(* ---------- ex12 ---------- *)

let f1 x = x + 1 ;;
f1 2 ;;

let f2 x = f1 x ;;
f2 2 ;;

let f3 x = 1 + x 5 ;;
f3 (fun y -> y + 1) ;;

let f4 x = x ;;
f4 5 ;;

(* ---------- ex13 ---------- *)

let rec succAll l =
	match l with
		| [] -> []
		| el::xl -> (el+1) :: succAll xl
;;

succAll [] ;;
succAll [3; 6; 1; 0; -4] ;;

(* ---------- ex14 ---------- *)

let rec belongs n l =
	match l with
		| [] -> false
		| el::xl -> if (el = n) then true else belongs n xl
;;

belongs 4 [1;2;3;4;5;6] ;;
belongs 4 [1;2] ;;

let rec union l1 l2 =
	match l1 with
		| [] -> l2
		| el::xl1 -> if (belongs el l2) then union xl1 l2 else el::union xl1 l2
;;
	
union [7;3;9] [2;1;9] ;;

let rec inter l1 l2 =
	match l1 with
		| [] -> []
		| el::xl1 -> if (belongs el l2) then el::inter xl1 l2 else inter xl1 l2
;;

inter [7;3;9] [2;1;9] ;;

let rec diff l1 l2 =
	match l1 with
		| [] -> []
		| el::xl1 -> if (belongs el l2) then diff xl1 l2 else el::diff xl1 l2
;;

diff [7;3;9] [2;1;9] ;;

let rec ins v l =
	match l with
		| [] -> []
		| x::xl -> (v::x) :: ins v xl
;;

let rec power l =
	match l with
		| [] -> [[]]
		| el::xl -> power xl @ ins el (power xl)
;;

power [] ;;
power [2;3] ;;
power [1;2;3] ;;

(* ---------- ex15 ---------- *)

let rec nat n = if (n=0) then [] else (n-1) :: nat (n-1) ;;

nat 0 ;;
nat 1 ;;
nat 2 ;;
nat 5 ;;

(* ---------- ex16 ---------- *)

let equal n l =
	match l with
		| [] -> false
		| el::l -> if (el = n) then true else false
;;

equal 1 [1; 0] ;;
equal 0 [0; 1] ;; 
equal 0 [1; 0] ;;


let rec count n l =
	match l with
		| [] -> 0
		| el::xl -> if (el = n) then 1 + count n xl else count n []
;;

count 10.1 [10.1; 10.1; 10.1; 10.1; 10.1; 10.1; 10.1; 10.0; 10.0; 10.1; 10.0] ;;
count 10.0 [10.1; 10.1; 10.1; 10.1; 10.1; 10.1; 10.1; 10.0; 10.0; 10.1; 10.0] ;; 
count 10.0 [10.0; 10.0; 10.1; 10.0] ;;

let rec remove n l =
	match l with
		| [] -> []
		| (el,_)::xl -> if (n = el) then remove n xl else l
;;

remove 10.1 [(10.1, 7); (10., 2); (10.1, 1); (10., 1)] ;;

let rec pack l =
	match l with
		| [] -> []
		| el::xl -> (el, count el l)::remove el (pack xl)
;;

pack [] ;;
pack [10.1; 10.1; 10.1; 10.1; 10.1; 10.1; 10.1; 10.0; 10.0; 10.1; 10.0] ;;

let rec unpackaux n el = if (n = 0) then [] else (el)::(unpackaux (n-1) el) ;;

unpackaux  7 10.1 ;;
unpackaux  2 10.0 ;;
unpackaux  1 10.1 ;;

let rec unpack l =
	match l with
		| [] -> []
		| (el,n)::xl -> (unpackaux n el)::unpack xl
;;

unpack [] ;;
unpack [(10.1, 7); (10.0, 2); (10.1, 1); (10.0,1)] ;;