Out of context (am I missing some earlier part of this thread?) I'm not entirely sure what you mean. Are you're talking about the disjunction elim rule in intuitionistic natural deduction: Gamma |- A + B Gamma, A |- C Gamma, B |- C ---------------------------------------------- Gamma |- C If so, this is just 'case'. If you annotate the rule with proof terms (programs in the simply-typed lambda-calculus), you get the typing rule for case: Gamma |- e : A + B Gamma, x1 : A |- e1 : C Gamma, x2 : B |- e2 : C ------------------------------------------------------ Gamma |- case e of { Inl x1 -> e1 ; Inr x2 -> e2 } : C I.e., when pattern matching on the following type data Or a b = Inl a | Inr b (this type is isomorphic to Either in the Prelude) you have two cases to consider, one where you have an 'a' and the other where you have a 'b'. E.g., let's prove a simple theorem: comm :: Or a b -> Or b a comm x = case x of Inl x1 -> Inr x1 Inr x2 -> Inl x2 Does that help? -Dan On Feb09, PR Stanley wrote:
Hi folks The disjunction elimination rule: I've been trying to make sense of it and I think I have had some success; however, it's far from adequate. I wonder, is there a way of demonstrating it in Haskell? A code frag with a jargon-free explanation would be mucho appreciated. Cheers, Paul
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