I don't understand how .add as defined could terminate.
Base case is 0 add y = 0
Recursion is Sx add y = Sy add x
Which is of course _swap_
Shouldn't it be = S (x add y)
Base case is 0 add y = 0
Recursion is Sx add y = Sy add x
Which is of course _swap_
Shouldn't it be = S (x add y)
S(2) add 5 (i.e. 3 + 5)
=> 2 add S(5) (i.e. 2 + 6)
=> S(1) add 6 (i.e. 2 + 6)
=> 1 add S(6) (i.e. 1 + 7)
=> S(0) add 7 (i.e. 1 + 7)
=> 0 add S(7) (i.e. 0 + 8)
=> 0 add 8
=> 8 (base case)
S(2) add 5
=> S(1 add 5)
=> S(S(0 add 5))
=> S(S(S(0 add 4)))
...
=> S(S(S(S(S(S(S(S(0 add 0))))))))
=> S(S(S(S(S(S(S(S(0))))))))
= 8 (that is the definition of 8)you are doing x add Sy which isn't the same as Sy add x
Number.prototype.add = function (y) {
var x = Number(this)
return x===0 ? y : (y+1).add(x-1)
}
console.log(Number(3).add(2)) // infinite S: innerX => S(y).add(innerX)
S: innerX => S(innerX).add(y)