Mathematical optimization has many applications in operations research, image processing, and machine learning, demanding not only computational efficiency but also convenience and correctness in constructing complex models. In this work, we introduce HashedExpression, an open-source algebraic modeling lan- guage (AML) that allows users to express unconstrained, box-constrained, and scalar-expressions-constrained optimization problems, aimed at embeddability, type-safety, and high-performance through symbolic transformation and code generation. Written in Haskell, a statically-typed, purely functional program- ming language, HashedExpression places a great emphasis on modeling correct- ness by providing users with a type-safe, correct-by-construction interface that uses Haskell type-level programming to express constraints on correctness which the compiler uses to flag many modelling errors as type errors (at compile time). We show how type-safety can be added in steps, first matching expressions’ shape and then associated physical units. The library implements symbolic ex- pressions with a hashed indexing scheme to implement common subexpression elimination (CSE). It abstracts away details of the underlying lookup table via monadic type class instances. We explain how using symbolic expressions with CSE enables performance-enhance transformations and automatic computation of derivatives without the issue of “expression swelling”. For high-performance purposes, we generate low-level C/C++ code for symbolic expressions and pro- vide bindings to open-source optimization solvers such as Ipopt or L-BFGS-B. We explain how this architecture lays the groundwork for future work on par- allelization including SIMDization and targetting multi-core CPUs and GPUs, and other hardware acceleration. / Thesis / Master of Science (MSc)

Cyber-physical systems are dynamic physical systems that are controlled by computers for their safe and sound operations (e.g., cars, satellites, robots, elevators, and many others). Consequently, the programs running cyber-physical systems have real-time requirements, which require the programs to compute not only correctly but also timely because dynamic physical systems need to move to correct positions within certain duration to ensure safe and sound operations. To satisfy real-time requirements in better ways, many real-time languages have been proposed in the literature. Nevertheless, the general-purpose non-real-time languages C and C++ have remained the de facto languages to program cyber-physical systems, including Mars rovers and F-35 jet fighters. Given this reality, the better ways to satisfy real-time requirements have been the use of model-based tools (e.g., MATLAB/Simulink) that allow cyber-physical systems to be designed by modeling and simulating them and the resulting models to be translated automatically to C programs. Model-based tools, however, leave the resulting C programs for manual integration with other C/C++ programs, such as legacy/third-party device drivers and libraries. Since manual integration could slip in some inconsistencies, which proved fatal in the maiden flight of Ariane-5 rocket, this work shows how the standard features of C++, which support active libraries, can be used to embed a model-based real-time language, called Tice, as a C++ active library that can be used to declaratively express models of real-time systems that are processable by off-the-shelf standard C++ compilers (e.g., GCC and Clang) that automatically not only translate the models into C/C++ programs but also check both the validity of the models and the consistency of the models with other C/C++ programs. Furthermore, being compilable by off-the-shelf standard C++ compilers also sets Tice apart from other real-time languages already proposed in the literature because the other languages require either their own special compilers/interpreters or non-standard C/C++ compilers. Consequently, while Tice itself either uses no C++ features that are unsuitable for cyber-physical systems (e.g., exception) or uses some in judicious manner (e.g., template instantiations to generate programs), Tice prevents no usage that is permitted by standard C++ compilers. Beside that, as C++ active libraries are indeed ordinary C++ libraries, C++ active libraries are seamlessly composable as ordinary C++ libraries, and therefore, as models play an increasingly important role in software engineering, this work shows the potential of C++ as a platform for language-oriented programming where different languages that express different kinds of models and are embedded as C++ active libraries could be composed seamlessly.