Explore " natural deduction " with insightful episodes like "Normalization of detours for implication inferences", "Normalization in natural deduction", "Natural deduction: or, the bad news!" and "Implication rules for natural deduction" from podcasts like ""Iowa Type Theory Commute", "Iowa Type Theory Commute", "Iowa Type Theory Commute" and "Iowa Type Theory Commute"" and more!
We talk about normalizing detours -- which are when an introduction inference is immediately followed by an elimination inference -- for the implication rules. Under Curry-Howard, this actually corresponds to beta-reduction, and could make the proof bigger (though less complex in a certain sense).
This episode explains the idea of normalization of proofs in natural deduction. We want to eliminate so-called detours in proofs, which occur when an introduction is immediately followed by an elimination.
We discuss the problem of the or-elimination rule in natural deduction, which does not have the correct form for natural deduction inferences. It is a research problem to fix this!
Don't forget to get in touch with me if you want to do the mini-course over Zoom next month, on normalization.
We discuss further inferences in natural deduction, in particular implication introduction and elimination.
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