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> A static type system is a mechanism whereby an algorithm determines if a program exhibits a property, P, and if the property is not found to hold, then the program is rejected.

Doesn't this definition encompass dynamically typed languages as well? e.g. P is syntactic validity?

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Syntactic validity is not a property of a program, but a property of a piece of text that makes it a program. In any case, the point is that type systems purport to identify some amount of "goodness" in a program. I agree that "The compiler will produce something" is a property, although I doubt it is a property any static type proponent would defend as particularly important.

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