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    <p>Yes, I'm posting another answer. And it still might not be exactly what you're looking for. But I think it might be of use nonetheless. It's in Haskell.</p> <pre><code>data LExpr = Lambda Char LExpr | Atom Char | App LExpr LExpr instance Show LExpr where show (Atom c) = [c] show (App l r) = "(" ++ show l ++ " " ++ show r ++ ")" show (Lambda c expr) = "(λ" ++ [c] ++ ". " ++ show expr ++ ")" </code></pre> <p>So here I cooked up a basic algebraic data type for expressing lambda calculus. I added a simple, but effective, custom Show instance.</p> <pre><code>ghci&gt; App (Lambda 'a' (Atom 'a')) (Atom 'b') ((λa. a) b) </code></pre> <p>For fun, I threw in a simple <code>reduce</code> method, with helper <code>replace</code>. Warning: not carefully thought out or tested. Do not use for industrial purposes. Cannot handle certain nasty expressions. :P</p> <pre><code>reduce (App (Lambda c target) expr) = reduce $ replace c (reduce expr) target reduce v = v replace c expr av@(Atom v) | v == c = expr | otherwise = av replace c expr ap@(App l r) = App (replace c expr l) (replace c expr r) replace c expr lv@(Lambda v e) | v == c = lv | otherwise = (Lambda v (replace c expr e)) </code></pre> <p>It seems to work, though that's really just me getting sidetracked. (<code>it</code> in ghci refers to the last value evaluated at the prompt)</p> <pre><code>ghci&gt; reduce it b </code></pre> <p>So now for the fun part, <code>rotate</code>. So I figure I can just peel off the first layer, and if it's a Lambda, great, I'll save the identifier and keep drilling down until I hit a non-Lambda. Then I'll just put the Lambda and identifier right back in at the "last" spot. If it wasn't a Lambda in the first place, then do nothing.</p> <pre><code>rotate (Lambda c e) = drill e where drill (Lambda c' e') = Lambda c' (drill e') -- keep drilling drill e' = Lambda c e' -- hit a non-Lambda, put c back rotate e = e </code></pre> <p>Forgive the unimaginative variable names. Sending this through ghci shows good signs:</p> <pre><code>ghci&gt; Lambda 'a' (Atom 'a') (λa. a) ghci&gt; rotate it (λa. a) ghci&gt; Lambda 'a' (Lambda 'b' (App (Atom 'a') (Atom 'b'))) (λa. (λb. (a b))) ghci&gt; rotate it (λb. (λa. (a b))) ghci&gt; Lambda 'a' (Lambda 'b' (Lambda 'c' (App (App (Atom 'a') (Atom 'b')) (Atom 'c')))) (λa. (λb. (λc. ((a b) c)))) ghci&gt; rotate it (λb. (λc. (λa. ((a b) c)))) </code></pre>
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    1. PORotate the first argument to a function to become nth
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    1. USDan Burton
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    1. COSo yeah, don't try reducing `((λx. x x) (λx. x x))` with my implementation of `reduce` ;)
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