Modelica - A Domain-Specific Language
Implementation and Overview of the OpenModelica Compiler
Martin Sjölund
Department of Computer and Information Science
Linköping University
2015-11-13
Overview
Part I
Part II
Part III
Background
Implementation of a Modelica Compiler
Conclusion
Part I
Background
Classic Compiler
I
Very structured.
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Translates from one intermediate representation to another.
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I
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Assumes it is straight-forward to translate code from one
representation to another.
Usually statement-based code (maybe some object
orientation).
Taught in courses TDDB44 and TDDD55.
The Phases of the Compiler
source program
sequence of chars:
’IF sum=5 THEN..’
Lexical
analysis
sequence of tokens:
’IF’ ’sum’ ’=’ ’5’
Syntactic
analysis
parse tree, derivation tree
Table
management
Semantic
analysis and
Intermediate
code gen
Code
optimization
Error
Management
internal form,
intermediate code
internal form
Code
generation
object program
TDDD55/B44, P Fritzson, IDA, LIU, 2011.
Systems Engineering
I
I
I
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Handling large, complex projects.
Combining requirements, modeling,
simulation, deployment, support,
etc.
Inter-disciplinary.
You often end up with many
different tools because different
domains traditionally used different
tools.
Domain-Specific Languages
I
I
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Many are similar to classic, general-purpose programming
languages (e.g. PHP).
Examples include HTML, regular expressions, parser
generators.
Compilers are usually implemented partially using
domain-specific languages (grammars, special languages to
describe architectures, etc).
Why? It is easier to program and maintain such code.
Modelica
I
g
Figure: An RC-circuit
implemented in Modelica.
c
C=1e-6
Centered around making it easy for
a (mechanical, electrical, etc)
engineer to use Modelica.
-
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Used for simulation and/or control
of multi-domain (physical) systems.
R=1e6
pv
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Modeling using a graphical user
interface (or the equivalent textual
representation).
r
+
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An equation-based object-oriented
modeling language (a DSL).
Simulating the RC-circuit
250
Voltage [V]
200
150
100
50
0
0
1
2
3
4
time [s]
Figure: Result of simulating the RC-circuit.
5
Equations
Physics is described by equations, not statements. Thus, Modelica
primarily uses equations instead of imperative programming (like
C).
I
Equations look like
V
R
=I
However, code needs to be translated to imperative programming
(or similar) in order to run numerical solvers on a CPU. So it could
be solved as either of:
I
V := R ∗ I
I
I :=
I
R
V
R
:= VI
Ordinary Differential Equations (ODEs)
The numerical solvers we use require an ODE formulation. For
example:
∂x
=y
∂t
d = 2.0 ∗ t
(1)
(2)
∂y
= −d ∗ x
(3)
∂t
Where these equations can be solved sequentially and the start
value for each state variable is known or can be solved during
initialization.
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00
x
3.00
y
2.00
∂x
∂t = y
d = 2.0 ∗ t
∂y
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00
x
3.00
y
2.00
∂x
2.00
∂t = y
d = 2.0 ∗ t
∂y
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00
x
3.00
y
2.00
∂x
2.00
∂t = y
d = 2.0 ∗ t
0.00
∂y
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00
x
3.00
y
2.00
∂x
2.00
∂t = y
d = 2.0 ∗ t
0.00
∂y
0.00
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00 0.25
x
3.00 3.50
y
2.00
∂x
2.00
∂t = y
d = 2.0 ∗ t
0.00
∂y
0.00
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00 0.25
x
3.00 3.50
y
2.00 2.00
∂x
2.00
∂t = y
d = 2.0 ∗ t
0.00
∂y
0.00
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00 0.25
x
3.00 3.50
y
2.00 2.00
∂x
2.00 2.00
∂t = y
d = 2.0 ∗ t
0.00 0.50
∂y
0.00 -1.75
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00 0.25
0.50
x
3.00 3.50
4.00
y
2.00 2.00 1.5625
∂x
2.00 2.00
∂t = y
d = 2.0 ∗ t
0.00 0.50
∂y
0.00 -1.75
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00 0.25
0.50
x
3.00 3.50
4.00
y
2.00 2.00 1.5625
∂x
2.00 2.00 1.5625
∂t = y
d = 2.0 ∗ t
0.00 0.50
1.00
∂y
0.00 -1.75 -4.00
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00 0.25
0.50
0.75
x
3.00 3.50
4.00
4.390625
y
2.00 2.00 1.5625
0.5625
∂x
2.00 2.00 1.5625
∂t = y
d = 2.0 ∗ t
0.00 0.50
1.00
∂y
0.00 -1.75 -4.00
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00 0.25
0.50
0.75
x
3.00 3.50
4.00
4.390625
y
2.00 2.00 1.5625
0.5625
∂x
2.00 2.00 1.5625
0.5625
∂t = y
d = 2.0 ∗ t
0.00 0.50
1.00
1.50
∂y
0.00 -1.75 -4.00 -6.5859375
∂t = −d ∗ x
Solving the Ordinary Differential Equation
Solving the ODE from t=0 to t=1 using a step size of 0.25 with
explicit (forward) Euler, using x(t = 0) = 3 and y(t = 0) = 2:
t
0.00 0.25
0.50
0.75
1.00
x
3.00 3.50
4.00
4.390625
4.53125
y
2.00 2.00 1.5625
0.5625
-1.083984375
∂x
2.00 2.00 1.5625
0.5625
∂t = y
d = 2.0 ∗ t
0.00 0.50
1.00
1.50
∂y
0.00 -1.75 -4.00 -6.5859375
∂t = −d ∗ x
Better Solutions for the Ordinary Differential Equation
Modelica tools need to know about ODEs, and
can solve them better than the explicit Euler.
The end values for different solvers:
I Euler stepSize=0.25, x=4.531, y=-1.084, 4 rhs calls
I Euler stepSize=0.10, x=4.087, y=-1.600, 10 rhs calls
I RK4 stepSize=1.00, x=3.667, y=-1.667, 4 rhs calls
I RK4 stepSize=0.25, x=3.747, y=-1.841, 16 rhs calls
I DASSL, tolerance=1e-3, x=3.745, y=-1.838, 15 rhs
calls
I DASSL, x=3.747, y=-1.842, 67 rhs calls
I Euler stepSize=1e-5, x=3.747, y=-1.842, 10000 rhs
calls
model ODE
Real d=2* time;
Real x(start
=3.0, fixed
=true);
Real y(start
=2.0, fixed
=true);
equation
der(x) = y;
der(y) = -d*x;
end ODE;
Multi-Domain Approach: Systems Engineering
Modelica is a multi-domain approach based on math:
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I
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It is suitable to simulate different physical domains
independently or multiple domains in the same model.
Can be used to simulate full systems or synthesize parts of a
system (such as digital controllers).
The language fulfills the requirements of Systems Engineering.
Part II
Implementation of a Modelica
Compiler
User in the Focus
Modelica is designed around the user of the language being the
focus:
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This makes implementation of the compiler harder.
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NP-hard problems need to be solved at compile-time.
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Compilation time is unbounded and includes interpretation of
arbitrary code.
Certain language features are a little weird when you consider
the textual representation, but make sense when for the
graphical user interface.
OpenModelica
OpenModelica is an open source
Modelica tool
I Open Source Modelica
Consortium (OSMC)
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46 org members Mar 2014
Founded Dec 4, 2007
Open-source community
services
Website and Support
Forum
Development courses
Main development at
Linköping University
Used for research prototypes
and industrial products
www.openmodelica.org
OpenModelica
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Version-controlled source base (git)
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Bug database (Trac)
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Continuous integration (Hudson)
Interactive Modelica compiler (OMC)
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Compiles the Modelica Language
Modelica and Python scripting
Efficient C-code, simulation run-time system
Extensive Modelica test suite
Environment for creating models
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OMShell – scripting commands
OMNotebook – interactive notebook
OMOptim parameter optimization tool
OpenModelica dynamic optimizer with collocation
MDT – Eclipse plug-in
ModelicaML UML-Modelica-Requirements Profile
OMEdit graphic connection Editor
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Debugger – finding model errors
OpenModelica
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Version-controlled source base (git)
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Bug database (Trac)
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Continuous integration (Hudson)
Interactive Modelica compiler (OMC)
I
I
I
I
I
Compiles the Modelica Language
Modelica and Python scripting
Efficient C-code, simulation run-time system
Extensive Modelica test suite
Environment for creating models
I
I
I
I
I
I
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OMShell – scripting commands
OMNotebook – interactive notebook
OMOptim parameter optimization tool
OpenModelica dynamic optimizer with collocation
MDT – Eclipse plug-in
ModelicaML UML-Modelica-Requirements Profile
OMEdit graphic connection Editor
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Debugger – finding model errors
OpenModelica
I
Version-controlled source base (git)
I
Bug database (Trac)
I
I
Continuous integration (Hudson)
Interactive Modelica compiler (OMC)
I
I
I
I
I
Compiles the Modelica Language
Modelica and Python scripting
Efficient C-code, simulation run-time system
Extensive Modelica test suite
Environment for creating models
I
I
I
I
I
I
I
OMShell – scripting commands
OMNotebook – interactive notebook
OMOptim parameter optimization tool
OpenModelica dynamic optimizer with collocation
MDT – Eclipse plug-in
ModelicaML UML-Modelica-Requirements Profile
OMEdit graphic connection Editor
I
Debugger – finding model errors
OpenModelica
I
Version-controlled source base (git)
I
Bug database (Trac)
I
I
Continuous integration (Hudson)
Interactive Modelica compiler (OMC)
I
I
I
I
I
Compiles the Modelica Language
Modelica and Python scripting
Efficient C-code, simulation run-time system
Extensive Modelica test suite
Environment for creating models
I
I
I
I
I
I
I
OMShell – scripting commands
OMNotebook – interactive notebook
OMOptim parameter optimization tool
OpenModelica dynamic optimizer with collocation
MDT – Eclipse plug-in
ModelicaML UML-Modelica-Requirements Profile
OMEdit graphic connection Editor
I
Debugger – finding model errors
User in the Focus – OMEdit Demo
The Compiler Design
A Modelica compiler needs to have lots of domain knowledge. It
also depends on heuristics to translate equations into ODEs (the
main job of a Modelica compiler), which are translated to
executable code.
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The heuristics may fail to create an ODE from the given code
when a solution exists.
Solutions do not necessarily exist.
Numerical solvers may fail solve the model (require infinite
resolution).
Solution: good error messages and debuggers.
In practice, this works very well.
OpenModelica Overview
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Written in MetaModelica (general-purpose programming
extension to Modelica).
The code generator uses our own DSL Susan for text
generation (which translates Susan code to MetaModelica).
Parser which translates code to C-code, and uses the C
interface to MetaModelica to create data types.
Kernel written in Modelica, MetaModelica, C, C++, Susan,
ANTLR.
OpenModelica Parts
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Parser (using the ANTLR parser generator).
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Front-end (semantic analysis, like a traditional compiler).
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Equation back-end (symbolic math, outputs imperative code
from equations).
Code generator (takes imperative code and generates of
C-code, skipping middle-end and back-end of a traditional
compiler).
Utilities.
Front-end + code generator handles MetaModelica
(functions).
The compiler is also written in Modelica (bootstrapping).
Compiler Bootstrapping
The compiler needs a working copy of itself in order to compile its
code (because there exist no other MetaModelica compilers). This
sounds annoying but has some benefits:
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Can implement language extensions in order to write a more
efficient compiler.
Performance improvements to the Modelica compiler also
improves the MetaModelica compiler.
The language looks similar to Modelica.
Testing a Modelica Compiler
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Testing a C-compiler is easier because the exact translation
semantics are specified.
In Modelica, a compiler needs to decide by itself how to
generate code.
Numerical differences depending on how an equation is solved.
Compare result-files with a relative+absolute tolerance and
some magic to align discrete event times.
Testing a Modelica Compiler
How is Everything Developed?
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The Modelica language is developed by committee.
OpenModelica developers implement new Modelica language
features and create pull requests on github.
The pull request is reviewed and automatically tested before it
is merged into the main repository.
Weekly meetings to coordinate between the Swedish and
German teams.
Infrequent developer weeks for larger changes to the compiler.
Part III
Conclusion
Software used by OpenModelica
OpenModelica is a huge project that combines many pieces of
software. You need software engineers to manage everything, as
well as mathematicians and mechanical engineers to help
implementing the symbolic and numerical solvers. The project
includes:
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A lexer/parser generator.
Its own symbolic processing libraries.
Numerical solvers:
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Linear algebra (dense / sparse).
Non-linear solvers (optimization/minimization formulations).
ODE solvers (euler, RK4, dassl, radau, lobatto).
Dynamic optimization.
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DSL for code (text) generation.
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C compilers.
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GUI toolkits.
More Reading
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https://modelica.org
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https://openmodelica.org
www.liu.se