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What's the difference between optional systems and gradual systems?

The author of Typed Clojure has done a presentation on that subject. https://www.youtube.com/watch?v=yG9CffLlXx0 So if I understood correctly: An optional type system can be toggled at any time but the type checking requires type annotations on all of your code (with all its dependencies). A gradual type system is also optional but can check portions of your program even if they call into un-typed portions of your program and also check typed code called from un-typed code.

The first footnote (numbered 1) in the PDF defines these terms.

I'm embarrassed now.

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