Modeling Kernel Language (MKL)

David BromanDavid Broman

Department of Computer and Information Science Linköping University, Sweden

david.broman@ida.liu.se

A formal and extensible approach to equation-based modeling languages

Guest Talk, EECS, Chess, UC Berkeley

February 17, 2011

David Bromandavid.broman@liu.se

Part IWhat is an EOO

language?

Part II

Why MKL?

Part IIIExpressiveness, Extensibility and Formalization

Agenda

Part I What is an EOO

Language?

Part II Why MKL?

Part III Expressiveness,

Extensibility, and Formalization

language?

Part II

Why MKL?

Part I

What is an EOO language?

language?

Part II

Why MKL?

What is Modeling and Simulation?

experiment on…

answer questions about…

System

Simulation

Modeling

Mathematical ModelDifferential-Algebraic

Equations (DAEs)

language?

Part II

Why MKL?

Equation-Based Object-Oriented (EOO)Languages

Equation-Based Object-Oriented

Domain-Specific Language (DSL)

• Primarily domain:Modeling of physical systems

Models and Objects

• Object in e.g., Java, C++:object = data + methods

• Multiple physical domains:e.g., mechanical, electrical, hydraulic

• Objects in EOO languages:object = data + equations

language?

Part II

Why MKL?

Models and Objects

EOO model (graphical)

objects (components)

connections

EOO model (textual)

language?

Part II

Why MKL?

Models and Objects

Acausality

• At the equation-levelu = R * i

• At the object connection level

language?

Part II

Why MKL?

Models and Objects

Acausality

acausal (non-causal)

Direction not determined at modeling time

causal

Variables

� Potential

� Flow

Physical topology

is lost

language?

Part II

Why MKL?

Models and Objects

Acausality

acausal (non-causal)

causal

language?

Part II

Why MKL?

Models and Objects

Acausality

• Modelica• VHDL-AMS• gPROMS

language?

Part II

Why MKL?

Part II

Why MKL?

language?

Part II

Why MKL?

Expressiveness

Expressiveness – ease and possibility of expressing complex models or tasks

A, v1.0 A, v1.1 A, v2.0 A, v2.2Language versions:

L, v1.0 L, v1.1 L, v2.0 L, v2.2Standard libraryversions:

language?

Part II

Why MKL?

Extensibility

• Simulation

• Optimization• Code generation for real-time • Model export• Grey-box system identificationetc.

A, v1.0 A, v1.1 A, v2.0 A, v2.2

gives larger and more complex languages

B, v1.0 A, v1.1

C, v1.0

gives many dialects and differentlanguages

Extensibility – mechanisms to add new language features

language?

Part II

Why MKL?

Formalization

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

Formalization – precise semantics “meaning” of the language

• hard to formalize e.g. Modelica due to size and complexity

language?

Part II

Why MKL?

What is MKL?

Modeling Kernel Language(MKL)

Purpose: Research language –explore new concepts

Bottom-up approach

Precise formal semantics

Small extensible language

Base it on a proven foundation – the lambda calculus

Platform for experimental equation-based DSLs(Continuous-time, hybrid, structural dynamic, and acusal models).

Statically typed functional language

language?

Part II

Why MKL?

Part III

Expressiveness, Extensibility, and Formaliztion

language?

Part II

Why MKL?

Expressiveness - 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.

Higher-Order Acusal Models (HOAM)

language?

Part II

Why MKL?

Expressiveness - HOAM

Replaces several of Modelica’s constructs with one concept, e.g.,

• Conditional components

• For-equations

• Redeclare construct

language?

Part II

Why MKL?

HOAM – Example

Example of a mechatronic system with a DC motor and a flexible shaft

How is this model defined?How is this model defined?

Creates a flexible shaft with 120 shaft elements.

language?

Part II

Why MKL?

HOAM – Example

language?

Part II

Why MKL?

HOAM – Example

One shaft element is created by standard

components.

language?

Part II

Why MKL?

HOAM – Example

The flexible shaft is recursively defined by creating ShaftElements.

The recursion terminates

after n steps (in the example 120 steps)

language?

Part II

Why MKL?

HOAM – Example

Do we always need a special recursive model?

language?

Part II

Why MKL?

HOAM – Example

Higher-order function that can compose any mechanical component in series

language?

Part II

Why MKL?

Modelica Environment

Modelica Model

LibraryModelLibrary

Library

Modelica

Result

(e.g., simulation)

Language Specification- Type checking- Collapsing the instance hierarchy

- Connection Semantics- Simulation (Runtime)

language?

Part II

Why MKL?

Language Specification- Type checking- Collapsing the instance hierarch

MKL Environment

MKL Model

LibraryModelLibrary

Library

Result

(e.g., simulation)

Language Specification- Type checking

- Collapsing the instance hierarchy- Connection Semantics

- Simulation (Runtime)

Library for using models- Connection Semantics- Simulation (Runtime)

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

language?

Part II

Why MKL?

Intensional Analysis and Model Lifting

Static Semantics

Type Checking

Model Lifting

Lifted Model

Collapsed using evaluation

Lifted Model

Equation System

Analysis, models treated as data.Connection Semantics,

Simulation, etc.

Result

Dynamic Semantics

MKL Model

language?

Part II

Why MKL?

Intensional Analysis – an Example

Computing the mapping from unknowns to initial values

language?

Part II

Why MKL?

Language Specification- Type checking- Collapsing the instance hierarch

Formalization of Semantics

MKL Model

LibraryModelLibrary

Library

Result

(e.g., simulation)

Library for using models- Connection Semantics- Simulation (Runtime)

Static Type System

Small-stepOperational Semantics

Formalization ofConnection Semantics

ExecutableSpecifcation

language?

Part II

Why MKL?

How do we verify our solution?

PrototypeImplementation

language?

Part II

Why MKL?

Syntax and Dynamic Semantics

Abstract Syntax (core of MKL)

Big-Step Semanitcs (selected rule)

language?

Part II

Why MKL?

Small-Step and Type System

Small-Step Semantics (selected rules)

Type System (selected rule)

language?

Part II

Why MKL?

Type Safety Proof

Main Lemmas

language?

Part II

Why MKL?

Conclusions

Expressivness

(HOAM)

Extensibility

(Library Approach)

Formalization

(Operational Semantics)

Thanks for listening!

Modeling Kernel Language (MKL)

Modeling Kernel Language (MKL)

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