src/ZF/co-inductive.ML

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+++ b/src/ZF/co-inductive.ML	Thu Sep 16 12:20:38 1993 +0200
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+(*  Title: 	ZF/co-inductive.ML
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Co-inductive Definitions for Zermelo-Fraenkel Set Theory
+
+Uses greatest fixedpoints with Quine-inspired products and sums
+
+Sums are used only for mutual recursion;
+Products are used only to derive "streamlined" induction rules for relations
+*)
+
+structure Gfp =
+  struct
+  val oper	= Const("gfp",      [iT,iT-->iT]--->iT)
+  val bnd_mono	= Const("bnd_mono", [iT,iT-->iT]--->oT)
+  val bnd_monoI	= bnd_monoI
+  val subs	= def_gfp_subset
+  val Tarski	= def_gfp_Tarski
+  val induct	= def_Collect_coinduct
+  end;
+
+structure Quine_Prod =
+  struct
+  val sigma	= Const("QSigma", [iT, iT-->iT]--->iT)
+  val pair	= Const("QPair", [iT,iT]--->iT)
+  val split_const	= Const("qsplit", [[iT,iT]--->iT, iT]--->iT)
+  val fsplit_const	= Const("qfsplit", [[iT,iT]--->oT, iT]--->oT)
+  val pair_iff	= QPair_iff
+  val split_eq	= qsplit
+  val fsplitI	= qfsplitI
+  val fsplitD	= qfsplitD
+  val fsplitE	= qfsplitE
+  end;
+
+structure Quine_Sum =
+  struct
+  val sum	= Const("op <+>", [iT,iT]--->iT)
+  val inl	= Const("QInl", iT-->iT)
+  val inr	= Const("QInr", iT-->iT)
+  val elim	= Const("qcase", [iT-->iT, iT-->iT, iT]--->iT)
+  val case_inl	= qcase_QInl
+  val case_inr	= qcase_QInr
+  val inl_iff	= QInl_iff
+  val inr_iff	= QInr_iff
+  val distinct	= QInl_QInr_iff
+  val distinct' = QInr_QInl_iff
+  end;
+
+signature CO_INDRULE =
+  sig
+  val co_induct : thm
+  end;
+
+
+functor Co_Inductive_Fun (Ind: INDUCTIVE) 
+          : sig include INTR_ELIM CO_INDRULE end =
+struct
+structure Intr_elim = 
+    Intr_elim_Fun(structure Ind=Ind and Fp=Gfp and 
+		  Pr=Quine_Prod and Su=Quine_Sum);
+
+open Intr_elim 
+val co_induct = raw_induct
+end;
+