src/ZF/ListFn.thy
changeset 0 a5a9c433f639
child 15 6c6d2f6e3185
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/ListFn.thy	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,44 @@
+(*  Title: 	ZF/list-fn
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Functions for Lists in Zermelo-Fraenkel Set Theory 
+
+map is a binding operator -- it applies to meta-level functions, not 
+object-level functions.  This simplifies the final form of term_rec_conv,
+although complicating its derivation.
+*)
+
+ListFn = List +
+consts
+  "@"	     :: "[i,i]=>i"      			(infixr 60)
+  list_rec   :: "[i, i, [i,i,i]=>i] => i"
+  map 	     :: "[i=>i, i] => i"
+  length,rev :: "i=>i"
+  flat       :: "i=>i"
+  list_add   :: "i=>i"
+
+ (* List Enumeration *)
+ "[]"        :: "i" 	                           	("[]")
+ "@List"     :: "args => i" 	                   	("[(_)]")
+
+
+translations
+  "[x, xs]"     == "Cons(x, [xs])"
+  "[x]"         == "Cons(x, [])"
+  "[]"          == "Nil"
+
+
+rules
+  list_rec_def
+      "list_rec(l,c,h) == Vrec(l, %l g.list_case(c, %x xs. h(x, xs, g`xs), l))"
+
+  map_def       "map(f,l)    == list_rec(l,  Nil,  %x xs r. Cons(f(x), r))"
+  length_def    "length(l)   == list_rec(l,  0,  %x xs r. succ(r))"
+  app_def       "xs@ys       == list_rec(xs, ys, %x xs r. Cons(x,r))"
+  rev_def       "rev(l)      == list_rec(l,  Nil,  %x xs r. r @ [x])"
+  flat_def      "flat(ls)    == list_rec(ls, Nil,  %l ls r. l @ r)"
+  list_add_def  "list_add(l) == list_rec(l, 0,  %x xs r. x#+r)"
+
+end