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(* Title: HOL/inductive.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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(Co)Inductive Definitions for HOL
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Inductive definitions use least fixedpoints with standard products and sums
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Coinductive definitions use greatest fixedpoints with Quine products and sums
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Sums are used only for mutual recursion;
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Products are used only to derive "streamlined" induction rules for relations
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*)
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local open Ind_Syntax
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in
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fun gen_fp_oper a (X,T,t) =
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let val setT = mk_setT T
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in Const(a, (setT-->setT)-->setT) $ absfree(X, setT, t) end;
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structure Lfp_items =
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struct
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val oper = gen_fp_oper "lfp"
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val Tarski = def_lfp_Tarski
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val induct = def_induct
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end;
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structure Gfp_items =
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struct
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val oper = gen_fp_oper "gfp"
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val Tarski = def_gfp_Tarski
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val induct = def_Collect_coinduct
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end;
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end;
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functor Ind_section_Fun (Inductive: sig include INDUCTIVE_ARG INDUCTIVE_I end)
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: sig include INTR_ELIM INDRULE end =
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struct
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structure Intr_elim = Intr_elim_Fun(structure Inductive=Inductive and
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Fp=Lfp_items);
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structure Indrule = Indrule_Fun
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(structure Inductive=Inductive and Intr_elim=Intr_elim);
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open Intr_elim Indrule
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end;
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structure Ind = Add_inductive_def_Fun (Lfp_items);
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signature INDUCTIVE_STRING =
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sig
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val thy_name : string (*name of the new theory*)
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val srec_tms : string list (*recursion terms*)
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val sintrs : string list (*desired introduction rules*)
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end;
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(*For upwards compatibility: can be called directly from ML*)
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functor Inductive_Fun
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(Inductive: sig include INDUCTIVE_STRING INDUCTIVE_ARG end)
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: sig include INTR_ELIM INDRULE end =
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Ind_section_Fun
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(open Inductive Ind_Syntax
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val sign = sign_of thy;
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val rec_tms = map (readtm sign termTVar) srec_tms
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and intr_tms = map (readtm sign propT) sintrs;
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val thy = thy |> Ind.add_fp_def_i(rec_tms, intr_tms)
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|> add_thyname thy_name);
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signature COINDRULE =
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sig
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val coinduct : thm
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end;
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functor CoInd_section_Fun
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(Inductive: sig include INDUCTIVE_ARG INDUCTIVE_I end)
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: sig include INTR_ELIM COINDRULE end =
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struct
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structure Intr_elim = Intr_elim_Fun(structure Inductive=Inductive and Fp=Gfp_items);
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open Intr_elim
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val coinduct = raw_induct
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end;
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structure CoInd = Add_inductive_def_Fun(Gfp_items);
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