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Diffstat (limited to 'snapshots/isabelle/lib/lem/Lem_map.thy')
| -rw-r--r-- | snapshots/isabelle/lib/lem/Lem_map.thy | 159 |
1 files changed, 159 insertions, 0 deletions
diff --git a/snapshots/isabelle/lib/lem/Lem_map.thy b/snapshots/isabelle/lib/lem/Lem_map.thy new file mode 100644 index 00000000..fbaed71a --- /dev/null +++ b/snapshots/isabelle/lib/lem/Lem_map.thy @@ -0,0 +1,159 @@ +chapter \<open>Generated by Lem from map.lem.\<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 |
