(* Lecture 25: Laws of Computability *)

(* no code *)

(*
Barber's paradox, connection to the undecidability if a function
halts on it own code.

Combining problems (we assume all domains are enumerable)

P(x) decidable => not P(x) decidable.
P1(x), P2(x) decidable => P1(x) and P2(x) decidable
P1(x), P2(x) decidable => P1(x) or P2(x) decidable
P(x,y) decidable => exist y. P(x,y) semi-decidable, but not nec. decidable

P(x) semi-decidable => not P(x) not necessearily semi-decidable
P1(x), P2(x) semi-decidable => P1(x) and P2(x) semi-decidable
P1(x), P2(x) semi-decidable => P1(x) or P2(x) semi-decidable [parallel-or]
P(x,y) semi-decidable => exists y. P(x,y) semi-decidable [dove-tailing]

Every closed statement (or statement over finit domain) is decidable
(even though we may not know which way!) [note: only in classical
logic!]
*)