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The Difference between Recursion & Induction : ezyang's blog

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Recursion and induction are closely related. When you were first taught recursion in an introductory computer science class, you were probably told to use induction to prove that your recursive algorithm was correct. (For the purposes of this post, let us exclude hairy recursive functions like the one in the Collatz conjecture which do not obviously terminate.) Induction suspiciously resembles recursion: the similarity comes from the fact that the inductive hypothesis looks a bit like the result of a “recursive call” to the theorem you are proving. If an ordinary recursive computation returns plain old values, you might wonder if an “induction computation” returns proof terms (which, by the Curry-Howard correspondence, could be thought of as a value). As it turns out, however, when you look at recursion and induction categorically, they are not equivalent! Intuitively, the difference lies in the fact that when you are performing induction, the data type you are performing induction ove

The Difference between Recursion & Induction April 27, 2013 Recursion and induction are closely related. When you were first taught recursion in an introductory computer science class, you were probably told to use induction to prove that your recursive algorithm was correct. (For the purposes of this post, let us exclude hairy recursive functions like the one in the Collatz conjecture which do not obviously terminate.) Induction suspiciously resembles recursion: the similarity comes from the fact that the inductive hypothesis looks a bit like the result of a “recursive call” to the theorem yo

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