src/ZF/list.ML
author paulson
Fri, 16 Feb 1996 18:00:47 +0100
changeset 1512 ce37c64244c0
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permissions -rw-r--r--
Elimination of fully-functorial style. Type tactic changed to a type abbrevation (from a datatype). Constructor tactic and function apply deleted.
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(*  Title: 	ZF/list.ML
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    ID:         $Id$
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    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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Datatype definition of Lists
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*)
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structure List = Datatype_Fun
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 (val thy        = Univ.thy
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  val rec_specs  = [("list", "univ(A)",
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                      [(["Nil"],    "i"), 
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                       (["Cons"],   "[i,i]=>i")])]
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  val rec_styp   = "i=>i"
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  val ext        = None
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  val sintrs     = ["Nil : list(A)",
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                    "[| a: A;  l: list(A) |] ==> Cons(a,l) : list(A)"]
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  val monos      = []
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  val type_intrs = datatype_intrs
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  val type_elims = datatype_elims);
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store_theory "List" List.thy;
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val [NilI, ConsI] = List.intrs;
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(*An elimination rule, for type-checking*)
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val ConsE = List.mk_cases List.con_defs "Cons(a,l) : list(A)";
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(*Proving freeness results*)
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val Cons_iff     = List.mk_free "Cons(a,l)=Cons(a',l') <-> a=a' & l=l'";
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val Nil_Cons_iff = List.mk_free "~ Nil=Cons(a,l)";
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(*Perform induction on l, then prove the major premise using prems. *)
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fun list_ind_tac a prems i = 
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    EVERY [res_inst_tac [("x",a)] List.induct i,
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	   rename_last_tac a ["1"] (i+2),
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	   ares_tac prems i];
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(**  Lemmas to justify using "list" in other recursive type definitions **)
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goalw List.thy List.defs "!!A B. A<=B ==> list(A) <= list(B)";
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by (rtac lfp_mono 1);
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by (REPEAT (rtac List.bnd_mono 1));
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by (REPEAT (ares_tac (univ_mono::basic_monos) 1));
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val list_mono = result();
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(*There is a similar proof by list induction.*)
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goalw List.thy (List.defs@List.con_defs) "list(univ(A)) <= univ(A)";
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by (rtac lfp_lowerbound 1);
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by (rtac (A_subset_univ RS univ_mono) 2);
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by (fast_tac (ZF_cs addSIs [zero_in_univ, Inl_in_univ, Inr_in_univ,
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			    Pair_in_univ]) 1);
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val list_univ = result();
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val list_subset_univ = standard ([list_mono, list_univ] MRS subset_trans);
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val major::prems = goal List.thy
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    "[| l: list(A);    \
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\       c: C(Nil);       \
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\       !!x y. [| x: A;  y: list(A) |] ==> h(x,y): C(Cons(x,y))  \
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\    |] ==> list_case(c,h,l) : C(l)";
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by (rtac (major RS List.induct) 1);
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by (ALLGOALS (asm_simp_tac (ZF_ss addsimps (List.case_eqns @ prems))));
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val list_case_type = result();
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(** For recursion **)
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goalw List.thy List.con_defs "rank(a) < rank(Cons(a,l))";
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by (simp_tac rank_ss 1);
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val rank_Cons1 = result();
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goalw List.thy List.con_defs "rank(l) < rank(Cons(a,l))";
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by (simp_tac rank_ss 1);
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val rank_Cons2 = result();
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