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I suggest reading about progressive types:

http://blog.brownplt.org/2012/09/01/progressive-types.html

Wow, thank you, that is exactly what I had in mind

GHC (a Haskell compiler) can defer type errors until runtime:

http://ghc.haskell.org/trac/ghc/wiki/DeferErrorsToRuntime

http://www.haskell.org/ghc/docs/7.6.1/html/users_guide/defer...

A few implementations of Common-Lisp (like SBCL) do this already (not surprisingly), and I find it very useful to compile misbehaving programs (and having not being segfaulted upon). Once you verify function behavior with a bunch of test cases, you declare types everywhere in the code and set the compiler optimization to full.