author | krauss |
Mon, 11 Feb 2008 15:40:21 +0100 | |
changeset 26056 | 6a0801279f4c |
child 26189 | 9808cca5c54d |
permissions | -rw-r--r-- |
26056
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1 |
(* 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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7 |
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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11 |
*) |
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header{*Inductive and Coinductive Definitions*} |
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|
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theory Inductive_ZF imports Fixedpt QPair Nat_ZF |
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16 |
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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21 |
"Tools/induct_tacs.ML" |
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"Tools/primrec_package.ML" begin |
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|
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setup IndCases.setup |
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setup DatatypeTactics.setup |
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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 = @{thm bnd_monoI} |
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val subs = @{thm def_lfp_subset} |
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val Tarski = @{thm def_lfp_unfold} |
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val induct = @{thm 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 = @{thm Pair_iff} |
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val split_eq = @{thm split} |
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val fsplitI = @{thm splitI} |
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val fsplitD = @{thm splitD} |
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val fsplitE = @{thm 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 = @{thm case_Inl} |
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val case_inr = @{thm case_Inr} |
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val inl_iff = @{thm Inl_iff} |
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val inr_iff = @{thm Inr_iff} |
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val distinct = @{thm Inl_Inr_iff} |
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val distinct' = @{thm 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 = @{thm bnd_monoI} |
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val subs = @{thm def_gfp_subset} |
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val Tarski = @{thm def_gfp_unfold} |
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val induct = @{thm 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 = @{thm QPair_iff} |
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val split_eq = @{thm qsplit} |
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val fsplitI = @{thm qsplitI} |
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val fsplitD = @{thm qsplitD} |
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val fsplitE = @{thm 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 = @{thm qcase_QInl} |
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val case_inr = @{thm qcase_QInr} |
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val inl_iff = @{thm QInl_iff} |
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val inr_iff = @{thm QInr_iff} |
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val distinct = @{thm QInl_QInr_iff} |
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val distinct' = @{thm 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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6a0801279f4c
Made theory names in ZF disjoint from HOL theory names to allow loading both developments
krauss
parents:
diff
changeset
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