Type checking is undecidable for type theories that are Turing-complete. Type theories are Turing complete if they can simulate a turing machine. Roughly, type

Type checking is undecidable for type theories that are Turing-complete. Type theories are Turing complete if they can simulate a turing machine. Roughly, type chicking for a type theory is undecidable if its not decidable whether every term has the type assigned to it by the programmer. The halting problem is the connection, which the website states but the author is inviting bug reports, so maybe its a good idea to ask them to clarify it.