diff -r df6b3bd14dcb -r 61620d959717 List.thy
--- a/List.thy	Fri Dec 02 16:09:49 1994 +0100
+++ b/List.thy	Fri Dec 02 16:13:34 1994 +0100
@@ -1,52 +1,32 @@
-(*  Title:      HOL/list
+(*  Title:      HOL/List.thy
     ID:         $Id$
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1993  University of Cambridge
+    Author:     Tobias Nipkow
+    Copyright   1994 TU Muenchen
 
-Definition of type 'a list by a least fixed point
+Definition of type 'a list as a datatype. This allows primrec to work.
 
-We use          list(A) == lfp(%Z. {NUMB(0)} <+> A <*> Z)
-and not         list    == lfp(%Z. {NUMB(0)} <+> range(Leaf) <*> Z)
-so that list can serve as a "functor" for defining other recursive types
 *)
 
-List = Sexp +
+List = Arith +
 
-types
-  'a list
-
-arities
-  list :: (term) term
-
+datatype 'a list = "[]" ("[]") | "#"('a,'a list) (infixr 65)
 
 consts
 
-  list      :: "'a item set => 'a item set"
-  Rep_list  :: "'a list => 'a item"
-  Abs_list  :: "'a item => 'a list"
-  NIL       :: "'a item"
-  CONS      :: "['a item, 'a item] => 'a item"
-  Nil       :: "'a list"
-  "#"       :: "['a, 'a list] => 'a list"                   	(infixr 65)
-  List_case :: "['b, ['a item, 'a item]=>'b, 'a item] => 'b"
-  List_rec  :: "['a item, 'b, ['a item, 'a item, 'b]=>'b] => 'b"
-  list_case :: "['b, ['a, 'a list]=>'b, 'a list] => 'b"
-  list_rec  :: "['a list, 'b, ['a, 'a list, 'b]=>'b] => 'b"
-  Rep_map   :: "('b => 'a item) => ('b list => 'a item)"
-  Abs_map   :: "('a item => 'b) => 'a item => 'b list"
   null      :: "'a list => bool"
   hd        :: "'a list => 'a"
   tl,ttl    :: "'a list => 'a list"
-  mem		:: "['a, 'a list] => bool"			(infixl 55)
+  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)
+  "@"	    :: "['a list, 'a list] => 'a list"		(infixr 65)
   filter    :: "['a => bool, 'a list] => 'a list"
+  foldl     :: "[['b,'a] => 'b, 'b, 'a list] => 'b"
+  length    :: "'a list => nat"
 
+syntax
   (* list Enumeration *)
-
-  "[]"      :: "'a list"                            ("[]")
-  "@list"   :: "args => 'a list"                    ("[(_)]")
+  "@list"   :: "args => 'a list"                        ("[(_)]")
 
   (* Special syntax for list_all and filter *)
   "@Alls"	:: "[idt, 'a list, bool] => bool"	("(2Alls _:_./ _)" 10)
@@ -55,66 +35,42 @@
 translations
   "[x, xs]"     == "x#[xs]"
   "[x]"         == "x#[]"
-  "[]"          == "Nil"
-
-  "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)"
 
-defs
-  (* Defining the Concrete Constructors *)
-  NIL_def       "NIL == In0(Numb(0))"
-  CONS_def      "CONS(M, N) == In1(M $ N)"
-
-inductive "list(A)"
-  intrs
-    NIL_I  "NIL: list(A)"
-    CONS_I "[| a: A;  M: list(A) |] ==> CONS(a,M) : list(A)"
-
-rules
-  (* Faking a Type Definition ... *)
-  Rep_list          "Rep_list(xs): list(range(Leaf))"
-  Rep_list_inverse  "Abs_list(Rep_list(xs)) = xs"
-  Abs_list_inverse  "M: list(range(Leaf)) ==> Rep_list(Abs_list(M)) = M"
-
-
-defs
-  (* Defining the Abstract Constructors *)
-  Nil_def       "Nil == Abs_list(NIL)"
-  Cons_def      "x#xs == Abs_list(CONS(Leaf(x), Rep_list(xs)))"
-
-  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, \
-\                         List_case(%g.c, %x y g. d(x, y, g(y))))"
-
-  list_rec_def
-   "list_rec(l, c, d) == \
-\   List_rec(Rep_list(l), c, %x y r. d(Inv(Leaf, x), Abs_list(y), r))"
-
-  (* Generalized Map Functionals *)
-
-  Rep_map_def "Rep_map(f, xs) == list_rec(xs, NIL, %x l r. CONS(f(x), r))"
-  Abs_map_def "Abs_map(g, M) == List_rec(M, Nil, %N L r. g(N)#r)"
-
-  null_def      "null(xs)            == list_rec(xs, True, %x xs r.False)"
-  hd_def        "hd(xs)              == list_rec(xs, @x.True, %x xs r.x)"
-  tl_def        "tl(xs)              == list_rec(xs, @xs.True, %x xs r.xs)"
-  (* a total version of tl: *)
-  ttl_def	"ttl(xs)             == list_rec(xs, [], %x xs r.xs)"
-
-  mem_def	"x mem xs            == \
-\		   list_rec(xs, False, %y ys r. if(y=x, True, r))"
-  list_all_def  "list_all(P, xs)     == list_rec(xs, True, %x l r. P(x) & r)"
-  map_def       "map(f, xs)          == list_rec(xs, [], %x l r. f(x)#r)"
-  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(a, f, xs) == list_rec(xs, a, %x xs r.f(x, xs))"
-
+primrec null list
+  null_Nil "null([]) = True"
+  null_Cons "null(x#xs) = False"
+primrec hd list
+  hd_Nil  "hd([]) = (@x.False)"
+  hd_Cons "hd(x#xs) = x"
+primrec tl list
+  tl_Nil  "tl([]) = (@x.False)"
+  tl_Cons "tl(x#xs) = xs"
+primrec ttl list
+  (* a "total" version of tl: *)
+  ttl_Nil  "ttl([]) = []"
+  ttl_Cons "ttl(x#xs) = xs"
+primrec "op mem" list
+  mem_Nil  "x mem [] = False"
+  mem_Cons "x mem (y#ys) = if(y=x, True, x mem ys)"
+primrec list_all list
+  list_all_Nil  "list_all(P,[]) = True"
+  list_all_Cons "list_all(P,x#xs) = (P(x) & list_all(P,xs))"
+primrec map list
+  map_Nil  "map(f,[]) = []"
+  map_Cons "map(f,x#xs) = f(x)#map(f,xs)"
+primrec "op @" list
+  append_Nil  "[] @ ys = ys"
+  append_Cons "(x#xs)@ys = x#(xs@ys)"
+primrec filter list
+  filter_Nil  "filter(P,[]) = []"
+  filter_Cons "filter(P,x#xs) = if(P(x), x#filter(P,xs), filter(P,xs))"
+primrec foldl list
+  foldl_Nil  "foldl(f,a,[]) = a"
+  foldl_Cons "foldl(f,a,x#xs) = foldl(f, f(a,x), xs)"
+primrec length list
+  length_Nil  "length([]) = 0"
+  length_Cons "length(x#xs) = Suc(length(xs))"
 end