diff -r 3fc2f9c40759 -r 0b9b8eb74101 List.thy --- a/List.thy Thu Aug 18 12:38:12 1994 +0200 +++ b/List.thy Thu Aug 18 12:42:19 1994 +0200 @@ -21,33 +21,33 @@ consts - List_Fun :: "['a node set set, 'a node set set] => 'a node set set" - List :: "'a node set set => 'a node set set" - Rep_List :: "'a list => 'a node set" - Abs_List :: "'a node set => 'a list" - NIL :: "'a node set" - CONS :: "['a node set, 'a node set] => 'a node set" - Nil :: "'a list" - "#" :: "['a, 'a list] => 'a list" (infixr 65) - List_case :: "['a node set, 'b, ['a node set, 'a node set]=>'b] => 'b" - List_rec :: "['a node set, 'b, ['a node set, 'a node set, 'b]=>'b] => 'b" - list_rec :: "['a list, 'b, ['a, 'a list, 'b]=>'b] => 'b" - Rep_map :: "('b => 'a node set) => ('b list => 'a node set)" - Abs_map :: "('a node set => 'b) => 'a node set => 'b list" - null :: "'a list => bool" - hd :: "'a list => 'a" - tl,ttl :: "'a list => 'a list" + List_Fun :: "['a node set set, 'a node set set] => 'a node set set" + List :: "'a node set set => 'a node set set" + Rep_List :: "'a list => 'a node set" + Abs_List :: "'a node set => 'a list" + NIL :: "'a node set" + CONS :: "['a node set, 'a node set] => 'a node set" + Nil :: "'a list" + "#" :: "['a, 'a list] => 'a list" (infixr 65) + List_case :: "['b, ['a node set, 'a node set]=>'b, 'a node set] => 'b" + List_rec :: "['a node set, 'b, ['a node set, 'a node set, 'b]=>'b] => 'b" + list_rec :: "['a list, 'b, ['a, 'a list, 'b]=>'b] => 'b" + Rep_map :: "('b => 'a node set) => ('b list => 'a node set)" + Abs_map :: "('a node set => 'b) => 'a node set => 'b list" + null :: "'a list => bool" + hd :: "'a list => 'a" + tl,ttl :: "'a list => 'a list" mem :: "['a, 'a list] => bool" (infixl 55) - list_all :: "('a => bool) => ('a list => bool)" - map :: "('a=>'b) => ('a list => 'b list)" - "@" :: "['a list, 'a list] => 'a list" (infixr 65) - list_case :: "['a list, 'b, ['a, 'a list]=>'b] => 'b" - filter :: "['a => bool, 'a list] => 'a list" + list_all :: "('a => bool) => ('a list => bool)" + map :: "('a=>'b) => ('a list => 'b list)" + "@" :: "['a list, 'a list] => 'a list" (infixr 65) + list_case :: "['b, ['a, 'a list]=>'b, 'a list] => 'b" + filter :: "['a => bool, 'a list] => 'a list" (* List Enumeration *) - "[]" :: "'a list" ("[]") - "@List" :: "args => 'a list" ("[(_)]") + "[]" :: "'a list" ("[]") + "@List" :: "args => 'a list" ("[(_)]") (* Special syntax for list_all and filter *) "@Alls" :: "[idt, 'a list, bool] => bool" ("(2Alls _:_./ _)" 10) @@ -58,7 +58,7 @@ "[x]" == "x#[]" "[]" == "Nil" - "case xs of Nil => a | y#ys => b" == "list_case(xs,a,%y ys.b)" + "case xs of Nil => a | y#ys => b" == "list_case(a, %y ys.b, xs)" "[x:xs . P]" == "filter(%x.P,xs)" "Alls x:xs.P" == "list_all(%x.P,xs)" @@ -84,13 +84,13 @@ Nil_def "Nil == Abs_List(NIL)" Cons_def "x#xs == Abs_List(CONS(Leaf(x), Rep_List(xs)))" - List_case_def "List_case(M, c, d) == Case(M, %x.c, %u. Split(u, %x y.d(x, y)))" + List_case_def "List_case(c, d) == Case(%x.c, Split(d))" (* List Recursion -- the trancl is Essential; see list.ML *) List_rec_def "List_rec(M, c, d) == wfrec(trancl(pred_Sexp), M, \ -\ %z g. List_case(z, c, %x y. d(x, y, g(y))))" +\ List_case(%g.c, %x y g. d(x, y, g(y))))" list_rec_def "list_rec(l, c, d) == \ @@ -115,6 +115,6 @@ append_def "xs@ys == list_rec(xs, ys, %x l r. x#r)" filter_def "filter(P,xs) == \ \ list_rec(xs, [], %x xs r. if(P(x), x#r, r))" - list_case_def "list_case(xs, a, f) == list_rec(xs, a, %x xs r.f(x, xs))" + list_case_def "list_case(a, f, xs) == list_rec(xs, a, %x xs r.f(x, xs))" end