src/ZF/list.ML
 author lcp Wed, 06 Oct 1993 09:58:53 +0100 changeset 30 d49df4181f0d parent 14 1c0926788772 child 55 331d93292ee0 permissions -rw-r--r--
Retrying yet again after network problems
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(*  Title: 	ZF/list.ML
ID:         \$Id\$
Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory

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 (List.defs@List.con_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(Nil);       \
\       !!x y. [| x: A;  y: list(A) |] ==> h(x,y): C(Cons(x,y))  \
\    |] ==> list_case(c,h,l) : C(l)";
by (rtac (major RS List.induct) 1);
by (ALLGOALS (asm_simp_tac (ZF_ss addsimps (List.case_eqns @ 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();

```