
diff -r f04b33ce250f -r a4dc62a46ee4 Set.thy
--- a/Set.thy	Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,145 +0,0 @@
-(*  Title:      HOL/Set.thy
-    ID:         $Id$
-    Author:     Tobias Nipkow
-    Copyright   1993  University of Cambridge
-*)
-
-Set = Ord +
-
-types
-  'a set
-
-arities
-  set :: (term) term
-
-instance
-  set :: (term) {ord, minus}
-
-consts
-  "{}"          :: "'a set"                           ("{}")
-  insert        :: "['a, 'a set] => 'a set"
-  Collect       :: "('a => bool) => 'a set"               (*comprehension*)
-  Compl         :: "('a set) => 'a set"                   (*complement*)
-  Int           :: "['a set, 'a set] => 'a set"       (infixl 70)
-  Un            :: "['a set, 'a set] => 'a set"       (infixl 65)
-  UNION, INTER  :: "['a set, 'a => 'b set] => 'b set"     (*general*)
-  UNION1        :: "['a => 'b set] => 'b set"         (binder "UN " 10)
-  INTER1        :: "['a => 'b set] => 'b set"         (binder "INT " 10)
-  Union, Inter  :: "(('a set)set) => 'a set"              (*of a set*)
-  Pow           :: "'a set => 'a set set"                 (*powerset*)
-  range         :: "('a => 'b) => 'b set"                 (*of function*)
-  Ball, Bex     :: "['a set, 'a => bool] => bool"         (*bounded quantifiers*)
-  inj, surj     :: "('a => 'b) => bool"                   (*inj/surjective*)
-  inj_onto      :: "['a => 'b, 'a set] => bool"
-  "``"          :: "['a => 'b, 'a set] => ('b set)"   (infixl 90)
-  ":"           :: "['a, 'a set] => bool"             (infixl 50) (*membership*)
-
-
-syntax
-
-  "~:"          :: "['a, 'a set] => bool"             (infixl 50)
-
-  "@Finset"     :: "args => 'a set"                   ("{(_)}")
-
-  "@Coll"       :: "[idt, bool] => 'a set"            ("(1{_./ _})")
-  "@SetCompr"   :: "['a, idts, bool] => 'a set"       ("(1{_ |/_./ _})")
-
-  (* Big Intersection / Union *)
-
-  "@INTER"      :: "[idt, 'a set, 'b set] => 'b set"  ("(3INT _:_./ _)" 10)
-  "@UNION"      :: "[idt, 'a set, 'b set] => 'b set"  ("(3UN _:_./ _)" 10)
-
-  (* Bounded Quantifiers *)
-
-  "@Ball"       :: "[idt, 'a set, bool] => bool"      ("(3! _:_./ _)" 10)
-  "@Bex"        :: "[idt, 'a set, bool] => bool"      ("(3? _:_./ _)" 10)
-  "*Ball"       :: "[idt, 'a set, bool] => bool"      ("(3ALL _:_./ _)" 10)
-  "*Bex"        :: "[idt, 'a set, bool] => bool"      ("(3EX _:_./ _)" 10)
-
-translations
-  "x ~: y"      == "~ (x : y)"
-  "{x, xs}"     == "insert(x, {xs})"
-  "{x}"         == "insert(x, {})"
-  "{x. P}"      == "Collect(%x. P)"
-  "INT x:A. B"  == "INTER(A, %x. B)"
-  "UN x:A. B"   == "UNION(A, %x. B)"
-  "! x:A. P"    == "Ball(A, %x. P)"
-  "? x:A. P"    == "Bex(A, %x. P)"
-  "ALL x:A. P"  => "Ball(A, %x. P)"
-  "EX x:A. P"   => "Bex(A, %x. P)"
-
-
-rules
-
-  (* Isomorphisms between Predicates and Sets *)
-
-  mem_Collect_eq    "(a : {x.P(x)}) = P(a)"
-  Collect_mem_eq    "{x.x:A} = A"
-
-
-defs
-  Ball_def      "Ball(A, P)     == ! x. x:A --> P(x)"
-  Bex_def       "Bex(A, P)      == ? x. x:A & P(x)"
-  subset_def    "A <= B         == ! x:A. x:B"
-  Compl_def     "Compl(A)       == {x. ~x:A}"
-  Un_def        "A Un B         == {x.x:A | x:B}"
-  Int_def       "A Int B        == {x.x:A & x:B}"
-  set_diff_def  "A - B          == {x. x:A & ~x:B}"
-  INTER_def     "INTER(A, B)    == {y. ! x:A. y: B(x)}"
-  UNION_def     "UNION(A, B)    == {y. ? x:A. y: B(x)}"
-  INTER1_def    "INTER1(B)      == INTER({x.True}, B)"
-  UNION1_def    "UNION1(B)      == UNION({x.True}, B)"
-  Inter_def     "Inter(S)       == (INT x:S. x)"
-  Union_def     "Union(S)       == (UN x:S. x)"
-  Pow_def       "Pow(A)         == {B. B <= A}"
-  empty_def     "{}             == {x. False}"
-  insert_def    "insert(a, B)   == {x.x=a} Un B"
-  range_def     "range(f)       == {y. ? x. y=f(x)}"
-  image_def     "f``A           == {y. ? x:A. y=f(x)}"
-  inj_def       "inj(f)         == ! x y. f(x)=f(y) --> x=y"
-  inj_onto_def  "inj_onto(f, A) == ! x:A. ! y:A. f(x)=f(y) --> x=y"
-  surj_def      "surj(f)        == ! y. ? x. y=f(x)"
-
-end
-
-ML
-
-local
-
-(* Translates between { e | x1..xn. P} and {u. ? x1..xn. u=e & P}      *)
-(* {y. ? x1..xn. y = e & P} is only translated if [0..n] subset bvs(e) *)
-
-val ex_tr = snd(mk_binder_tr("? ","Ex"));
-
-fun nvars(Const("_idts",_) $ _ $ idts) = nvars(idts)+1
-  | nvars(_) = 1;
-
-fun setcompr_tr[e,idts,b] =
-  let val eq = Syntax.const("op =") $ Bound(nvars(idts)) $ e
-      val P = Syntax.const("op &") $ eq $ b
-      val exP = ex_tr [idts,P]
-  in Syntax.const("Collect") $ Abs("",dummyT,exP) end;
-
-val ex_tr' = snd(mk_binder_tr' ("Ex","DUMMY"));
-
-fun setcompr_tr'[Abs(_,_,P)] =
-  let fun ok(Const("Ex",_)$Abs(_,_,P),n) = ok(P,n+1)
-        | ok(Const("op &",_) $ (Const("op =",_) $ Bound(m) $ e) $ _, n) =
-            if n>0 andalso m=n andalso
-              ((0 upto (n-1)) subset add_loose_bnos(e,0,[]))
-            then () else raise Match
-
-      fun tr'(_ $ abs) =
-        let val _ $ idts $ (_ $ (_ $ _ $ e) $ Q) = ex_tr'[abs]
-        in Syntax.const("@SetCompr") $ e $ idts $ Q end
-  in ok(P,0); tr'(P) end;
-
-in
-
-val parse_translation = [("@SetCompr", setcompr_tr)];
-val print_translation = [("Collect", setcompr_tr')];
-val print_ast_translation =
-  map HOL.alt_ast_tr' [("@Ball", "*Ball"), ("@Bex", "*Bex")];
-
-end;
-




