author | wenzelm |
Wed, 03 Oct 2007 22:33:17 +0200 | |
changeset 24826 | 78e6a3cea367 |
parent 22814 | 4cd25f1706bb |
child 24893 | b8ef7afe3a6b |
permissions | -rw-r--r-- |
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(* Title: ZF/Inductive.thy |
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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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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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ZF/Inductive.thy,.ML: renamed from "inductive" to allow re-building without
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header{*Inductive and Coinductive Definitions*} |
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theory Inductive imports Fixedpt QPair |
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uses |
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"ind_syntax.ML" |
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"Tools/cartprod.ML" |
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"Tools/ind_cases.ML" |
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"Tools/inductive_package.ML" |
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"Tools/induct_tacs.ML" |
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"Tools/primrec_package.ML" begin |
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setup IndCases.setup |
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setup DatatypeTactics.setup |
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Now a non-trivial theory so that require_thy can find it
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ML_setup {* |
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val iT = Ind_Syntax.iT |
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and oT = FOLogic.oT; |
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structure Lfp = |
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struct |
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val oper = Const("Fixedpt.lfp", [iT,iT-->iT]--->iT) |
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val bnd_mono = Const("Fixedpt.bnd_mono", [iT,iT-->iT]--->oT) |
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val bnd_monoI = bnd_monoI |
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val subs = def_lfp_subset |
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val Tarski = def_lfp_unfold |
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val induct = def_induct |
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end; |
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structure Standard_Prod = |
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struct |
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val sigma = Const("Sigma", [iT, iT-->iT]--->iT) |
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val pair = Const("Pair", [iT,iT]--->iT) |
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val split_name = "split" |
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val pair_iff = Pair_iff |
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val split_eq = split |
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val fsplitI = splitI |
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val fsplitD = splitD |
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val fsplitE = splitE |
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end; |
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structure Standard_CP = CartProd_Fun (Standard_Prod); |
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structure Standard_Sum = |
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struct |
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val sum = Const(@{const_name sum}, [iT,iT]--->iT) |
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val inl = Const("Inl", iT-->iT) |
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val inr = Const("Inr", iT-->iT) |
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val elim = Const("case", [iT-->iT, iT-->iT, iT]--->iT) |
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val case_inl = case_Inl |
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val case_inr = case_Inr |
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val inl_iff = Inl_iff |
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val inr_iff = Inr_iff |
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val distinct = Inl_Inr_iff |
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val distinct' = Inr_Inl_iff |
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val free_SEs = Ind_Syntax.mk_free_SEs |
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[distinct, distinct', inl_iff, inr_iff, Standard_Prod.pair_iff] |
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end; |
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structure Ind_Package = |
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Add_inductive_def_Fun |
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(structure Fp=Lfp and Pr=Standard_Prod and CP=Standard_CP |
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and Su=Standard_Sum val coind = false); |
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structure Gfp = |
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struct |
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val oper = Const("Fixedpt.gfp", [iT,iT-->iT]--->iT) |
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val bnd_mono = Const("Fixedpt.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_unfold |
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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("QPair.QSigma", [iT, iT-->iT]--->iT) |
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val pair = Const("QPair.QPair", [iT,iT]--->iT) |
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val split_name = "QPair.qsplit" |
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val pair_iff = QPair_iff |
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val split_eq = qsplit |
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val fsplitI = qsplitI |
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val fsplitD = qsplitD |
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val fsplitE = qsplitE |
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end; |
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structure Quine_CP = CartProd_Fun (Quine_Prod); |
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structure Quine_Sum = |
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struct |
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val sum = Const("QPair.op <+>", [iT,iT]--->iT) |
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val inl = Const("QPair.QInl", iT-->iT) |
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val inr = Const("QPair.QInr", iT-->iT) |
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val elim = Const("QPair.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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val free_SEs = Ind_Syntax.mk_free_SEs |
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[distinct, distinct', inl_iff, inr_iff, Quine_Prod.pair_iff] |
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end; |
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structure CoInd_Package = |
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Add_inductive_def_Fun(structure Fp=Gfp and Pr=Quine_Prod and CP=Quine_CP |
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and Su=Quine_Sum val coind = true); |
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*} |
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2870
6d6fd10a9fdc
Now a non-trivial theory so that require_thy can find it
paulson
parents:
805
diff
changeset
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end |