Program Termination and the Curry-Howard Isomorphism
from Iowa Type Theory Commute Hosted by Aaron Stump
For programs to make sense as proofs, they need to be terminating (cannot run forever), since otherwise you can write infinite loops that have any type. Under Curry-Howard this means any formula is provable, which is one way to define inconsistency. (And logics have to be consistent to be useful.)
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