Here are three important combinators, which are lambda terms with no free variables: . I A.x...

   

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Here are three important combinators, which are lambda terms with no free variables: . I A.x (this is the identity function) K = Xx.Ay.x S=Ax.Ay.Az(xz(yz)) It can be show that any combinators can be generated from S and K using only function application (a) Show that the expression SSK reduces to the identity function I (b) Show the result of applying 3-reduction to the expression (S(KS)K)xyz until no more beta reductions can be applied. Here are three important combinators, which are lambda terms with no free variables: . I A.x (this is the identity function) K = Xx.Ay.x S=Ax.Ay.Az(xz(yz)) It can be show that any combinators can be generated from S and K using only function application (a) Show that the expression SSK reduces to the identity function I (b) Show the result of applying 3-reduction to the expression (S(KS)K)xyz until no more beta reductions can be applied.

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a Showing SSK reduces to the identity function I We can break down the reduction stepbystep Innermost K application KS K a K takes two arguments a fun... View the full answer