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For one, the tools to prove correctness of programs can't deal with data other than integers. This is the first time I hear such claim. Which tools are you tal

• Confusion 15y ago
  For performance reasons. The SPIN model checker, which is the state of the art in terms of performance, employs only integers. Has Coq ever been used to solve an actual practical industrial or business problem, either by generating code from a known correct program or by using the Coq model as an oracle to drive automatic testing? If not, then there's your answer: academically useful proof assistants cannot deal with real world data. Proof assistants useful in the real world can only deal with limited data types to be able to achieve their goal.