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This dissertation describes the implementation of the mathematical expressiveness in the Diderot programming language.,Diderot is a domain-specific language for scientific visualization and image analysis. ,The datasets are produced by digital imaging technologies that sample physical objects at discrete points.,Algorithms in this domain are used to visually explore the data and compute features and properties.,Diderot is designed to enable the translation of visualization ideas into code by providing a mathematically familiar syntax and high-level language.,The work in this dissertation enables a high-level of programmability by, designing and implementing our intermediate representation and addressing the technical challenges that arise.,We evaluate the correctness of our implementation with two complimenting parts; formalizing the properties in our rewrite system and automated testing of our implementation. ,Lastly, we take the first step to extend the language to another domain.,As a result, the Diderot user can write intuitive code, compile programs with complicated tensor math, and believe in the correctness of the compiler., It is important and challenging work to improve the expressivity of the language.,We rely on the expressivity of the Diderot language to support the implementation of visualization ideas.,With a richer language we can push the boundaries for the type of programs written with the Diderot language.


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