FASE 2011 - Formalizing and Operationalizing Industrial Standards

Formalizing and Operationalizing Industrial Standards Dominik Dietrich Lutz Schr¨der o Ewaryst Schulz DFKI Bremen, Germany ewaryst.schulz@dfki.de International Conference on Fundamental Approaches to Software Engineering Saarbr¨cken, Germany u March 30 2011Formalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Overview The problem Assure proper functioning of safety critical systems Required functional properties of mechanical sub-components must be satisfied Our solution Use engineering calculation methods Formal language for engineering calculations Architecture allowing efficient execution and formal verificationFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Outline 1 Motivation 2 The Industrial Standard EN 1591 3 The engineering calculation language EnCL 4 Formal verification of calculations 5 Integration into Hets framework 6 ConclusionFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Reliable Mechanical Engineering Principal motivation Assure proper functioning of system, e.g., pipeline of chemical plant Verification of functional properties of sub-components, e.g., flange connection withstands some given pressure Some possible approaches Formulating properties from first principles (mechanics, geometry) → level of abstraction not adequate Instead: Relying on established practice in engineering → industrial standards, engineering calculations, e.g., standard for flange connections EN 1591Formalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

The Industrial Standard EN 1591 A standard for gasketed circular flange connections Consists of applicability, nomenclature and calculation method Assures impermeability and mechanical strength of the systemFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Calculation Method Parameter The input parameters to the calculation method Flange data, e.g., dimensions and material constants Data for operating states such as pressure and temperatureFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Calculation Method Control Flow Explicit back-jumps require conditional loops Evaluation order determined by dependency in definitions Piecewise function definitions require conditionalsFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Calculation Method analyzed The standard involves calculations using √ Real arithmetic with real functions, e.g., cos, n Special functions such as maximization Requirements for formalizing the calculation method Specify dependencies in arbitrary order (subject to well-formedness requirements) Imperative control flow Schematic expressions Observation: little control but a lot of dependencies → division into program part and dependency storeFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

The Engineering Calculation Language EnCL The main building blocks Terms over a {bool, real}-sorted Signature Σ with predefined part Σpre = {��, cos, ...} and user-defined part Σuser = {c1 , c2 , ...} Special term constructions Predefined binders: e.g., solve(t = s, x) convergence predicate in loop conditions: convergence(0.001, c) Dependency stores are sets of dependencies c(x1 , ..., xn ) = t Programs constructs Assignment: c(x1 , ..., xn ) := t Sequence: p1 ; ...; pn Loop: repeat p until b Conditional: case b : pFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

EnCL and Computer Algebra Systems Running EnCL program p with dependency store �� CAS provides many predefined Interpreter CAS functions start session CAS supports dependency stores CAS-interface send(��) evaluate terms assign terms to constants ⎧ assign(c, t) Send dependencies to the CAS ⎪ t′ run ⎨ . . . Run program p program⎪ eval(u) u′ ⎩ The interpreter maintains dependency store (in parallel to CAS)Formalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

A Small Example Calculating a root of cos in EnCL using Newton’s Method The EnCL specification Dependency Graph x = 10 %(A)% y = cos(x) %(B)% A z = sin(x) %(C)% x ------------------------ B C repeat y z x := x + y/z %(D)% until convergence(0.001, x) D Behaves like A;B;C;repeat x’:=x;D;B;C; until reldistLe(x, x’, 0.001)Formalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

EnCL Semantics Σ-algebras with standard interpretation for predefined part Σpre [[t]]�� ∈ R is the interpretation of t in the Σ-algebra �� [[t]]�� is the term t ′ after full substitution of t w.r.t. �� If �� is a model of �� then [[[[t]]�� ]]�� = [[t]]�� [[c(x1 , ..., xn ) := t]]�� = �� [c(x1 , ..., xn ) = [[t]]�� ]Formalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Formal Verification Correctness of calculations crucial for safety critical applications The CAS cannot be fully trusted However, results of the CAS can be formally verified Mark selected subterms as verification points Produce verification conditions Use Hets to prove verification conditions EnCL term semantics defined in HO-CASL, i.e., axiomatization of Σpre Checking solutions is easier than finding themFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Verification Conditions: Example EnCL program Insert verification point at solve . CAS computes solve(t = s, x) in . Dependency Store = �� . context �� and returns r y := solve(t=s, x) Verification condition . . ⋀︀ . �� ⇒ solve(t = s, x) = r Semantics of solve in HO-CASL Translate to HO-CASL for provingFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Integration of EnCL into Hets The Hets Framework HO-CASL Higher Order Logic EnCL Specification Interpreter Language CAS InterfaceFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Conclusion Formal verification of functional properties of mechanical systems Formal executable language for engineering calculations EnCL Integration into Institution Framework Implementation based on Hets Framework Generic CAS interface in Hets instantiated for Mathematica, Maple and Reduce Support for uncertain numerical values EnCL-formalization of calculation method from EN 1591 Future Work Statement and proof of properties of calculation method Partial instantiations of the standard ensuing simplification Structuring of multiple calculation methodsFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Thank you for your attention.Formalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Formalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Uncertainty Some situations require dealing with uncertain numeric values Input parameters up to an error value, e.g., 1.53 ± 0.01 CAS returns only approximation Require tracking of uncertainty throughout the CAS session → Mathematica’s Numerical-Precision Tracking (NPT) Adapt verification condition generation → replace numbers by intervalsFormalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

Formalizing Industrial Standards German Research CenterD. Dietrich, L. Schr¨der, E. Schulz o for Artificial Intelligence

FASE 2011 - Formalizing and Operationalizing Industrial Standards

by Ewaryst Schulz on Jun 17, 2011

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FASE 2011 - Formalizing and Operationalizing Industrial Standards — Presentation Transcript