Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 46.
    Example Verifyinga 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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 47.
    Example Verifyinga 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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 48.
    Example Verifyinga 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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 49.
    Example Verifyinga 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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 50.
    Example Verifyinga 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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 51.
    Example Verifyinga 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 proving Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 52.
    CSL, CAS andHets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 53.
    CSL, CAS andHets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL CSL Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 54.
    CSL, CAS andHets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL Reduce CSL Maxima Mathematica CAS Interface Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 55.
    CSL, CAS andHets CSL and the Hets Logic Graph Logic Graph Isabelle Prover Isabelle HasCASL Reduce CSL Maxima Mathematica CAS Interface Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 56.
    CSL, CAS andHets 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 57.
    CSL, CAS andHets 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 58.
    CSL, CAS andHets 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 59.
    CSL, CAS andHets 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 60.
    CSL, CAS andHets 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 valuation Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence
  • 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 standard Industrial Standards, and Formal Verification German Research Center D. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence