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Explore a conference presentation that introduces a generalized framework for turtle graphics capable of creating domain-specific languages for vector graphics drawing. Learn how Alice Rixte from the University of Bordeaux extends traditional turtle geometry beyond its conventional limitations by developing an extensible language system that supports both relative and absolute positioning. Discover two practical specializations of this framework: one that generates Bézier paths and another that combines and manipulates these paths for comprehensive vector graphics creation. Examine the systematic approach to extending turtle state that enables generic equational reasoning on programming languages similar to turtle graphics, while providing rich specification capabilities for media arts applications. Understand the theoretical foundations including denotational semantics, monadic semantics, and field polymorphism that underpin this innovative approach to domain-specific language design. Gain insights into how this generalization maintains the intuitive nature of turtle graphics while significantly expanding its expressive power for modern vector graphics applications.