I have a funtion f: BOOL ⇒ Bool, sich that f(x,y) is true when x=y and false otherwise. Im trying to exhibit a touring machine and a lambda term. for the second part I know that in boolean logic, x ⇒ y iff ¬x ∨ y and these definitions
true := λx. λy. x
false := λx. λy. y
cond := λb. λx. λy. b x y
I came up with the definition for or ∨=λx.λy.(if x then true else y)=λx.λy.cond x true y=λx.λy.x true y., but im unsure how to construct the implication. I know that if x is true, then x→y is equal to y; whereas if x is false, then x→y is always true. For touring machine, I have no idea where to start. any advise?