CS 6520 HW 6

Just as functions can encode true and false, they can also encode pairs. The following are abbreviations for mkpair, fst, and snd, which constructs pairs, extracts the first element, and extracts the second element, respectively:

mkpair = (lambda x . (lambda y . (lambda s . ((s x) y))))
   fst = (lambda p . (p (lambda x . (lambda y . x))))
   snd = (lambda p . (p (lambda x . (lambda y . y))))

Show that, for any values V₁ and V₂, (fst ((mkpair V₁) V₂)) reduces to V₁ in six function-call steps.