Version 1 of Combinator engine: answers to exercises

Updated 2002-12-04 17:34:48

This page contains proofs to some assertions that are left as exercises in Combinator engine.

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I = S K K

To prove this, remember that

    S x y z = x z { y z }

and

    K x y = x

So what is S K K p?

    S K K p = K p { K p }
            = p

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B = S {K S} K

Remember, we want

    B x y z = x { y z }

So, let's see:

    S { K S } K x y z = K S x { K x } y z
                      = S { K x } y z
                      = K x z { y z }
                      = x { y z }                []

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