Every iterated paraproduct has local Taylor-type expansions described by one universal regularity structure, and every paracontrolled system lifts to a modelled distribution on that structure.
Formalizing line editors in Coq
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abstract
Text editors represent one of the fundamental tools that writers use - software developers, book authors, mathematicians. A text editor must work as intended in that it should allow the users to do their job. We start by introducing a small subset of a text editor - line editor. Next, we will give a concrete definition (specification) of what a complete text editor means. Afterward, we will provide an implementation of a line editor in Coq, and then we will prove that it is a complete text editor.
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Local expansion properties of paracontrolled systems
Every iterated paraproduct has local Taylor-type expansions described by one universal regularity structure, and every paracontrolled system lifts to a modelled distribution on that structure.