An Exercise in Composition

Problem

Given the composition condition, show that for any birds A, B, and C, there is a bird D such that for every bird x, D(x) === A(B(C(x))).

Solution

Assume a bird E that composes B and C:

const E = compose(B, C);

Note that, if you call A with E(x) (where x is another arbitrary bird), you get the A(B(C)) nesting we're looking for:

A(E(x)); // => A(B(C(x)));

Now we do the same trick again and assume a bird D that composes A with E:

const D = compose(A, E);

Thus, D(x) evaluates to A(E(x)) evaluates to A(B(C(x))), regardless of the values of A, B, and C.

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