
diff -r b93cc55cb7ab -r df6b3bd14dcb ex/SList.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ex/SList.thy	Fri Dec 02 16:09:49 1994 +0100
@@ -0,0 +1,120 @@
+(*  Title:      HOL/ex/SList.thy
+    ID:         $Id$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Definition of type 'a list (strict lists) by a least fixed point
+
+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
+*)
+
+SList = Sexp +
+
+types
+  'a list
+
+arities
+  list :: (term) term
+
+
+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)
+  list_all  :: "('a => bool) => ('a list => bool)"
+  map       :: "('a=>'b) => ('a list => 'b list)"
+  "@"	    :: "['a list, 'a list] => 'a list"			(infixr 65)
+  filter    :: "['a => bool, 'a list] => 'a list"
+
+  (* list Enumeration *)
+
+  "[]"      :: "'a list"                            ("[]")
+  "@list"   :: "args => 'a list"                    ("[(_)]")
+
+  (* Special syntax for list_all and filter *)
+  "@Alls"	:: "[idt, 'a list, bool] => bool"	("(2Alls _:_./ _)" 10)
+  "@filter"	:: "[idt, 'a list, bool] => 'a list"	("(1[_:_ ./ _])")
+
+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))"
+
+end




