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(* Title: ZF/ex/data.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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Sample datatype definition.
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It has four contructors, of arities 0-3, and two parameters A and B.
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*)
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structure Data = Datatype_Fun
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(val thy = Univ.thy;
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val rec_specs =
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[("data", "univ(A Un B)",
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[(["Zero"], "i"),
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(["One"], "i=>i"),
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(["Two"], "[i,i]=>i"),
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(["Three"], "[i,i,i]=>i")])];
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val rec_styp = "[i,i]=>i";
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val ext = None
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val sintrs =
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["Zero : data(A,B)",
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"[| a: A |] ==> One(a) : data(A,B)",
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"[| a: A; b: B |] ==> Two(a,b) : data(A,B)",
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"[| a: A; b: B; d: data(A,B) |] ==> Three(a,b,d) : data(A,B)"];
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val monos = [];
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val type_intrs = data_typechecks
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val type_elims = data_elims);
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(** Lemmas to justify using "data" in other recursive type definitions **)
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goalw Data.thy Data.defs "!!A B. [| A<=C; B<=D |] ==> data(A,B) <= data(C,D)";
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by (rtac lfp_mono 1);
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by (REPEAT (rtac Data.bnd_mono 1));
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by (REPEAT (ares_tac (univ_mono::Un_mono::basic_monos) 1));
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val data_mono = result();
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goalw Data.thy (Data.defs@Data.con_defs) "data(univ(A),univ(A)) <= univ(A)";
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by (rtac lfp_lowerbound 1);
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by (rtac ([A_subset_univ, Un_upper1] MRS subset_trans 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 data_univ = result();
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val data_subset_univ = standard ([data_mono, data_univ] MRS subset_trans);
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