Right. Computability says that you can compute any computable function with the lambda calculus. But I'm saying something broader, which is that anything you're trying to model with computation has a type system. IOW, computability theory says that one can model any computable function, while type theory says that one can properly constrain it.
In essence you need both. You can compute if the number five is greater than the color red, but you may want to ensure that you never do.
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Right. Computability says that you can compute any computable function with the lambda calculus. But I'm saying something broader, which is that anything you're trying to model with computation has a type system. IOW, computability theory says that one can model any computable function, while type theory says that one can properly constrain it.
In essence you need both. You can compute if the number five is greater than the color red, but you may want to ensure that you never do.