There are many different ways to encode lists. You are using the Church encoding, where a value is a fold, nil = λn.λc.n cons = λx.λxs.λn.λc.c x (xs n

There are many different ways to encode lists. You are using the Church encoding, where a value is a fold, nil = λn.λc.n cons = λx.λxs.λn.λc.c x (xs n c) fold = λf.λz.λxs.xs z f Another option is the Scott encoding, where a value is a case distinction nil = λn.λc.n cons = λx.λxs.λn.λc.c x xs fold = Y (λfold.λf.λz.λxs.xs z (λhead.λtail.f head (fold f z tail))) And then there is the 3-tuple thing proposed in the article.