[mathw]

You could, but why should you spend the cycles on that at runtime when you could've done it just once in the compile phase and errored out at a useful time instead of six weeks later when you hit the one branch you neglected to write unit tests for?

[rbehrends]

Because designing a type system that is sound and expressive and simple is bloody hard. Haskell frequently has a number of `{-# LANGUAGE ... #-}` directives at the top of source files, OCaml has acquired no less than six different ways of doing runtime polymorphism: as an extreme case, the module system has morphed into a fully functional OO system in addition to the one OCaml already has.

Runtime type checks allow you to greatly simplify the difficult parts of the type system or make it more expressive.

People often forget how many expressiveness shortcuts we take so that our type systems keep working out. We have integers (which are in actually practice often just elements of a finite ring), but introduce natural numbers and suddenly a lot of static type checks stop working out. How about interactions between the natural numbers with and without zero? Integers modulo your wordsize vs. infinite precision integers? Can you statically check overflow or underflow? Dart has both `num`, `int`, and `double` types, and `int` and `double` are subtypes of `num`, but `int` is not a subtype of `double`; readAsBytesSync() returns an `Uint8List` that conforms to `List<int>`. From a mathematician's perspective, computer science type systems are usually painfully simplistic. They usually capture something about the representation of the data, not its actual mathematical properties. Their role is often is to prevent undefined behavior, not to capture the actual semantics. Computer science typing often tends to be opportunistic rather than semantically oriented, based on what's easily possible rather than what one wants to express (see the entire family of covariance issues).

As an extreme example, consider GAP's [1] type system. We're dealing with computer algebra here, and some of the types simply cannot be captured at compile-time. Any type annotations would have to be checked at runtime, other than the trivial ones (and even integers are basically a subtype of the rationals or any polynomial ring with integer coefficients).

If I want to do effective implementations of matrices and vectors over finite fields, I pack several finite field elements into a machine word and extract them; no static type system in existence has even remotely the power to statically typecheck these operations for me, unless layered over a ton of unsafe code, and then only for some languages.

From the computer science side of things (I have a background in formal methods), type systems are underpowered specification languages that just pick a small subset of a formal spec that happens to be convenient to prove. They can express only a subset of program behavior (compare what types in even (say) Haskell do to a full-blown formal specification in Z) and often not even the interesting ones. As a result, I don't particularly stress out over whether checks only occur at compile time. Runtime type checking is simply a different tradeoff in that you move from the set of types that you can build a sound type system around to predicates that can be expressed at runtime. It's simply a different set of tradeoffs.

[1] http://www.gap-system.org/