Re: [Haskell-cafe] Slightly Offtopic in Part

It should be emphasized that a type needs to be inhabited by (at least one) *total* function to prove a theorem. Otherwise, you could have the following partial function purporting to prove the phony theorem that "A or B implies A": phony :: Either a b -> a phony (Left a) = a Dan Dan Weston wrote:

For more details, look for a function called "orElim" in the write-up

http://www.thenewsh.com/~newsham/formal/curryhoward/

Dan

Ryan Ingram wrote:

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I'm assuming you mean the rule described in http://en.wikibooks.org/wiki/Formal_Logic/Sentential_Logic/Inference_Rules

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type Disj a b = Either a b

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disj_elim :: Disj a b -> (a -> c) -> (b -> c) -> c disj_elim (Left a) a2c b2c = a2c a disj_elim (Right b) a2c b2c = b2c b