(*Generated by Lem from map_extra.lem.*)
open HolKernel Parse boolLib bossLib;
open lem_boolTheory lem_basic_classesTheory lem_functionTheory lem_assert_extraTheory lem_maybeTheory lem_listTheory lem_numTheory lem_setTheory lem_mapTheory;

val _ = numLib.prefer_num();



val _ = new_theory "lem_map_extra"



(*open import Bool Basic_classes Function Assert_extra Maybe List Num Set Map*)

(* -------------------------------------------------------------------------- *)
(* find                                                                       *)
(* -------------------------------------------------------------------------- *)

(*val find : forall 'k 'v. MapKeyType 'k => 'k -> map 'k 'v -> 'v*)
(*let find k m=  match (lookup k m) with Just x -> x | Nothing -> failwith "Map_extra.find" end*)



(* -------------------------------------------------------------------------- *)
(* from sets / domain / range                                                 *)
(* -------------------------------------------------------------------------- *)


(*val fromSet : forall 'k 'v. MapKeyType 'k => ('k -> 'v) -> set 'k -> map 'k 'v*)
(*let fromSet f s=  Set_helpers.fold (fun k m -> Map.insert k (f k) m) s Map.empty*)

(*
assert fromSet_0: (fromSet succ (Set.empty : set nat) = Map.empty)
assert fromSet_1: (fromSet succ {(2:nat); 3; 4}) = Map.fromList [(2,3); (3, 4); (4, 5)]
*)

(* -------------------------------------------------------------------------- *)
(* fold                                                                       *)
(* -------------------------------------------------------------------------- *)

(*val fold : forall 'k 'v 'r. MapKeyType 'k, SetType 'k, SetType 'v => ('k -> 'v -> 'r -> 'r) -> map 'k 'v -> 'r -> 'r*)
val _ = Define `
 ((fold:('k -> 'v -> 'r -> 'r) ->('k,'v)fmap -> 'r -> 'r) f m v=  (ITSET (\ (k, v) r .  f k v r) (FMAP_TO_SET m) v))`;


(*
assert fold_1: (fold (fun k v a -> (a+k)) (Map.fromList [((2:nat),(3:nat)); (3, 4); (4, 5)]) 0 = 9)
assert fold_2: (fold (fun k v a -> (a+v)) (Map.fromList [((2:nat),(3:nat)); (3, 4); (4, 5)]) 0 = 12)
*)

(*val toList: forall 'k 'v. MapKeyType 'k => map 'k 'v -> list ('k * 'v)*)
(* declare compile_message toList = "Map_extra.toList is only defined for the ocaml, isabelle and coq backend" *)

(* more 'map' functions *)

(* TODO: this function is in map_extra rather than map just for implementation reasons *)
(*val mapMaybe : forall 'a 'b 'c. MapKeyType 'a => ('a -> 'b -> maybe 'c) -> map 'a 'b -> map 'a 'c*)
(* OLD: TODO: mapMaybe depends on toList that is not defined for hol and isabelle *)
val _ = Define `
 ((option_map:('a -> 'b -> 'c option) ->('a,'b)fmap ->('a,'c)fmap) f m=
   (FOLDL
    (\ m' (k, v) . 
      (case f k v of
          NONE => m'
        | SOME v' =>m' |+ (k, v')
      ))
    FEMPTY
    (MAP_TO_LIST m)))`;


val _ = export_theory()