In lambda calculus, true and false are conventionally represented as functions lambda x. lambda y. x and lambda x. lambda y. y so that "if b then x

In lambda calculus, true and false are conventionally represented as functions lambda x. lambda y. x and lambda x. lambda y. y so that "if b then x else y" is represented by "b x y". When identifying booleans with bits, it seems natural to write this as "bit x_0 x_1" rather than "bit x_1 x_0" where the arguments seem to be in the wrong order. This is one possible justification for identifying true with 0 and false with 1.