Modeling Kernel Language (MKL)
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1 Modeling Kernel Language (MKL) A formal and extensible approach to equation-based modeling languages Guest Talk, EECS, Chess, UC Berkeley February 17, 2011 Department of Computer and Information Science Linköping University, Sweden david.broman@ida.liu.se Agenda 2 Language? I Expressiveness, Extensibility, I
2 3 I What is Modeling and Simulation? 4 experiment on Simulation Model Mathematical Model Differential-Algebraic Equations (DAEs) Modeling answer questions about System I
3 Equation-Based Object-Oriented (EOO) Languages 5 Domain-Specific Language (DSL) Primarily domain: Modeling of physical systems Multiple physical domains: e.g., mechanical, electrical, hydraulic Equation-Based Object-Oriented (EOO) Models and Objects Object in e.g., Java, C++: object = data + methods Objects in EOO languages: object = data + equations I Equation-Based Object-Oriented (EOO) Languages 6 Domain-Specific Language (DSL) Primarily domain: Modeling of physical systems connections Multiple physical domains: e.g., mechanical, electrical, hydraulic ports Equation-Based Object-Oriented (EOO) objects (components) Models and Objects Object in e.g., Java, C++: object = data + methods Objects in EOO languages: object = data + equations EOO model (textual) EOO model (graphical) I
4 Equation-Based Object-Oriented (EOO) Languages 7 Domain-Specific Language (DSL) Primarily domain: Modeling of physical systems Multiple physical domains: e.g., mechanical, electrical, hydraulic Equation-Based Object-Oriented (EOO) Models and Objects Object in e.g., Java, C++: object = data + methods Objects in EOO languages: object = data + equations Acausality At the equation-level u = R * i At the object connection level I Equation-Based Object-Oriented (EOO) Languages 8 Domain-Specific Language (DSL) Primarily domain: Modeling of physical systems Multiple physical domains: e.g., mechanical, electrical, hydraulic Direction not determined at modeling time Equation-Based acausal (non-causal) Object-Oriented (EOO) Models and Objects Object in e.g., Java, C++: object = data + methods Variables Objects in EOO languages: Potential object = data + equations Flow Acausality causal At the equation-level Physical topology u = R is * lost i At the object connection level I
5 Equation-Based Object-Oriented (EOO) Languages 9 Domain-Specific Language (DSL) Primarily domain: Modeling of physical systems Multiple physical domains: e.g., mechanical, electrical, hydraulic Equation-Based acausal (non-causal) Object-Oriented (EOO) Models and Objects Object in e.g., Java, C++: object = data + methods Objects in EOO languages: object = data + equations Acausality causal At the equation-level u = R * i At the object connection level I Equation-Based Object-Oriented (EOO) Languages 10 Domain-Specific Language (DSL) Primarily domain: Modeling of physical systems Multiple physical domains: e.g., mechanical, electrical, hydraulic Equation-Based Object-Oriented (EOO) Models and Objects Object in e.g., Java, C++: object = data + methods Objects in EOO languages: object = data + equations Modelica VHDL-AMS gproms Acausality At the equation-level u = R * i At the object connection level I
6 11 I Expressiveness 12 Expressiveness ease and possibility of expressing complex models or tasks Language versions: A, v1.0 A, v1.1 A, v2.0 A, v2.2 Standard library versions: L, v1.0 L, v1.1 L, v2.0 L, v2.2 I
7 Extensibility 13 Extensibility mechanisms to add new language features Uses Simulation Optimization Code generation for real-time Model export Grey-box system identification etc. C, v1.0 gives many dialects and different languages B, v1.0 A, v1.1 A, v1.0 A, v1.1 A, v2.0 A, v2.2 gives larger and more complex languages I Formalization 14 Formalization precise semantics meaning of the language Language Specifications of state-of-the-art are informally defined hard to interpret unambiguously when developing compilers hard to reason about when extending the language hard to formalize e.g. Modelica due to size and complexity I
8 What is MKL? 15 Purpose: Research language explore new concepts Modeling Kernel Language (MKL) Bottom-up approach Small extensible language Precise formal semantics Base it on a proven foundation the lambda calculus Statically typed functional language Platform for experimental equation-based DSLs (Continuous-time, hybrid, structural dynamic, and acusal models). I 16 I, and Formaliztion I
9 Expressiveness - HOAM 17 Higher-Order Acusal Models (HOAM) Higher-Order Functions I.e. first class citizens, can be passed around as any value + Acausal Models Models in EOO languages, composing DAEs and other interconnected models. = Higher-Order Acausal Models I.e., first class acausal models. I Expressiveness - HOAM 18 Replaces several of Modelica s constructs with one concept, e.g., Conditional components For-equations Redeclare construct I
10 HOAM Example Example of a mechatronic system with a DC motor and a flexible shaft 19 Creates a flexible shaft with 120 shaft elements. How How is is this this model model defined? defined? I HOAM Example Example of a mechatronic system with a DC motor and a flexible shaft 20 I
11 HOAM Example Example of a mechatronic system with a DC motor and a flexible shaft 21 One shaft element is created by standard components. I HOAM Example Example of a mechatronic system with a DC motor and a flexible shaft 22 The flexible shaft is recursively defined by creating ShaftElements. The recursion terminates after n steps (in the example 120 steps) I
12 HOAM Example Example of a mechatronic system with a DC motor and a flexible shaft 23 Do Do we we always always need need a special special recursive recursive model? model? I HOAM Example 24 Example of a mechatronic system with a DC motor and a flexible shaft Higher-order function that can compose any mechanical component in series I
13 Modelica Environment 25 Model Model Library Model Library Library Modelica Model Modelica Tool Result (e.g., simulation) Language Specification - Type checking - Collapsing the instance hierarchy - Connection Semantics - Simulation (Runtime) I MKL Environment 26 Model Model Library Model Library Library Benefits Tool vendors no need to update tool after lib ext. Library developer - less dependent on tool vendors A model behaves the same way in different tools MKL Model MKL Tool Result (e.g., simulation) Library for using models - Connection Library for Semantics using models Library for using models - Simulation - Connection (Runtime) Semantics - Connection Semantics - Simulation (Runtime) - Simulation (Runtime) Language Specification - Type checking - Collapsing the instance hierarchy - Connection Semantics - Simulation (Runtime) I
14 Intensional Analysis and Model Lifting 27 Static Semantics Dynamic Semantics Lifted Model Lifted Model Model Lifting Collapsed using evaluation Type Checking MKL Model Equation System Analysis, models treated as data. Connection Semantics, Simulation, etc. Result I Intensional Analysis an Example 28 Computing the mapping from unknowns to initial values I
15 Formalization of Semantics 29 Model Model Library Model Library Library MKL Model MKL Tool Result (e.g., simulation) Formalization of Library for using models - Connection Library for Connection Semantics using models Semantics Library for using models - Simulation - Connection (Runtime) Semantics - Connection Semantics - Simulation (Runtime) - Simulation (Runtime) Executable Specifcation Static Type System Language Specification - Type checking - Collapsing the instance hierarch Small-step Operational Semantics I How do we verify our solution? 30 Prototype Implementation I
16 Syntax and Dynamic Semantics 31 Abstract Syntax (core of MKL) Big-Step Semanitcs (selected rule) I Small-Step and Type System 32 Small-Step Semantics (selected rules) Type System (selected rule) I
17 Type Safety Proof 33 Main Lemmas I Conclusions 34 Expressivness (HOAM) Extensibility (Library Approach) Formalization (Operational Semantics) Modeling Kernel Language (MKL) Thanks for listening! I
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