[grumpyprole]

"Dynamic typing" is really just case analysis at runtime. Every static language is capable of dynamic typing, it's not some feature that statically typed languages lack. A dynamic language is really just a static language with one type.

[kbp]

Why aren't statically typed programs really just dynamically typed programs where all the types happen to be statically inferable?

[grumpyprole]

Because most statically typed languages allow us to define our own types, add type signatures to constrain etc. Dependently typed languages also allow types to depend on values. Inference is useful, but only one aspect of static typing.