lambdacube-2008.12.24: listmisc.cube

iota :: Nat -> List Nat;
iota n =
    let LNat :: *;
    	LNat = List Nat;
        T :: *;
        T = Pair Nat LNat;
        step :: T -> T;
        step nl = split Nat LNat T
                        (\ (n::Nat) (l::LNat) -> PairC Nat LNat
			   	    	     	       (Succ n) (Cons Nat n l))
			nl;
	start :: T;
	start = PairC Nat LNat 0 (Nil Nat);
        res :: T;
	res = natprim T step start n;
    in  reverse Nat (snd Nat LNat res);

replicate :: forall (a::*) . Nat -> a -> List a;
replicate a n x = map Nat a (\ i :: Nat -> x) (iota n);

any :: forall a::* . (a -> Bool) -> List a -> Bool;
any a p = foldr a Bool (\ (x::a) -> or (p x)) False;

all :: forall a::* . (a -> Bool) -> List a -> Bool;
all a p = foldr a Bool (\ (x::a) -> and (p x)) True;