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.
Industrial Standards, Computer Algebra, and Formal Verication
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 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 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
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 Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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 Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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 Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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 temperature
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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 temperature
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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 temperature
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
10. Calculation Method and Iteration
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
11. Calculation Method and Iteration
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
12. Calculation Method and Iteration
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
13. Calculation Method and Iteration
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
14. Calculation Method and Maximize
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
15. Calculation Method and Maximize
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
16. Calculation Method and Maximize
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
17. Calculation Method and Maximize
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 Heterogeneous Tool 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 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
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) < 0.001
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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) < 0.001
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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) < 0.001
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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) < 0.001
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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) < 0.001
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
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
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
proving
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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
proving
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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
proving
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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
proving
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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
proving
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
52. 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
53. 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
54. 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
55. 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
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 valuation
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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 valuation
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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 valuation
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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 valuation
Industrial Standards, and Formal Verification German Research Center
D. Dietrich, L. Schr¨der, E. Schulz
o for Artificial Intelligence
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 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