I think you're saying a type is the range of inputs to function1 which succeed by not crashing; given function2 and a noun in the type, we may use function1 to infer the range of values which function2 must accept? Maybe?
In any language, a type defines a set of values and some semantics for manipulating those values. It so happens that our way of defining common sets is to build a function whose range is some useful set.
Actually any gene (ie, expression) has a product range. It doesn't even need to be a function. So the range of the constant
[%foo %bar]
whatever the subject is, is always [%foo %bar], ie, the pair [7.303.014 7.496.034].
You're not a big believer in airbags, are ya.
Generally we don't actually use these functions unless we're normalizing foreign data. Then, we do. Because anyone on the Internets can send a bull into your steer pen...