src/ZF/List.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/List.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,80 @@
+(*  Title: 	ZF/list.ML
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Datatype definition of Lists
+*)
+
+structure List = Datatype_Fun
+ (val thy = Univ.thy;
+  val rec_specs = 
+      [("list", "univ(A)",
+	  [(["Nil"],	"i"), 
+	   (["Cons"],	"[i,i]=>i")])];
+  val rec_styp = "i=>i";
+  val ext = None
+  val sintrs = 
+      ["Nil : list(A)",
+       "[| a: A;  l: list(A) |] ==> Cons(a,l) : list(A)"];
+  val monos = [];
+  val type_intrs = data_typechecks
+  val type_elims = []);
+
+val [NilI, ConsI] = List.intrs;
+
+(*An elimination rule, for type-checking*)
+val ConsE = List.mk_cases List.con_defs "Cons(a,l) : list(A)";
+
+(*Proving freeness results*)
+val Cons_iff     = List.mk_free "Cons(a,l)=Cons(a',l') <-> a=a' & l=l'";
+val Nil_Cons_iff = List.mk_free "~ Nil=Cons(a,l)";
+
+(*Perform induction on l, then prove the major premise using prems. *)
+fun list_ind_tac a prems i = 
+    EVERY [res_inst_tac [("x",a)] List.induct i,
+	   rename_last_tac a ["1"] (i+2),
+	   ares_tac prems i];
+
+(**  Lemmas to justify using "list" in other recursive type definitions **)
+
+goalw List.thy List.defs "!!A B. A<=B ==> list(A) <= list(B)";
+by (rtac lfp_mono 1);
+by (REPEAT (rtac List.bnd_mono 1));
+by (REPEAT (ares_tac (univ_mono::basic_monos) 1));
+val list_mono = result();
+
+(*There is a similar proof by list induction.*)
+goalw List.thy ([e-mail]_defs) "list(univ(A)) <= univ(A)";
+by (rtac lfp_lowerbound 1);
+by (rtac (A_subset_univ RS univ_mono) 2);
+by (fast_tac (ZF_cs addSIs [zero_in_univ, Inl_in_univ, Inr_in_univ,
+			    Pair_in_univ]) 1);
+val list_univ = result();
+
+val list_subset_univ = standard
+    (list_mono RS (list_univ RSN (2,subset_trans)));
+
+(*****
+val major::prems = goal List.thy
+    "[| l: list(A);    \
+\       c: C(0);       \
+\       !!x y. [| x: A;  y: list(A) |] ==> h(x,y): C(<x,y>)  \
+\    |] ==> list_case(l,c,h) : C(l)";
+by (rtac (major RS list_induct) 1);
+by (ALLGOALS (ASM_SIMP_TAC (ZF_ss addrews
+			    ([list_case_0,list_case_Pair]@prems))));
+val list_case_type = result();
+****)
+
+
+(** For recursion **)
+
+goalw List.thy List.con_defs "rank(a) : rank(Cons(a,l))";
+by (SIMP_TAC rank_ss 1);
+val rank_Cons1 = result();
+
+goalw List.thy List.con_defs "rank(l) : rank(Cons(a,l))";
+by (SIMP_TAC rank_ss 1);
+val rank_Cons2 = result();
+