Via the ATS mailing list:

However, there is a huge difference between mathematical proofs and programs.

A mathematical proof is often very robust in the sense that mistakes in handling minor details can likely be remedied. A popular saying is that mathematical theorems are almost always true while mathematical proofs almost always contain mistakes. On the other hand, programs are not robust at all: a typo is all you need to crash a program. The very selling point of programming-with-theorem-proving as is supported in ATS is to facilitate the construction of correct programs by taking advantage of the inherent robustness of mathematical proofs: force your programs to go through rigorous typechecking while trusting your theorems (without proofs).

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