src/ZF/coinductive.ML
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(*  Title: 	ZF/co-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 Zermelo-Fraenkel Set Theory
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Uses greatest fixedpoints with Quine-inspired 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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structure Gfp =
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  struct
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  val oper	= Const("gfp",      [iT,iT-->iT]--->iT)
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  val bnd_mono	= Const("bnd_mono", [iT,iT-->iT]--->oT)
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  val bnd_monoI	= bnd_monoI
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  val subs	= def_gfp_subset
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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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structure Quine_Prod =
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  struct
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  val sigma	= Const("QSigma", [iT, iT-->iT]--->iT)
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  val pair	= Const("QPair", [iT,iT]--->iT)
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  val split_const	= Const("qsplit", [[iT,iT]--->iT, iT]--->iT)
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  val fsplit_const	= Const("qfsplit", [[iT,iT]--->oT, iT]--->oT)
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  val pair_iff	= QPair_iff
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  val split_eq	= qsplit
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  val fsplitI	= qfsplitI
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  val fsplitD	= qfsplitD
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  val fsplitE	= qfsplitE
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  end;
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structure Quine_Sum =
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  struct
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  val sum	= Const("op <+>", [iT,iT]--->iT)
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  val inl	= Const("QInl", iT-->iT)
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  val inr	= Const("QInr", iT-->iT)
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  val elim	= Const("qcase", [iT-->iT, iT-->iT, iT]--->iT)
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  val case_inl	= qcase_QInl
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  val case_inr	= qcase_QInr
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  val inl_iff	= QInl_iff
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  val inr_iff	= QInr_iff
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  val distinct	= QInl_QInr_iff
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  val distinct' = QInr_QInl_iff
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  end;
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signature CO_INDRULE =
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  sig
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  val co_induct : thm
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  end;
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functor Co_Inductive_Fun (Ind: INDUCTIVE) 
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          : sig include INTR_ELIM CO_INDRULE end =
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struct
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structure Intr_elim = 
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    Intr_elim_Fun(structure Ind=Ind and Fp=Gfp and 
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		  Pr=Quine_Prod and Su=Quine_Sum);
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open Intr_elim 
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val co_induct = raw_induct
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end;
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