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Lem_map.thy
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chapter \<open>Generated by Lem from \<open>map.lem\<close>.\<close>
theory "Lem_map"
imports
Main
"Lem_bool"
"Lem_basic_classes"
"Lem_function"
"Lem_maybe"
"Lem_list"
"Lem_tuple"
"Lem_set"
"Lem_num"
begin
(*open import Bool Basic_classes Function Maybe List Tuple Set Num*)
(*open import {hol} `finite_mapTheory` `finite_mapLib`*)
(*type map 'k 'v*)
(* -------------------------------------------------------------------------- *)
(* Map equality. *)
(* -------------------------------------------------------------------------- *)
(*val mapEqual : forall 'k 'v. Eq 'k, Eq 'v => map 'k 'v -> map 'k 'v -> bool*)
(*val mapEqualBy : forall 'k 'v. ('k -> 'k -> bool) -> ('v -> 'v -> bool) -> map 'k 'v -> map 'k 'v -> bool*)
(* -------------------------------------------------------------------------- *)
(* Map type class *)
(* -------------------------------------------------------------------------- *)
(*class ( MapKeyType 'a )
val {ocaml;coq} mapKeyCompare : 'a -> 'a -> ordering
end*)
(* -------------------------------------------------------------------------- *)
(* Empty maps *)
(* -------------------------------------------------------------------------- *)
(*val empty : forall 'k 'v. MapKeyType 'k => map 'k 'v*)
(*val emptyBy : forall 'k 'v. ('k -> 'k -> ordering) -> map 'k 'v*)
(* -------------------------------------------------------------------------- *)
(* Insertion *)
(* -------------------------------------------------------------------------- *)
(*val insert : forall 'k 'v. MapKeyType 'k => 'k -> 'v -> map 'k 'v -> map 'k 'v*)
(* -------------------------------------------------------------------------- *)
(* Singleton *)
(* -------------------------------------------------------------------------- *)
(*val singleton : forall 'k 'v. MapKeyType 'k => 'k -> 'v -> map 'k 'v*)
(* -------------------------------------------------------------------------- *)
(* Emptyness check *)
(* -------------------------------------------------------------------------- *)
(*val null : forall 'k 'v. MapKeyType 'k, Eq 'k, Eq 'v => map 'k 'v -> bool*)
(* -------------------------------------------------------------------------- *)
(* lookup *)
(* -------------------------------------------------------------------------- *)
(*val lookupBy : forall 'k 'v. ('k -> 'k -> ordering) -> 'k -> map 'k 'v -> maybe 'v*)
(*val lookup : forall 'k 'v. MapKeyType 'k => 'k -> map 'k 'v -> maybe 'v*)
(* -------------------------------------------------------------------------- *)
(* findWithDefault *)
(* -------------------------------------------------------------------------- *)
(*val findWithDefault : forall 'k 'v. MapKeyType 'k => 'k -> 'v -> map 'k 'v -> 'v*)
(* -------------------------------------------------------------------------- *)
(* from lists *)
(* -------------------------------------------------------------------------- *)
(*val fromList : forall 'k 'v. MapKeyType 'k => list ('k * 'v) -> map 'k 'v*)
(*let fromList l= foldl (fun m (k,v) -> insert k v m) empty l*)
(* -------------------------------------------------------------------------- *)
(* to sets / domain / range *)
(* -------------------------------------------------------------------------- *)
(*val toSet : forall 'k 'v. MapKeyType 'k, SetType 'k, SetType 'v => map 'k 'v -> set ('k * 'v)*)
(*val toSetBy : forall 'k 'v. (('k * 'v) -> ('k * 'v) -> ordering) -> map 'k 'v -> set ('k * 'v)*)
(*val domainBy : forall 'k 'v. ('k -> 'k -> ordering) -> map 'k 'v -> set 'k*)
(*val domain : forall 'k 'v. MapKeyType 'k, SetType 'k => map 'k 'v -> set 'k*)
(*val range : forall 'k 'v. MapKeyType 'k, SetType 'v => map 'k 'v -> set 'v*)
(*val rangeBy : forall 'k 'v. ('v -> 'v -> ordering) -> map 'k 'v -> set 'v*)
(* -------------------------------------------------------------------------- *)
(* member *)
(* -------------------------------------------------------------------------- *)
(*val member : forall 'k 'v. MapKeyType 'k, SetType 'k, Eq 'k => 'k -> map 'k 'v -> bool*)
(*val notMember : forall 'k 'v. MapKeyType 'k, SetType 'k, Eq 'k => 'k -> map 'k 'v -> bool*)
(* -------------------------------------------------------------------------- *)
(* Quantification *)
(* -------------------------------------------------------------------------- *)
(*val any : forall 'k 'v. MapKeyType 'k, Eq 'v => ('k -> 'v -> bool) -> map 'k 'v -> bool*)
(*val all : forall 'k 'v. MapKeyType 'k, Eq 'v => ('k -> 'v -> bool) -> map 'k 'v -> bool*)
(*let all P m= (forall k v. (P k v && ((Instance_Basic_classes_Eq_Maybe_maybe.=) (lookup k m) (Just v))))*)
(* -------------------------------------------------------------------------- *)
(* Set-like operations. *)
(* -------------------------------------------------------------------------- *)
(*val deleteBy : forall 'k 'v. ('k -> 'k -> ordering) -> 'k -> map 'k 'v -> map 'k 'v*)
(*val delete : forall 'k 'v. MapKeyType 'k => 'k -> map 'k 'v -> map 'k 'v*)
(*val deleteSwap : forall 'k 'v. MapKeyType 'k => map 'k 'v -> 'k -> map 'k 'v*)
(*val union : forall 'k 'v. MapKeyType 'k => map 'k 'v -> map 'k 'v -> map 'k 'v*)
(*val unions : forall 'k 'v. MapKeyType 'k => list (map 'k 'v) -> map 'k 'v*)
(* -------------------------------------------------------------------------- *)
(* Maps (in the functor sense). *)
(* -------------------------------------------------------------------------- *)
(*val map : forall 'k 'v 'w. MapKeyType 'k => ('v -> 'w) -> map 'k 'v -> map 'k 'w*)
(*val mapi : forall 'k 'v 'w. MapKeyType 'k => ('k -> 'v -> 'w) -> map 'k 'v -> map 'k 'w*)
(* -------------------------------------------------------------------------- *)
(* Cardinality *)
(* -------------------------------------------------------------------------- *)
(*val size : forall 'k 'v. MapKeyType 'k, SetType 'k => map 'k 'v -> nat*)
(* instance of SetType *)
definition map_setElemCompare :: "(('d*'c)set \<Rightarrow>('b*'a)set \<Rightarrow> 'e)\<Rightarrow>('d,'c)Map.map \<Rightarrow>('b,'a)Map.map \<Rightarrow> 'e " where
" map_setElemCompare cmp x y = (
cmp (map_to_set x) (map_to_set y))"
end