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|
(*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()
|
