Actually it is possible to implement all three evaluation orders within the same final tagless framework, using the same interpretation of types and reusing most of the code save the semantics of lam. That is where the three orders differ, by their own definition. In call-by-name, we have lam f = S . return $ (unS . f . S) In call-by-value, we have lam f = S . return $ (\x -> x >>= unS . f . S . return) In call-by-need, we have lam f = S . return $ (\x -> share x >>= unS . f . S) In CBV, the function first evaluates its argument, whether the value will be needed or not. In call-by-need, we arrange for the sharing of the result should the computation be evaluated. Here is an illustrative test t2 :: HOAS exp => exp IntT t2 = (lam $ \z -> lam $ \x -> let_ (x `add` x) $ \y -> y `add` y) `app` (int 100 `sub` int 10) `app` (int 5 `add` int 5) t2SN = runName t2 >>= print {- *CB> t2SN Adding Adding Adding Adding Adding Adding Adding 40 -} In CBN, the result of subtraction was not needed, and so it was not performed OTH, (int 5 `add` int 5) was computed four times. t2SV = runValue t2 >>= print {- *CB> t2SV Subtracting Adding Adding Adding 40 -} In CBV, although the result of subtraction was not needed, it was still performed. OTH, (int 5 `add` int 5) was computed only once. t2SL = runLazy t2 >>= print {- *CB> t2SL Adding Adding Adding 40 -} Now, Lazy is better than both CBN and CBV: subtraction was not needed, and it was not performed. All other expressions were needed, and evaluated once. The complete code is at http://okmij.org/ftp/tagless-final/CB.hs