Conditionals in Lambda Calculus

?x. ?y. ?z. ((x y) z)

Example evaluation of a conditional

(a case where the condition is true).

if true then apple else pear

?x. ?y. ?z. ((x y) z) true apple pear

?x. ?y. ?z. ((x y) z) ?x?.?y?.x? apple pear

?y. ?z. ((?x?.?y?.x? y) z) apple pear

?z. ((?x?.?y?.x? apple ) z) pear

((?x?.?y?.x? apple ) pear)

(?y?. apple ) pear)

apple