Well, it depends on what you mean by "Haskell's" type system. The standard Haskell type system, as defined by the Haskell 98 spec, is decidable (and hence not Turing complete).

Thus Typo uses a number of GHC-specific type system extensions, one of which has "Undecidable" in its name. They're hidden in Prelude.hs.

    {-# LANGUAGE NoImplicitPrelude #-}
    {-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-}
    {-# LANGUAGE FlexibleInstances, UndecidableInstances #-}
    {-# LANGUAGE OverlappingInstances #-}

It's very common to use some extensions, but AFAIK pretty rare to use UndecidableInstances. I'm not actually sure what it does.