Added the new theory Map.
(* Title: HOL/Map.thy
ID: $Id$
Author: Tobias Nipkow, based on a theory by David von Oheimb
Copyright 1997 TU Muenchen
The datatype of `maps' (written ~=>); strongly resembles maps in VDM.
*)
Map = List + Option +
types ('a,'b) "~=>" = 'a => 'b option (infixr 0)
consts
empty :: "'a ~=> 'b"
update :: "('a ~=> 'b) => 'a => 'b => ('a ~=> 'b)"
("_/[_/|->/_]" [900,0,0] 900)
override:: "('a ~=> 'b) => ('a ~=> 'b) => ('a ~=> 'b)" (infixl "++" 100)
dom :: "('a ~=> 'b) => 'a set"
ran :: "('a ~=> 'b) => 'b set"
map_of :: "('a * 'b)list => 'a ~=> 'b"
syntax (symbols)
"~=>" :: [type, type] => type
(infixr "\\<leadsto>" 0)
update :: "('a ~=> 'b) => 'a => 'b => ('a ~=> 'b)"
("_/[_/\\<mapsto>/_]" [900,0,0] 900)
override :: "('a ~=> 'b) => ('a ~=> 'b) => ('a ~=> 'b)"
(infixl "\\<oplus>" 100)
defs
empty_def "empty == %x. None"
update_def "m[a|->b] == %x. if x=a then Some b else m x"
override_def "m1++m2 == %x. case m2 x of None => m1 x | Some y => Some y"
dom_def "dom(m) == {a. m a ~= None}"
ran_def "ran(m) == {b. ? a. m a = Some b}"
primrec map_of list
"map_of [] = empty"
"map_of (p#ps) = (map_of ps)[fst p |-> snd p]"
end