module HelloWorld;

inductive ℕ {
  zero : ℕ;
  suc : ℕ → ℕ;
};

inductive V {
  zeroV : V;
  sucV : V;
};


infixl 6 +;
+ : ℕ → ℕ → ℕ;
+ zero b := b;
+ (suc a) b := suc (a + b);

infixl 7 *;
* : ℕ → ℕ → ℕ;
* zero b := zero;
* (suc a) b := b + (a * b);

axiom Action : Type;
compile Action {
 ghc ↦ "IO ()";
};

infixl 1 >>;
axiom >> : Action → Action → Action;
compile >> {
  ghc ↦ "(>>)";
};

axiom String : Type;

axiom putStr : String → Action;
compile putStr {
  ghc ↦ "putStrLn";
};

doTimes : ℕ → Action → Action;
doTimes zero _ := putStr "done";
doTimes (suc n) a := a >> doTimes n a;

three : ℕ;
three := suc (suc (suc zero));

main : Action;
main := doTimes three (putStr "hello world");

end;