author | wenzelm |
Wed, 06 Dec 2006 01:12:43 +0100 | |
changeset 21672 | 29c346b165d4 |
parent 21669 | c68717c16013 |
child 21858 | 05f57309170c |
permissions | -rw-r--r-- |
19494 | 1 |
(* Title: HOL/Nominal/nominal_package.ML |
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ID: $Id$ |
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Author: Stefan Berghofer and Christian Urban, TU Muenchen |
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Nominal datatype package for Isabelle/HOL. |
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*) |
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signature NOMINAL_PACKAGE = |
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sig |
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val add_nominal_datatype : bool -> string list -> (string list * bstring * mixfix * |
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(bstring * string list * mixfix) list) list -> theory -> theory |
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type nominal_datatype_info |
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val get_nominal_datatypes : theory -> nominal_datatype_info Symtab.table |
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val get_nominal_datatype : theory -> string -> nominal_datatype_info option |
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val setup: theory -> theory |
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end |
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structure NominalPackage : NOMINAL_PACKAGE = |
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struct |
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val Finites_emptyI = thm "Finites.emptyI"; |
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val finite_Diff = thm "finite_Diff"; |
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val finite_Un = thm "finite_Un"; |
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val Un_iff = thm "Un_iff"; |
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val In0_eq = thm "In0_eq"; |
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val In1_eq = thm "In1_eq"; |
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val In0_not_In1 = thm "In0_not_In1"; |
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val In1_not_In0 = thm "In1_not_In0"; |
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val Un_assoc = thm "Un_assoc"; |
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val Collect_disj_eq = thm "Collect_disj_eq"; |
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val empty_def = thm "empty_def"; |
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open DatatypeAux; |
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open NominalAtoms; |
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(** FIXME: DatatypePackage should export this function **) |
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local |
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fun dt_recs (DtTFree _) = [] |
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| dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts) |
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| dt_recs (DtRec i) = [i]; |
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fun dt_cases (descr: descr) (_, args, constrs) = |
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let |
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fun the_bname i = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i))); |
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val bnames = map the_bname (distinct op = (List.concat (map dt_recs args))); |
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in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end; |
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fun induct_cases descr = |
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DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr))); |
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fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i)); |
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in |
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fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr); |
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fun mk_case_names_exhausts descr new = |
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map (RuleCases.case_names o exhaust_cases descr o #1) |
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(List.filter (fn ((_, (name, _, _))) => name mem_string new) descr); |
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end; |
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(* data kind 'HOL/nominal_datatypes' *) |
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type nominal_datatype_info = |
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{index : int, |
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descr : descr, |
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sorts : (string * sort) list, |
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rec_names : string list, |
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rec_rewrites : thm list, |
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induction : thm, |
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distinct : thm list, |
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inject : thm list}; |
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structure NominalDatatypesData = TheoryDataFun |
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(struct |
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val name = "HOL/nominal_datatypes"; |
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type T = nominal_datatype_info Symtab.table; |
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val empty = Symtab.empty; |
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val copy = I; |
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val extend = I; |
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fun merge _ tabs : T = Symtab.merge (K true) tabs; |
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fun print sg tab = |
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Pretty.writeln (Pretty.strs ("nominal datatypes:" :: |
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map #1 (NameSpace.extern_table (Sign.type_space sg, tab)))); |
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end); |
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val get_nominal_datatypes = NominalDatatypesData.get; |
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val put_nominal_datatypes = NominalDatatypesData.put; |
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val map_nominal_datatypes = NominalDatatypesData.map; |
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val get_nominal_datatype = Symtab.lookup o get_nominal_datatypes; |
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val setup = NominalDatatypesData.init; |
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(**** make datatype info ****) |
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fun make_dt_info descr sorts induct reccomb_names rec_thms |
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(((i, (_, (tname, _, _))), distinct), inject) = |
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(tname, |
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{index = i, |
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descr = descr, |
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sorts = sorts, |
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rec_names = reccomb_names, |
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rec_rewrites = rec_thms, |
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induction = induct, |
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distinct = distinct, |
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inject = inject}); |
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(*******************************) |
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma); |
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fun read_typ sign ((Ts, sorts), str) = |
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let |
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val T = Type.no_tvars (Sign.read_typ (sign, (AList.lookup op =) |
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(map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg |
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in (Ts @ [T], add_typ_tfrees (T, sorts)) end; |
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(** taken from HOL/Tools/datatype_aux.ML **) |
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fun indtac indrule indnames i st = |
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let |
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val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule)); |
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val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop |
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(Logic.strip_imp_concl (List.nth (prems_of st, i - 1)))); |
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val getP = if can HOLogic.dest_imp (hd ts) then |
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(apfst SOME) o HOLogic.dest_imp else pair NONE; |
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fun abstr (t1, t2) = (case t1 of |
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NONE => (case filter (fn Free (s, _) => s mem indnames | _ => false) |
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(term_frees t2) of |
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[Free (s, T)] => absfree (s, T, t2) |
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| _ => sys_error "indtac") |
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| SOME (_ $ t') => Abs ("x", fastype_of t', abstract_over (t', t2))) |
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val cert = cterm_of (Thm.sign_of_thm st); |
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val Ps = map (cert o head_of o snd o getP) ts; |
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val indrule' = cterm_instantiate (Ps ~~ |
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(map (cert o abstr o getP) ts')) indrule |
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in |
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rtac indrule' i st |
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end; |
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fun mk_subgoal i f st = |
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let |
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val cg = List.nth (cprems_of st, i - 1); |
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val g = term_of cg; |
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val revcut_rl' = Thm.lift_rule cg revcut_rl; |
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val v = head_of (Logic.strip_assums_concl (hd (prems_of revcut_rl'))); |
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val ps = Logic.strip_params g; |
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val cert = cterm_of (sign_of_thm st); |
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in |
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compose_tac (false, |
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Thm.instantiate ([], [(cert v, cert (list_abs (ps, |
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f (rev ps) (Logic.strip_assums_hyp g) (Logic.strip_assums_concl g))))]) |
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revcut_rl', 2) i st |
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end; |
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(** simplification procedure for sorting permutations **) |
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val dj_cp = thm "dj_cp"; |
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fun dest_permT (Type ("fun", [Type ("List.list", [Type ("*", [T, _])]), |
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Type ("fun", [_, U])])) = (T, U); |
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fun permTs_of (Const ("Nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u |
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| permTs_of _ = []; |
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fun perm_simproc' thy ss (Const ("Nominal.perm", T) $ t $ (u as Const ("Nominal.perm", U) $ r $ s)) = |
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let |
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val (aT as Type (a, []), S) = dest_permT T; |
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val (bT as Type (b, []), _) = dest_permT U |
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in if aT mem permTs_of u andalso aT <> bT then |
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let |
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val a' = Sign.base_name a; |
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val b' = Sign.base_name b; |
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val cp = PureThy.get_thm thy (Name ("cp_" ^ a' ^ "_" ^ b' ^ "_inst")); |
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val dj = PureThy.get_thm thy (Name ("dj_" ^ b' ^ "_" ^ a')); |
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val dj_cp' = [cp, dj] MRS dj_cp; |
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val cert = SOME o cterm_of thy |
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in |
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SOME (mk_meta_eq (Drule.instantiate' [SOME (ctyp_of thy S)] |
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[cert t, cert r, cert s] dj_cp')) |
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end |
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else NONE |
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end |
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| perm_simproc' thy ss _ = NONE; |
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val perm_simproc = |
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Simplifier.simproc (the_context ()) "perm_simp" ["pi1 \\<bullet> (pi2 \\<bullet> x)"] perm_simproc'; |
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val allE_Nil = read_instantiate_sg (the_context()) [("x", "[]")] allE; |
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val meta_spec = thm "meta_spec"; |
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fun projections rule = |
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ProjectRule.projections (ProofContext.init (Thm.theory_of_thm rule)) rule |
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|> map (standard #> RuleCases.save rule); |
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val supp_prod = thm "supp_prod"; |
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val fresh_prod = thm "fresh_prod"; |
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val supports_fresh = thm "supports_fresh"; |
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val supports_def = thm "Nominal.op supports_def"; |
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val fresh_def = thm "fresh_def"; |
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val supp_def = thm "supp_def"; |
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val rev_simps = thms "rev.simps"; |
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val app_simps = thms "op @.simps"; |
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val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq]; |
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fun gen_add_nominal_datatype prep_typ err flat_names new_type_names dts thy = |
214 |
let |
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215 |
(* this theory is used just for parsing *) |
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val tmp_thy = thy |> |
218 |
Theory.copy |> |
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219 |
Theory.add_types (map (fn (tvs, tname, mx, _) => |
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220 |
(tname, length tvs, mx)) dts); |
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221 |
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222 |
val sign = Theory.sign_of tmp_thy; |
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223 |
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224 |
val atoms = atoms_of thy; |
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225 |
val classes = map (NameSpace.map_base (fn s => "pt_" ^ s)) atoms; |
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226 |
val cp_classes = List.concat (map (fn atom1 => map (fn atom2 => |
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227 |
Sign.intern_class thy ("cp_" ^ Sign.base_name atom1 ^ "_" ^ |
|
228 |
Sign.base_name atom2)) atoms) atoms); |
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229 |
fun augment_sort S = S union classes; |
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230 |
val augment_sort_typ = map_type_tfree (fn (s, S) => TFree (s, augment_sort S)); |
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232 |
fun prep_constr ((constrs, sorts), (cname, cargs, mx)) = |
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233 |
let val (cargs', sorts') = Library.foldl (prep_typ sign) (([], sorts), cargs) |
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234 |
in (constrs @ [(cname, cargs', mx)], sorts') end |
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235 |
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236 |
fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) = |
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237 |
let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs) |
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238 |
in (dts @ [(tvs, tname, mx, constrs')], sorts') end |
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240 |
val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts); |
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241 |
val sorts' = map (apsnd augment_sort) sorts; |
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242 |
val tyvars = map #1 dts'; |
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243 |
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244 |
val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts'; |
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245 |
val constr_syntax = map (fn (tvs, tname, mx, constrs) => |
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246 |
map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts'; |
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248 |
val ps = map (fn (_, n, _, _) => |
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249 |
(Sign.full_name sign n, Sign.full_name sign (n ^ "_Rep"))) dts; |
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250 |
val rps = map Library.swap ps; |
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fun replace_types (Type ("Nominal.ABS", [T, U])) = |
19494 | 253 |
Type ("fun", [T, Type ("Nominal.noption", [replace_types U])]) |
17870 | 254 |
| replace_types (Type (s, Ts)) = |
255 |
Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts) |
|
256 |
| replace_types T = T; |
|
257 |
||
258 |
val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, tname ^ "_Rep", NoSyn, |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
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diff
changeset
|
259 |
map (fn (cname, cargs, mx) => (cname ^ "_Rep", |
17870 | 260 |
map (augment_sort_typ o replace_types) cargs, NoSyn)) constrs)) dts'; |
261 |
||
262 |
val new_type_names' = map (fn n => n ^ "_Rep") new_type_names; |
|
263 |
val full_new_type_names' = map (Sign.full_name (sign_of thy)) new_type_names'; |
|
264 |
||
18045 | 265 |
val ({induction, ...},thy1) = |
17870 | 266 |
DatatypePackage.add_datatype_i err flat_names new_type_names' dts'' thy; |
267 |
||
268 |
val SOME {descr, ...} = Symtab.lookup |
|
269 |
(DatatypePackage.get_datatypes thy1) (hd full_new_type_names'); |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
270 |
fun nth_dtyp i = typ_of_dtyp descr sorts' (DtRec i); |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
271 |
|
17870 | 272 |
(**** define permutation functions ****) |
273 |
||
274 |
val permT = mk_permT (TFree ("'x", HOLogic.typeS)); |
|
275 |
val pi = Free ("pi", permT); |
|
276 |
val perm_types = map (fn (i, _) => |
|
277 |
let val T = nth_dtyp i |
|
278 |
in permT --> T --> T end) descr; |
|
19494 | 279 |
val perm_names = replicate (length new_type_names) "Nominal.perm" @ |
17870 | 280 |
DatatypeProp.indexify_names (map (fn i => Sign.full_name (sign_of thy1) |
281 |
("perm_" ^ name_of_typ (nth_dtyp i))) |
|
282 |
(length new_type_names upto length descr - 1)); |
|
283 |
val perm_names_types = perm_names ~~ perm_types; |
|
284 |
||
285 |
val perm_eqs = List.concat (map (fn (i, (_, _, constrs)) => |
|
286 |
let val T = nth_dtyp i |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
287 |
in map (fn (cname, dts) => |
17870 | 288 |
let |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
289 |
val Ts = map (typ_of_dtyp descr sorts') dts; |
17870 | 290 |
val names = DatatypeProp.make_tnames Ts; |
291 |
val args = map Free (names ~~ Ts); |
|
292 |
val c = Const (cname, Ts ---> T); |
|
293 |
fun perm_arg (dt, x) = |
|
294 |
let val T = type_of x |
|
295 |
in if is_rec_type dt then |
|
296 |
let val (Us, _) = strip_type T |
|
297 |
in list_abs (map (pair "x") Us, |
|
298 |
Const (List.nth (perm_names_types, body_index dt)) $ pi $ |
|
299 |
list_comb (x, map (fn (i, U) => |
|
19494 | 300 |
Const ("Nominal.perm", permT --> U --> U) $ |
17870 | 301 |
(Const ("List.rev", permT --> permT) $ pi) $ |
302 |
Bound i) ((length Us - 1 downto 0) ~~ Us))) |
|
303 |
end |
|
19494 | 304 |
else Const ("Nominal.perm", permT --> T --> T) $ pi $ x |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
305 |
end; |
17870 | 306 |
in |
307 |
(("", HOLogic.mk_Trueprop (HOLogic.mk_eq |
|
308 |
(Const (List.nth (perm_names_types, i)) $ |
|
309 |
Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $ |
|
310 |
list_comb (c, args), |
|
311 |
list_comb (c, map perm_arg (dts ~~ args))))), []) |
|
312 |
end) constrs |
|
313 |
end) descr); |
|
314 |
||
20179 | 315 |
val (perm_simps, thy2) = thy1 |> |
17870 | 316 |
Theory.add_consts_i (map (fn (s, T) => (Sign.base_name s, T, NoSyn)) |
317 |
(List.drop (perm_names_types, length new_type_names))) |> |
|
19635 | 318 |
PrimrecPackage.add_primrec_unchecked_i "" perm_eqs; |
17870 | 319 |
|
320 |
(**** prove that permutation functions introduced by unfolding are ****) |
|
321 |
(**** equivalent to already existing permutation functions ****) |
|
322 |
||
323 |
val _ = warning ("length descr: " ^ string_of_int (length descr)); |
|
324 |
val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names)); |
|
325 |
||
326 |
val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types); |
|
327 |
val perm_fun_def = PureThy.get_thm thy2 (Name "perm_fun_def"); |
|
328 |
||
329 |
val unfolded_perm_eq_thms = |
|
330 |
if length descr = length new_type_names then [] |
|
331 |
else map standard (List.drop (split_conj_thm |
|
20046 | 332 |
(Goal.prove_global thy2 [] [] |
17870 | 333 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
334 |
(map (fn (c as (s, T), x) => |
|
335 |
let val [T1, T2] = binder_types T |
|
336 |
in HOLogic.mk_eq (Const c $ pi $ Free (x, T2), |
|
19494 | 337 |
Const ("Nominal.perm", T) $ pi $ Free (x, T2)) |
17870 | 338 |
end) |
18010 | 339 |
(perm_names_types ~~ perm_indnames)))) |
340 |
(fn _ => EVERY [indtac induction perm_indnames 1, |
|
17870 | 341 |
ALLGOALS (asm_full_simp_tac |
342 |
(simpset_of thy2 addsimps [perm_fun_def]))])), |
|
343 |
length new_type_names)); |
|
344 |
||
345 |
(**** prove [] \<bullet> t = t ****) |
|
346 |
||
347 |
val _ = warning "perm_empty_thms"; |
|
348 |
||
349 |
val perm_empty_thms = List.concat (map (fn a => |
|
350 |
let val permT = mk_permT (Type (a, [])) |
|
351 |
in map standard (List.take (split_conj_thm |
|
20046 | 352 |
(Goal.prove_global thy2 [] [] |
17870 | 353 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
354 |
(map (fn ((s, T), x) => HOLogic.mk_eq |
|
355 |
(Const (s, permT --> T --> T) $ |
|
356 |
Const ("List.list.Nil", permT) $ Free (x, T), |
|
357 |
Free (x, T))) |
|
358 |
(perm_names ~~ |
|
18010 | 359 |
map body_type perm_types ~~ perm_indnames)))) |
360 |
(fn _ => EVERY [indtac induction perm_indnames 1, |
|
17870 | 361 |
ALLGOALS (asm_full_simp_tac (simpset_of thy2))])), |
362 |
length new_type_names)) |
|
363 |
end) |
|
364 |
atoms); |
|
365 |
||
366 |
(**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****) |
|
367 |
||
368 |
val _ = warning "perm_append_thms"; |
|
369 |
||
370 |
(*FIXME: these should be looked up statically*) |
|
371 |
val at_pt_inst = PureThy.get_thm thy2 (Name "at_pt_inst"); |
|
372 |
val pt2 = PureThy.get_thm thy2 (Name "pt2"); |
|
373 |
||
374 |
val perm_append_thms = List.concat (map (fn a => |
|
375 |
let |
|
376 |
val permT = mk_permT (Type (a, [])); |
|
377 |
val pi1 = Free ("pi1", permT); |
|
378 |
val pi2 = Free ("pi2", permT); |
|
379 |
val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst")); |
|
380 |
val pt2' = pt_inst RS pt2; |
|
381 |
val pt2_ax = PureThy.get_thm thy2 |
|
382 |
(Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "2") a)); |
|
383 |
in List.take (map standard (split_conj_thm |
|
20046 | 384 |
(Goal.prove_global thy2 [] [] |
17870 | 385 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
386 |
(map (fn ((s, T), x) => |
|
387 |
let val perm = Const (s, permT --> T --> T) |
|
388 |
in HOLogic.mk_eq |
|
389 |
(perm $ (Const ("List.op @", permT --> permT --> permT) $ |
|
390 |
pi1 $ pi2) $ Free (x, T), |
|
391 |
perm $ pi1 $ (perm $ pi2 $ Free (x, T))) |
|
392 |
end) |
|
393 |
(perm_names ~~ |
|
18010 | 394 |
map body_type perm_types ~~ perm_indnames)))) |
395 |
(fn _ => EVERY [indtac induction perm_indnames 1, |
|
17870 | 396 |
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))), |
397 |
length new_type_names) |
|
398 |
end) atoms); |
|
399 |
||
400 |
(**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****) |
|
401 |
||
402 |
val _ = warning "perm_eq_thms"; |
|
403 |
||
404 |
val pt3 = PureThy.get_thm thy2 (Name "pt3"); |
|
405 |
val pt3_rev = PureThy.get_thm thy2 (Name "pt3_rev"); |
|
406 |
||
407 |
val perm_eq_thms = List.concat (map (fn a => |
|
408 |
let |
|
409 |
val permT = mk_permT (Type (a, [])); |
|
410 |
val pi1 = Free ("pi1", permT); |
|
411 |
val pi2 = Free ("pi2", permT); |
|
412 |
(*FIXME: not robust - better access these theorems using NominalData?*) |
|
413 |
val at_inst = PureThy.get_thm thy2 (Name ("at_" ^ Sign.base_name a ^ "_inst")); |
|
414 |
val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst")); |
|
415 |
val pt3' = pt_inst RS pt3; |
|
416 |
val pt3_rev' = at_inst RS (pt_inst RS pt3_rev); |
|
417 |
val pt3_ax = PureThy.get_thm thy2 |
|
418 |
(Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "3") a)); |
|
419 |
in List.take (map standard (split_conj_thm |
|
20046 | 420 |
(Goal.prove_global thy2 [] [] (Logic.mk_implies |
19494 | 421 |
(HOLogic.mk_Trueprop (Const ("Nominal.prm_eq", |
17870 | 422 |
permT --> permT --> HOLogic.boolT) $ pi1 $ pi2), |
423 |
HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
|
424 |
(map (fn ((s, T), x) => |
|
425 |
let val perm = Const (s, permT --> T --> T) |
|
426 |
in HOLogic.mk_eq |
|
427 |
(perm $ pi1 $ Free (x, T), |
|
428 |
perm $ pi2 $ Free (x, T)) |
|
429 |
end) |
|
430 |
(perm_names ~~ |
|
18010 | 431 |
map body_type perm_types ~~ perm_indnames))))) |
432 |
(fn _ => EVERY [indtac induction perm_indnames 1, |
|
17870 | 433 |
ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))), |
434 |
length new_type_names) |
|
435 |
end) atoms); |
|
436 |
||
437 |
(**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****) |
|
438 |
||
439 |
val cp1 = PureThy.get_thm thy2 (Name "cp1"); |
|
440 |
val dj_cp = PureThy.get_thm thy2 (Name "dj_cp"); |
|
441 |
val pt_perm_compose = PureThy.get_thm thy2 (Name "pt_perm_compose"); |
|
442 |
val pt_perm_compose_rev = PureThy.get_thm thy2 (Name "pt_perm_compose_rev"); |
|
443 |
val dj_perm_perm_forget = PureThy.get_thm thy2 (Name "dj_perm_perm_forget"); |
|
444 |
||
445 |
fun composition_instance name1 name2 thy = |
|
446 |
let |
|
447 |
val name1' = Sign.base_name name1; |
|
448 |
val name2' = Sign.base_name name2; |
|
449 |
val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2'); |
|
450 |
val permT1 = mk_permT (Type (name1, [])); |
|
451 |
val permT2 = mk_permT (Type (name2, [])); |
|
452 |
val augment = map_type_tfree |
|
453 |
(fn (x, S) => TFree (x, cp_class :: S)); |
|
454 |
val Ts = map (augment o body_type) perm_types; |
|
455 |
val cp_inst = PureThy.get_thm thy |
|
456 |
(Name ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst")); |
|
457 |
val simps = simpset_of thy addsimps (perm_fun_def :: |
|
458 |
(if name1 <> name2 then |
|
459 |
let val dj = PureThy.get_thm thy (Name ("dj_" ^ name2' ^ "_" ^ name1')) |
|
460 |
in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end |
|
461 |
else |
|
462 |
let |
|
463 |
val at_inst = PureThy.get_thm thy (Name ("at_" ^ name1' ^ "_inst")); |
|
464 |
val pt_inst = PureThy.get_thm thy (Name ("pt_" ^ name1' ^ "_inst")) |
|
465 |
in |
|
466 |
[cp_inst RS cp1 RS sym, |
|
467 |
at_inst RS (pt_inst RS pt_perm_compose) RS sym, |
|
468 |
at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym] |
|
469 |
end)) |
|
20046 | 470 |
val thms = split_conj_thm (Goal.prove_global thy [] [] |
17870 | 471 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
472 |
(map (fn ((s, T), x) => |
|
473 |
let |
|
474 |
val pi1 = Free ("pi1", permT1); |
|
475 |
val pi2 = Free ("pi2", permT2); |
|
476 |
val perm1 = Const (s, permT1 --> T --> T); |
|
477 |
val perm2 = Const (s, permT2 --> T --> T); |
|
19494 | 478 |
val perm3 = Const ("Nominal.perm", permT1 --> permT2 --> permT2) |
17870 | 479 |
in HOLogic.mk_eq |
480 |
(perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)), |
|
481 |
perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T))) |
|
482 |
end) |
|
18010 | 483 |
(perm_names ~~ Ts ~~ perm_indnames)))) |
484 |
(fn _ => EVERY [indtac induction perm_indnames 1, |
|
20046 | 485 |
ALLGOALS (asm_full_simp_tac simps)])) |
17870 | 486 |
in |
19275 | 487 |
foldl (fn ((s, tvs), thy) => AxClass.prove_arity |
17870 | 488 |
(s, replicate (length tvs) (cp_class :: classes), [cp_class]) |
19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset
|
489 |
(ClassPackage.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy) |
17870 | 490 |
thy (full_new_type_names' ~~ tyvars) |
491 |
end; |
|
492 |
||
18381
246807ef6dfb
changed the types in accordance with Florian's changes
urbanc
parents:
18366
diff
changeset
|
493 |
val (perm_thmss,thy3) = thy2 |> |
17870 | 494 |
fold (fn name1 => fold (composition_instance name1) atoms) atoms |> |
495 |
curry (Library.foldr (fn ((i, (tyname, args, _)), thy) => |
|
19275 | 496 |
AxClass.prove_arity (tyname, replicate (length args) classes, classes) |
19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset
|
497 |
(ClassPackage.intro_classes_tac [] THEN REPEAT (EVERY |
17870 | 498 |
[resolve_tac perm_empty_thms 1, |
499 |
resolve_tac perm_append_thms 1, |
|
500 |
resolve_tac perm_eq_thms 1, assume_tac 1])) thy)) |
|
501 |
(List.take (descr, length new_type_names)) |> |
|
502 |
PureThy.add_thmss |
|
503 |
[((space_implode "_" new_type_names ^ "_unfolded_perm_eq", |
|
18759 | 504 |
unfolded_perm_eq_thms), [Simplifier.simp_add]), |
17870 | 505 |
((space_implode "_" new_type_names ^ "_perm_empty", |
18759 | 506 |
perm_empty_thms), [Simplifier.simp_add]), |
17870 | 507 |
((space_implode "_" new_type_names ^ "_perm_append", |
18759 | 508 |
perm_append_thms), [Simplifier.simp_add]), |
17870 | 509 |
((space_implode "_" new_type_names ^ "_perm_eq", |
18759 | 510 |
perm_eq_thms), [Simplifier.simp_add])]; |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
511 |
|
17870 | 512 |
(**** Define representing sets ****) |
513 |
||
514 |
val _ = warning "representing sets"; |
|
515 |
||
21021 | 516 |
val rep_set_names = DatatypeProp.indexify_names |
517 |
(map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr); |
|
17870 | 518 |
val big_rep_name = |
519 |
space_implode "_" (DatatypeProp.indexify_names (List.mapPartial |
|
19494 | 520 |
(fn (i, ("Nominal.noption", _, _)) => NONE |
17870 | 521 |
| (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set"; |
522 |
val _ = warning ("big_rep_name: " ^ big_rep_name); |
|
523 |
||
524 |
fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) = |
|
525 |
(case AList.lookup op = descr i of |
|
19494 | 526 |
SOME ("Nominal.noption", _, [(_, [dt']), _]) => |
17870 | 527 |
apfst (cons dt) (strip_option dt') |
528 |
| _ => ([], dtf)) |
|
19494 | 529 |
| strip_option (DtType ("fun", [dt, DtType ("Nominal.noption", [dt'])])) = |
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
530 |
apfst (cons dt) (strip_option dt') |
17870 | 531 |
| strip_option dt = ([], dt); |
532 |
||
19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset
|
533 |
val dt_atomTs = distinct op = (map (typ_of_dtyp descr sorts') |
18280
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset
|
534 |
(List.concat (map (fn (_, (_, _, cs)) => List.concat |
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset
|
535 |
(map (List.concat o map (fst o strip_option) o snd) cs)) descr))); |
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset
|
536 |
|
17870 | 537 |
fun make_intr s T (cname, cargs) = |
538 |
let |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
539 |
fun mk_prem (dt, (j, j', prems, ts)) = |
17870 | 540 |
let |
541 |
val (dts, dt') = strip_option dt; |
|
542 |
val (dts', dt'') = strip_dtyp dt'; |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
543 |
val Ts = map (typ_of_dtyp descr sorts') dts; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
544 |
val Us = map (typ_of_dtyp descr sorts') dts'; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
545 |
val T = typ_of_dtyp descr sorts' dt''; |
17870 | 546 |
val free = mk_Free "x" (Us ---> T) j; |
547 |
val free' = app_bnds free (length Us); |
|
548 |
fun mk_abs_fun (T, (i, t)) = |
|
549 |
let val U = fastype_of t |
|
19494 | 550 |
in (i + 1, Const ("Nominal.abs_fun", [T, U, T] ---> |
551 |
Type ("Nominal.noption", [U])) $ mk_Free "y" T i $ t) |
|
17870 | 552 |
end |
553 |
in (j + 1, j' + length Ts, |
|
554 |
case dt'' of |
|
555 |
DtRec k => list_all (map (pair "x") Us, |
|
21021 | 556 |
HOLogic.mk_Trueprop (Free (List.nth (rep_set_names, k), |
557 |
T --> HOLogic.boolT) $ free')) :: prems |
|
17870 | 558 |
| _ => prems, |
559 |
snd (foldr mk_abs_fun (j', free) Ts) :: ts) |
|
560 |
end; |
|
561 |
||
562 |
val (_, _, prems, ts) = foldr mk_prem (1, 1, [], []) cargs; |
|
21021 | 563 |
val concl = HOLogic.mk_Trueprop (Free (s, T --> HOLogic.boolT) $ |
564 |
list_comb (Const (cname, map fastype_of ts ---> T), ts)) |
|
17870 | 565 |
in Logic.list_implies (prems, concl) |
566 |
end; |
|
567 |
||
21021 | 568 |
val (intr_ts, (rep_set_names', recTs')) = |
569 |
apfst List.concat (apsnd ListPair.unzip (ListPair.unzip (List.mapPartial |
|
19494 | 570 |
(fn ((_, ("Nominal.noption", _, _)), _) => NONE |
17870 | 571 |
| ((i, (_, _, constrs)), rep_set_name) => |
572 |
let val T = nth_dtyp i |
|
573 |
in SOME (map (make_intr rep_set_name T) constrs, |
|
21021 | 574 |
(rep_set_name, T)) |
17870 | 575 |
end) |
21021 | 576 |
(descr ~~ rep_set_names)))); |
577 |
val rep_set_names'' = map (Sign.full_name thy3) rep_set_names'; |
|
17870 | 578 |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
579 |
val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy4) = |
17870 | 580 |
setmp InductivePackage.quiet_mode false |
21021 | 581 |
(TheoryTarget.init NONE #> |
582 |
InductivePackage.add_inductive_i false big_rep_name false true false |
|
583 |
(map (fn (s, T) => (s, SOME (T --> HOLogic.boolT), NoSyn)) |
|
584 |
(rep_set_names' ~~ recTs')) |
|
585 |
[] (map (fn x => (("", []), x)) intr_ts) [] #> |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
586 |
apsnd (ProofContext.theory_of o LocalTheory.exit)) thy3; |
17870 | 587 |
|
588 |
(**** Prove that representing set is closed under permutation ****) |
|
589 |
||
590 |
val _ = warning "proving closure under permutation..."; |
|
591 |
||
592 |
val perm_indnames' = List.mapPartial |
|
19494 | 593 |
(fn (x, (_, ("Nominal.noption", _, _))) => NONE | (x, _) => SOME x) |
17870 | 594 |
(perm_indnames ~~ descr); |
595 |
||
596 |
fun mk_perm_closed name = map (fn th => standard (th RS mp)) |
|
20046 | 597 |
(List.take (split_conj_thm (Goal.prove_global thy4 [] [] |
17870 | 598 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map |
21021 | 599 |
(fn ((s, T), x) => |
17870 | 600 |
let |
21021 | 601 |
val T = map_type_tfree |
602 |
(fn (s, cs) => TFree (s, cs union cp_classes)) T; |
|
603 |
val S = Const (s, T --> HOLogic.boolT); |
|
17870 | 604 |
val permT = mk_permT (Type (name, [])) |
21021 | 605 |
in HOLogic.mk_imp (S $ Free (x, T), |
606 |
S $ (Const ("Nominal.perm", permT --> T --> T) $ |
|
607 |
Free ("pi", permT) $ Free (x, T))) |
|
608 |
end) (rep_set_names'' ~~ recTs' ~~ perm_indnames')))) |
|
18010 | 609 |
(fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *) |
17870 | 610 |
[indtac rep_induct [] 1, |
611 |
ALLGOALS (simp_tac (simpset_of thy4 addsimps |
|
612 |
(symmetric perm_fun_def :: PureThy.get_thms thy4 (Name ("abs_perm"))))), |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
613 |
ALLGOALS (resolve_tac rep_intrs |
17870 | 614 |
THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])), |
615 |
length new_type_names)); |
|
616 |
||
617 |
(* FIXME: theorems are stored in database for testing only *) |
|
618 |
val perm_closed_thmss = map mk_perm_closed atoms; |
|
20483
04aa552a83bc
TypedefPackage.add_typedef_* now yields name of introduced type constructor
haftmann
parents:
20411
diff
changeset
|
619 |
val (_, thy5) = PureThy.add_thmss [(("perm_closed", List.concat perm_closed_thmss), [])] thy4; |
17870 | 620 |
|
621 |
(**** typedef ****) |
|
622 |
||
623 |
val _ = warning "defining type..."; |
|
624 |
||
18366 | 625 |
val (typedefs, thy6) = |
20483
04aa552a83bc
TypedefPackage.add_typedef_* now yields name of introduced type constructor
haftmann
parents:
20411
diff
changeset
|
626 |
thy5 |
21021 | 627 |
|> fold_map (fn ((((name, mx), tvs), (cname, U)), name') => fn thy => |
17870 | 628 |
setmp TypedefPackage.quiet_mode true |
21021 | 629 |
(TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx) |
630 |
(Const ("Collect", (U --> HOLogic.boolT) --> HOLogic.mk_setT U) $ |
|
631 |
Const (cname, U --> HOLogic.boolT)) NONE |
|
632 |
(rtac exI 1 THEN rtac CollectI 1 THEN |
|
17870 | 633 |
QUIET_BREADTH_FIRST (has_fewer_prems 1) |
20483
04aa552a83bc
TypedefPackage.add_typedef_* now yields name of introduced type constructor
haftmann
parents:
20411
diff
changeset
|
634 |
(resolve_tac rep_intrs 1))) thy |> (fn ((_, r), thy) => |
17870 | 635 |
let |
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset
|
636 |
val permT = mk_permT (TFree (Name.variant tvs "'a", HOLogic.typeS)); |
17870 | 637 |
val pi = Free ("pi", permT); |
638 |
val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs; |
|
639 |
val T = Type (Sign.intern_type thy name, tvs'); |
|
18366 | 640 |
in apfst (pair r o hd) |
19635 | 641 |
(PureThy.add_defs_unchecked_i true [(("prm_" ^ name ^ "_def", Logic.mk_equals |
19494 | 642 |
(Const ("Nominal.perm", permT --> T --> T) $ pi $ Free ("x", T), |
17870 | 643 |
Const (Sign.intern_const thy ("Abs_" ^ name), U --> T) $ |
19494 | 644 |
(Const ("Nominal.perm", permT --> U --> U) $ pi $ |
17870 | 645 |
(Const (Sign.intern_const thy ("Rep_" ^ name), T --> U) $ |
646 |
Free ("x", T))))), [])] thy) |
|
647 |
end)) |
|
18366 | 648 |
(types_syntax ~~ tyvars ~~ |
21021 | 649 |
List.take (rep_set_names'' ~~ recTs', length new_type_names) ~~ |
650 |
new_type_names); |
|
17870 | 651 |
|
652 |
val perm_defs = map snd typedefs; |
|
21021 | 653 |
val Abs_inverse_thms = map (collect_simp o #Abs_inverse o fst) typedefs; |
18016 | 654 |
val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs; |
21021 | 655 |
val Rep_thms = map (collect_simp o #Rep o fst) typedefs; |
17870 | 656 |
|
18016 | 657 |
val big_name = space_implode "_" new_type_names; |
658 |
||
659 |
||
17870 | 660 |
(** prove that new types are in class pt_<name> **) |
661 |
||
662 |
val _ = warning "prove that new types are in class pt_<name> ..."; |
|
663 |
||
664 |
fun pt_instance ((class, atom), perm_closed_thms) = |
|
21021 | 665 |
fold (fn ((((((Abs_inverse, Rep_inverse), Rep), |
17870 | 666 |
perm_def), name), tvs), perm_closed) => fn thy => |
19275 | 667 |
AxClass.prove_arity |
17870 | 668 |
(Sign.intern_type thy name, |
669 |
replicate (length tvs) (classes @ cp_classes), [class]) |
|
19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset
|
670 |
(EVERY [ClassPackage.intro_classes_tac [], |
17870 | 671 |
rewrite_goals_tac [perm_def], |
672 |
asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1, |
|
673 |
asm_full_simp_tac (simpset_of thy addsimps |
|
674 |
[Rep RS perm_closed RS Abs_inverse]) 1, |
|
675 |
asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy |
|
676 |
(Name ("pt_" ^ Sign.base_name atom ^ "3"))]) 1]) thy) |
|
21021 | 677 |
(Abs_inverse_thms ~~ Rep_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ |
678 |
new_type_names ~~ tyvars ~~ perm_closed_thms); |
|
17870 | 679 |
|
680 |
||
681 |
(** prove that new types are in class cp_<name1>_<name2> **) |
|
682 |
||
683 |
val _ = warning "prove that new types are in class cp_<name1>_<name2> ..."; |
|
684 |
||
685 |
fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy = |
|
686 |
let |
|
687 |
val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2; |
|
688 |
val class = Sign.intern_class thy name; |
|
689 |
val cp1' = PureThy.get_thm thy (Name (name ^ "_inst")) RS cp1 |
|
21021 | 690 |
in fold (fn ((((((Abs_inverse, Rep), |
17870 | 691 |
perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy => |
19275 | 692 |
AxClass.prove_arity |
17870 | 693 |
(Sign.intern_type thy name, |
694 |
replicate (length tvs) (classes @ cp_classes), [class]) |
|
19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset
|
695 |
(EVERY [ClassPackage.intro_classes_tac [], |
17870 | 696 |
rewrite_goals_tac [perm_def], |
697 |
asm_full_simp_tac (simpset_of thy addsimps |
|
698 |
((Rep RS perm_closed1 RS Abs_inverse) :: |
|
699 |
(if atom1 = atom2 then [] |
|
700 |
else [Rep RS perm_closed2 RS Abs_inverse]))) 1, |
|
18016 | 701 |
cong_tac 1, |
17870 | 702 |
rtac refl 1, |
703 |
rtac cp1' 1]) thy) |
|
21021 | 704 |
(Abs_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ new_type_names ~~ |
705 |
tyvars ~~ perm_closed_thms1 ~~ perm_closed_thms2) thy |
|
17870 | 706 |
end; |
707 |
||
708 |
val thy7 = fold (fn x => fn thy => thy |> |
|
709 |
pt_instance x |> |
|
710 |
fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss)) |
|
711 |
(classes ~~ atoms ~~ perm_closed_thmss) thy6; |
|
712 |
||
713 |
(**** constructors ****) |
|
714 |
||
715 |
fun mk_abs_fun (x, t) = |
|
716 |
let |
|
717 |
val T = fastype_of x; |
|
718 |
val U = fastype_of t |
|
719 |
in |
|
19494 | 720 |
Const ("Nominal.abs_fun", T --> U --> T --> |
721 |
Type ("Nominal.noption", [U])) $ x $ t |
|
17870 | 722 |
end; |
723 |
||
18016 | 724 |
val (ty_idxs, _) = foldl |
19494 | 725 |
(fn ((i, ("Nominal.noption", _, _)), p) => p |
18016 | 726 |
| ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr; |
727 |
||
728 |
fun reindex (DtType (s, dts)) = DtType (s, map reindex dts) |
|
729 |
| reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i)) |
|
730 |
| reindex dt = dt; |
|
731 |
||
732 |
fun strip_suffix i s = implode (List.take (explode s, size s - i)); |
|
733 |
||
734 |
(** strips the "_Rep" in type names *) |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
735 |
fun strip_nth_name i s = |
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
736 |
let val xs = NameSpace.unpack s; |
18045 | 737 |
in NameSpace.pack (Library.nth_map (length xs - i) (strip_suffix 4) xs) end; |
18016 | 738 |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
739 |
val (descr'', ndescr) = ListPair.unzip (List.mapPartial |
19494 | 740 |
(fn (i, ("Nominal.noption", _, _)) => NONE |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
741 |
| (i, (s, dts, constrs)) => |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
742 |
let |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
743 |
val SOME index = AList.lookup op = ty_idxs i; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
744 |
val (constrs1, constrs2) = ListPair.unzip |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
745 |
(map (fn (cname, cargs) => apfst (pair (strip_nth_name 2 (strip_nth_name 1 cname))) |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
746 |
(foldl_map (fn (dts, dt) => |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
747 |
let val (dts', dt') = strip_option dt |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
748 |
in (dts @ dts' @ [reindex dt'], (length dts, length dts')) end) |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
749 |
([], cargs))) constrs) |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
750 |
in SOME ((index, (strip_nth_name 1 s, map reindex dts, constrs1)), |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
751 |
(index, constrs2)) |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
752 |
end) descr); |
18045 | 753 |
|
19489 | 754 |
val (descr1, descr2) = chop (length new_type_names) descr''; |
18016 | 755 |
val descr' = [descr1, descr2]; |
756 |
||
19710 | 757 |
fun partition_cargs idxs xs = map (fn (i, j) => |
758 |
(List.take (List.drop (xs, i), j), List.nth (xs, i + j))) idxs; |
|
759 |
||
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
760 |
val pdescr = map (fn ((i, (s, dts, constrs)), (_, idxss)) => (i, (s, dts, |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
761 |
map (fn ((cname, cargs), idxs) => (cname, partition_cargs idxs cargs)) |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
762 |
(constrs ~~ idxss)))) (descr'' ~~ ndescr); |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
763 |
|
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
764 |
fun nth_dtyp' i = typ_of_dtyp descr'' sorts' (DtRec i); |
17870 | 765 |
|
766 |
val rep_names = map (fn s => |
|
767 |
Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names; |
|
768 |
val abs_names = map (fn s => |
|
769 |
Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names; |
|
770 |
||
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
771 |
val recTs = get_rec_types descr'' sorts'; |
18016 | 772 |
val newTs' = Library.take (length new_type_names, recTs'); |
773 |
val newTs = Library.take (length new_type_names, recTs); |
|
17870 | 774 |
|
775 |
val full_new_type_names = map (Sign.full_name (sign_of thy)) new_type_names; |
|
776 |
||
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
777 |
fun make_constr_def tname T T' ((thy, defs, eqns), |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
778 |
(((cname_rep, _), (cname, cargs)), (cname', mx))) = |
17870 | 779 |
let |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
780 |
fun constr_arg ((dts, dt), (j, l_args, r_args)) = |
17870 | 781 |
let |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
782 |
val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' sorts' dt) i) |
17870 | 783 |
(dts ~~ (j upto j + length dts - 1)) |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
784 |
val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts) |
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
785 |
in |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
786 |
(j + length dts + 1, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
787 |
xs @ x :: l_args, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
788 |
foldr mk_abs_fun |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
789 |
(case dt of |
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
790 |
DtRec k => if k < length new_type_names then |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
791 |
Const (List.nth (rep_names, k), typ_of_dtyp descr'' sorts' dt --> |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
792 |
typ_of_dtyp descr sorts' dt) $ x |
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
793 |
else error "nested recursion not (yet) supported" |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
794 |
| _ => x) xs :: r_args) |
17870 | 795 |
end |
796 |
||
797 |
val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs; |
|
798 |
val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname); |
|
799 |
val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname); |
|
800 |
val constrT = map fastype_of l_args ---> T; |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
801 |
val lhs = list_comb (Const (cname, constrT), l_args); |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
802 |
val rhs = list_comb (Const (cname_rep, map fastype_of r_args ---> T'), r_args); |
17870 | 803 |
val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs); |
804 |
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq |
|
805 |
(Const (rep_name, T --> T') $ lhs, rhs)); |
|
806 |
val def_name = (Sign.base_name cname) ^ "_def"; |
|
18366 | 807 |
val ([def_thm], thy') = thy |> |
17870 | 808 |
Theory.add_consts_i [(cname', constrT, mx)] |> |
809 |
(PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)] |
|
810 |
in (thy', defs @ [def_thm], eqns @ [eqn]) end; |
|
811 |
||
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
812 |
fun dt_constr_defs ((thy, defs, eqns, dist_lemmas), ((((((_, (_, _, constrs)), |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
813 |
(_, (_, _, constrs'))), tname), T), T'), constr_syntax)) = |
17870 | 814 |
let |
815 |
val rep_const = cterm_of thy |
|
816 |
(Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T')); |
|
817 |
val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma); |
|
818 |
val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T') |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
819 |
((Theory.add_path tname thy, defs, []), constrs ~~ constrs' ~~ constr_syntax) |
17870 | 820 |
in |
821 |
(parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist]) |
|
822 |
end; |
|
823 |
||
824 |
val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs |
|
825 |
((thy7, [], [], []), List.take (descr, length new_type_names) ~~ |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
826 |
List.take (pdescr, length new_type_names) ~~ |
17870 | 827 |
new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax); |
828 |
||
21021 | 829 |
val abs_inject_thms = map (collect_simp o #Abs_inject o fst) typedefs |
830 |
val rep_inject_thms = map (#Rep_inject o fst) typedefs |
|
17870 | 831 |
|
832 |
(* prove theorem Rep_i (Constr_j ...) = Constr'_j ... *) |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
833 |
|
17870 | 834 |
fun prove_constr_rep_thm eqn = |
835 |
let |
|
836 |
val inj_thms = map (fn r => r RS iffD1) abs_inject_thms; |
|
21021 | 837 |
val rewrites = constr_defs @ map mk_meta_eq Rep_inverse_thms |
20046 | 838 |
in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY |
17870 | 839 |
[resolve_tac inj_thms 1, |
840 |
rewrite_goals_tac rewrites, |
|
841 |
rtac refl 3, |
|
842 |
resolve_tac rep_intrs 2, |
|
21021 | 843 |
REPEAT (resolve_tac Rep_thms 1)]) |
17870 | 844 |
end; |
845 |
||
846 |
val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns; |
|
847 |
||
848 |
(* prove theorem pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *) |
|
849 |
||
850 |
fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th => |
|
851 |
let |
|
21021 | 852 |
val _ $ (_ $ (Rep $ x)) = Logic.unvarify (prop_of th); |
17870 | 853 |
val Type ("fun", [T, U]) = fastype_of Rep; |
854 |
val permT = mk_permT (Type (atom, [])); |
|
855 |
val pi = Free ("pi", permT); |
|
856 |
in |
|
20046 | 857 |
Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq |
19494 | 858 |
(Const ("Nominal.perm", permT --> U --> U) $ pi $ (Rep $ x), |
859 |
Rep $ (Const ("Nominal.perm", permT --> T --> T) $ pi $ x)))) |
|
18010 | 860 |
(fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @ |
20046 | 861 |
perm_closed_thms @ Rep_thms)) 1) |
17870 | 862 |
end) Rep_thms; |
863 |
||
864 |
val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm |
|
865 |
(atoms ~~ perm_closed_thmss)); |
|
866 |
||
867 |
(* prove distinctness theorems *) |
|
868 |
||
18016 | 869 |
val distinct_props = setmp DatatypeProp.dtK 1000 |
870 |
(DatatypeProp.make_distincts new_type_names descr' sorts') thy8; |
|
17870 | 871 |
|
872 |
val dist_rewrites = map (fn (rep_thms, dist_lemma) => |
|
873 |
dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])) |
|
874 |
(constr_rep_thmss ~~ dist_lemmas); |
|
875 |
||
876 |
fun prove_distinct_thms (_, []) = [] |
|
877 |
| prove_distinct_thms (p as (rep_thms, dist_lemma), t::ts) = |
|
878 |
let |
|
20046 | 879 |
val dist_thm = Goal.prove_global thy8 [] [] t (fn _ => |
880 |
simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1) |
|
17870 | 881 |
in dist_thm::(standard (dist_thm RS not_sym)):: |
882 |
(prove_distinct_thms (p, ts)) |
|
883 |
end; |
|
884 |
||
885 |
val distinct_thms = map prove_distinct_thms |
|
886 |
(constr_rep_thmss ~~ dist_lemmas ~~ distinct_props); |
|
887 |
||
888 |
(** prove equations for permutation functions **) |
|
889 |
||
890 |
val abs_perm = PureThy.get_thms thy8 (Name "abs_perm"); (* FIXME *) |
|
891 |
||
892 |
val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) => |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
893 |
let val T = nth_dtyp' i |
17870 | 894 |
in List.concat (map (fn (atom, perm_closed_thms) => |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
895 |
map (fn ((cname, dts), constr_rep_thm) => |
17870 | 896 |
let |
897 |
val cname = Sign.intern_const thy8 |
|
898 |
(NameSpace.append tname (Sign.base_name cname)); |
|
899 |
val permT = mk_permT (Type (atom, [])); |
|
900 |
val pi = Free ("pi", permT); |
|
901 |
||
902 |
fun perm t = |
|
903 |
let val T = fastype_of t |
|
19494 | 904 |
in Const ("Nominal.perm", permT --> T --> T) $ pi $ t end; |
17870 | 905 |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
906 |
fun constr_arg ((dts, dt), (j, l_args, r_args)) = |
17870 | 907 |
let |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
908 |
val Ts = map (typ_of_dtyp descr'' sorts') dts; |
17870 | 909 |
val xs = map (fn (T, i) => mk_Free "x" T i) |
910 |
(Ts ~~ (j upto j + length dts - 1)) |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
911 |
val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts) |
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
912 |
in |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
913 |
(j + length dts + 1, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
914 |
xs @ x :: l_args, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
915 |
map perm (xs @ [x]) @ r_args) |
17870 | 916 |
end |
917 |
||
918 |
val (_, l_args, r_args) = foldr constr_arg (1, [], []) dts; |
|
919 |
val c = Const (cname, map fastype_of l_args ---> T) |
|
920 |
in |
|
20046 | 921 |
Goal.prove_global thy8 [] [] |
17870 | 922 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
18010 | 923 |
(perm (list_comb (c, l_args)), list_comb (c, r_args)))) |
924 |
(fn _ => EVERY |
|
17870 | 925 |
[simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1, |
926 |
simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @ |
|
927 |
constr_defs @ perm_closed_thms)) 1, |
|
928 |
TRY (simp_tac (HOL_basic_ss addsimps |
|
929 |
(symmetric perm_fun_def :: abs_perm)) 1), |
|
930 |
TRY (simp_tac (HOL_basic_ss addsimps |
|
931 |
(perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @ |
|
20046 | 932 |
perm_closed_thms)) 1)]) |
17870 | 933 |
end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss)) |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
934 |
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); |
17870 | 935 |
|
936 |
(** prove injectivity of constructors **) |
|
937 |
||
938 |
val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms; |
|
939 |
val alpha = PureThy.get_thms thy8 (Name "alpha"); |
|
940 |
val abs_fresh = PureThy.get_thms thy8 (Name "abs_fresh"); |
|
941 |
||
942 |
val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) => |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
943 |
let val T = nth_dtyp' i |
17870 | 944 |
in List.mapPartial (fn ((cname, dts), constr_rep_thm) => |
945 |
if null dts then NONE else SOME |
|
946 |
let |
|
947 |
val cname = Sign.intern_const thy8 |
|
948 |
(NameSpace.append tname (Sign.base_name cname)); |
|
949 |
||
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
950 |
fun make_inj ((dts, dt), (j, args1, args2, eqs)) = |
17870 | 951 |
let |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
952 |
val Ts_idx = map (typ_of_dtyp descr'' sorts') dts ~~ (j upto j + length dts - 1); |
17870 | 953 |
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx; |
954 |
val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx; |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
955 |
val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts); |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
956 |
val y = mk_Free "y" (typ_of_dtyp descr'' sorts' dt) (j + length dts) |
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
957 |
in |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
958 |
(j + length dts + 1, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
959 |
xs @ (x :: args1), ys @ (y :: args2), |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
960 |
HOLogic.mk_eq |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
961 |
(foldr mk_abs_fun x xs, foldr mk_abs_fun y ys) :: eqs) |
17870 | 962 |
end; |
963 |
||
964 |
val (_, args1, args2, eqs) = foldr make_inj (1, [], [], []) dts; |
|
965 |
val Ts = map fastype_of args1; |
|
966 |
val c = Const (cname, Ts ---> T) |
|
967 |
in |
|
20046 | 968 |
Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq |
17870 | 969 |
(HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)), |
18010 | 970 |
foldr1 HOLogic.mk_conj eqs))) |
971 |
(fn _ => EVERY |
|
17870 | 972 |
[asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: |
973 |
rep_inject_thms')) 1, |
|
974 |
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def :: |
|
975 |
alpha @ abs_perm @ abs_fresh @ rep_inject_thms @ |
|
17874
8be65cf94d2e
Improved proof of injectivity theorems to make it work on
berghofe
parents:
17873
diff
changeset
|
976 |
perm_rep_perm_thms)) 1), |
8be65cf94d2e
Improved proof of injectivity theorems to make it work on
berghofe
parents:
17873
diff
changeset
|
977 |
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def :: |
20046 | 978 |
expand_fun_eq :: rep_inject_thms @ perm_rep_perm_thms)) 1)]) |
17870 | 979 |
end) (constrs ~~ constr_rep_thms) |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
980 |
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); |
17870 | 981 |
|
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
982 |
(** equations for support and freshness **) |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
983 |
|
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
984 |
val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
985 |
(map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') => |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
986 |
let val T = nth_dtyp' i |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
987 |
in List.concat (map (fn (cname, dts) => map (fn atom => |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
988 |
let |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
989 |
val cname = Sign.intern_const thy8 |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
990 |
(NameSpace.append tname (Sign.base_name cname)); |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
991 |
val atomT = Type (atom, []); |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
992 |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
993 |
fun process_constr ((dts, dt), (j, args1, args2)) = |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
994 |
let |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
995 |
val Ts_idx = map (typ_of_dtyp descr'' sorts') dts ~~ (j upto j + length dts - 1); |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
996 |
val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx; |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
997 |
val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts) |
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
998 |
in |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
999 |
(j + length dts + 1, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
1000 |
xs @ (x :: args1), foldr mk_abs_fun x xs :: args2) |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1001 |
end; |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1002 |
|
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1003 |
val (_, args1, args2) = foldr process_constr (1, [], []) dts; |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1004 |
val Ts = map fastype_of args1; |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1005 |
val c = list_comb (Const (cname, Ts ---> T), args1); |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1006 |
fun supp t = |
19494 | 1007 |
Const ("Nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t; |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1008 |
fun fresh t = |
19494 | 1009 |
Const ("Nominal.fresh", atomT --> fastype_of t --> HOLogic.boolT) $ |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1010 |
Free ("a", atomT) $ t; |
20046 | 1011 |
val supp_thm = Goal.prove_global thy8 [] [] |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1012 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1013 |
(supp c, |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1014 |
if null dts then Const ("{}", HOLogic.mk_setT atomT) |
18010 | 1015 |
else foldr1 (HOLogic.mk_binop "op Un") (map supp args2)))) |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1016 |
(fn _ => |
18010 | 1017 |
simp_tac (HOL_basic_ss addsimps (supp_def :: |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1018 |
Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un :: |
21669 | 1019 |
symmetric empty_def :: Finites_emptyI :: simp_thms @ |
20046 | 1020 |
abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1) |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1021 |
in |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1022 |
(supp_thm, |
20046 | 1023 |
Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1024 |
(fresh c, |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1025 |
if null dts then HOLogic.true_const |
18010 | 1026 |
else foldr1 HOLogic.mk_conj (map fresh args2)))) |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1027 |
(fn _ => |
20046 | 1028 |
simp_tac (simpset_of thy8 addsimps [fresh_def, supp_thm]) 1)) |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1029 |
end) atoms) constrs) |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
1030 |
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps'))); |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
1031 |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1032 |
(**** weak induction theorem ****) |
18016 | 1033 |
|
1034 |
fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) = |
|
1035 |
let |
|
1036 |
val Rep_t = Const (List.nth (rep_names, i), T --> U) $ |
|
1037 |
mk_Free "x" T i; |
|
1038 |
||
1039 |
val Abs_t = Const (List.nth (abs_names, i), U --> T) |
|
1040 |
||
21021 | 1041 |
in (prems @ [HOLogic.imp $ |
1042 |
(Const (List.nth (rep_set_names'', i), U --> HOLogic.boolT) $ Rep_t) $ |
|
18016 | 1043 |
(mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], |
1044 |
concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i]) |
|
1045 |
end; |
|
1046 |
||
1047 |
val (indrule_lemma_prems, indrule_lemma_concls) = |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1048 |
Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs')); |
18016 | 1049 |
|
20046 | 1050 |
val indrule_lemma = Goal.prove_global thy8 [] [] |
18016 | 1051 |
(Logic.mk_implies |
1052 |
(HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems), |
|
1053 |
HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY |
|
1054 |
[REPEAT (etac conjE 1), |
|
1055 |
REPEAT (EVERY |
|
1056 |
[TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1, |
|
20046 | 1057 |
etac mp 1, resolve_tac Rep_thms 1])]); |
18016 | 1058 |
|
1059 |
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); |
|
1060 |
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else |
|
1061 |
map (Free o apfst fst o dest_Var) Ps; |
|
1062 |
val indrule_lemma' = cterm_instantiate |
|
1063 |
(map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma; |
|
1064 |
||
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
1065 |
val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms; |
18016 | 1066 |
|
1067 |
val dt_induct_prop = DatatypeProp.make_ind descr' sorts'; |
|
20046 | 1068 |
val dt_induct = Goal.prove_global thy8 [] |
18016 | 1069 |
(Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop) |
1070 |
(fn prems => EVERY |
|
1071 |
[rtac indrule_lemma' 1, |
|
1072 |
(DatatypeAux.indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1, |
|
1073 |
EVERY (map (fn (prem, r) => (EVERY |
|
1074 |
[REPEAT (eresolve_tac Abs_inverse_thms' 1), |
|
1075 |
simp_tac (HOL_basic_ss addsimps [symmetric r]) 1, |
|
1076 |
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) |
|
20046 | 1077 |
(prems ~~ constr_defs))]); |
18016 | 1078 |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1079 |
val case_names_induct = mk_case_names_induct descr''; |
18016 | 1080 |
|
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1081 |
(**** prove that new datatypes have finite support ****) |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1082 |
|
18246
676d2e625d98
added fsub.thy (poplmark challenge) to the examples
urbanc
parents:
18245
diff
changeset
|
1083 |
val _ = warning "proving finite support for the new datatype"; |
676d2e625d98
added fsub.thy (poplmark challenge) to the examples
urbanc
parents:
18245
diff
changeset
|
1084 |
|
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1085 |
val indnames = DatatypeProp.make_tnames recTs; |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1086 |
|
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1087 |
val abs_supp = PureThy.get_thms thy8 (Name "abs_supp"); |
18067 | 1088 |
val supp_atm = PureThy.get_thms thy8 (Name "supp_atm"); |
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1089 |
|
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1090 |
val finite_supp_thms = map (fn atom => |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1091 |
let val atomT = Type (atom, []) |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1092 |
in map standard (List.take |
20046 | 1093 |
(split_conj_thm (Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop |
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1094 |
(foldr1 HOLogic.mk_conj (map (fn (s, T) => HOLogic.mk_mem |
19494 | 1095 |
(Const ("Nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T), |
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1096 |
Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT atomT)))) |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1097 |
(indnames ~~ recTs)))) |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1098 |
(fn _ => indtac dt_induct indnames 1 THEN |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1099 |
ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps |
18067 | 1100 |
(abs_supp @ supp_atm @ |
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1101 |
PureThy.get_thms thy8 (Name ("fs_" ^ Sign.base_name atom ^ "1")) @ |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1102 |
List.concat supp_thms))))), |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1103 |
length new_type_names)) |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1104 |
end) atoms; |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1105 |
|
18759 | 1106 |
val simp_atts = replicate (length new_type_names) [Simplifier.simp_add]; |
18658 | 1107 |
|
1108 |
val (_, thy9) = thy8 |> |
|
1109 |
Theory.add_path big_name |> |
|
1110 |
PureThy.add_thms [(("induct_weak", dt_induct), [case_names_induct])] ||>> |
|
1111 |
PureThy.add_thmss [(("inducts_weak", projections dt_induct), [case_names_induct])] ||> |
|
1112 |
Theory.parent_path ||>> |
|
1113 |
DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms ||>> |
|
1114 |
DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss ||>> |
|
1115 |
DatatypeAux.store_thmss_atts "perm" new_type_names simp_atts perm_simps' ||>> |
|
1116 |
DatatypeAux.store_thmss "inject" new_type_names inject_thms ||>> |
|
1117 |
DatatypeAux.store_thmss "supp" new_type_names supp_thms ||>> |
|
1118 |
DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||> |
|
1119 |
fold (fn (atom, ths) => fn thy => |
|
1120 |
let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom) |
|
19275 | 1121 |
in fold (fn T => AxClass.prove_arity |
18658 | 1122 |
(fst (dest_Type T), |
1123 |
replicate (length sorts) [class], [class]) |
|
19133
7e84a1a3741c
Adapted to Florian's recent changes to the AxClass package.
berghofe
parents:
18759
diff
changeset
|
1124 |
(ClassPackage.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy |
18658 | 1125 |
end) (atoms ~~ finite_supp_thms); |
1126 |
||
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1127 |
(**** strong induction theorem ****) |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1128 |
|
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1129 |
val pnames = if length descr'' = 1 then ["P"] |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1130 |
else map (fn i => "P" ^ string_of_int i) (1 upto length descr''); |
18245
65e60434b3c2
Fixed problem with strong induction theorem for datatypes containing
berghofe
parents:
18142
diff
changeset
|
1131 |
val ind_sort = if null dt_atomTs then HOLogic.typeS |
19649 | 1132 |
else Sign.certify_sort thy9 (map (fn T => Sign.intern_class thy9 ("fs_" ^ |
18658 | 1133 |
Sign.base_name (fst (dest_Type T)))) dt_atomTs); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1134 |
val fsT = TFree ("'n", ind_sort); |
18658 | 1135 |
val fsT' = TFree ("'n", HOLogic.typeS); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1136 |
|
18658 | 1137 |
val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' --> HOLogic.mk_setT T))) |
1138 |
(DatatypeProp.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs); |
|
1139 |
||
1140 |
fun make_pred fsT i T = |
|
18302
577e5d19b33c
Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents:
18280
diff
changeset
|
1141 |
Free (List.nth (pnames, i), fsT --> T --> HOLogic.boolT); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1142 |
|
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1143 |
fun mk_fresh1 xs [] = [] |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1144 |
| mk_fresh1 xs ((y as (_, T)) :: ys) = map (fn x => HOLogic.mk_Trueprop |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1145 |
(HOLogic.mk_not (HOLogic.mk_eq (Free y, Free x)))) |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1146 |
(filter (fn (_, U) => T = U) (rev xs)) @ |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1147 |
mk_fresh1 (y :: xs) ys; |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1148 |
|
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1149 |
fun mk_fresh2 xss [] = [] |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1150 |
| mk_fresh2 xss ((p as (ys, _)) :: yss) = List.concat (map (fn y as (_, T) => |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1151 |
map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1152 |
(Const ("Nominal.fresh", T --> U --> HOLogic.boolT) $ Free y $ Free x)) |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1153 |
(rev xss @ yss)) ys) @ |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1154 |
mk_fresh2 (p :: xss) yss; |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1155 |
|
18658 | 1156 |
fun make_ind_prem fsT f k T ((cname, cargs), idxs) = |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1157 |
let |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1158 |
val recs = List.filter is_rec_type cargs; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1159 |
val Ts = map (typ_of_dtyp descr'' sorts') cargs; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1160 |
val recTs' = map (typ_of_dtyp descr'' sorts') recs; |
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset
|
1161 |
val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1162 |
val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs)); |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1163 |
val frees = tnames ~~ Ts; |
19710 | 1164 |
val frees' = partition_cargs idxs frees; |
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset
|
1165 |
val z = (Name.variant tnames "z", fsT); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1166 |
|
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1167 |
fun mk_prem ((dt, s), T) = |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1168 |
let |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1169 |
val (Us, U) = strip_type T; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1170 |
val l = length Us |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1171 |
in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop |
18658 | 1172 |
(make_pred fsT (body_index dt) U $ Bound l $ app_bnds (Free (s, T)) l)) |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1173 |
end; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1174 |
|
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1175 |
val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs'); |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1176 |
val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop |
19710 | 1177 |
(f T (Free p) (Free z))) (List.concat (map fst frees')) @ |
1178 |
mk_fresh1 [] (List.concat (map fst frees')) @ |
|
1179 |
mk_fresh2 [] frees' |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1180 |
|
18302
577e5d19b33c
Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents:
18280
diff
changeset
|
1181 |
in list_all_free (frees @ [z], Logic.list_implies (prems' @ prems, |
18658 | 1182 |
HOLogic.mk_Trueprop (make_pred fsT k T $ Free z $ |
18302
577e5d19b33c
Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents:
18280
diff
changeset
|
1183 |
list_comb (Const (cname, Ts ---> T), map Free frees)))) |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1184 |
end; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1185 |
|
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1186 |
val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) => |
18658 | 1187 |
map (make_ind_prem fsT (fn T => fn t => fn u => |
19494 | 1188 |
Const ("Nominal.fresh", T --> fsT --> HOLogic.boolT) $ t $ u) i T) |
18658 | 1189 |
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs)); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1190 |
val tnames = DatatypeProp.make_tnames recTs; |
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset
|
1191 |
val zs = Name.variant_list tnames (replicate (length descr'') "z"); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1192 |
val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") |
18658 | 1193 |
(map (fn ((((i, _), T), tname), z) => |
1194 |
make_pred fsT i T $ Free (z, fsT) $ Free (tname, T)) |
|
1195 |
(descr'' ~~ recTs ~~ tnames ~~ zs))); |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1196 |
val induct = Logic.list_implies (ind_prems, ind_concl); |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1197 |
|
18658 | 1198 |
val ind_prems' = |
1199 |
map (fn (_, f as Free (_, T)) => list_all_free ([("x", fsT')], |
|
1200 |
HOLogic.mk_Trueprop (HOLogic.mk_mem (f $ Free ("x", fsT'), |
|
1201 |
Const ("Finite_Set.Finites", HOLogic.mk_setT (body_type T)))))) fresh_fs @ |
|
1202 |
List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) => |
|
1203 |
map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $ |
|
1204 |
HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T) |
|
1205 |
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs)); |
|
1206 |
val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") |
|
1207 |
(map (fn ((((i, _), T), tname), z) => |
|
1208 |
make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T)) |
|
1209 |
(descr'' ~~ recTs ~~ tnames ~~ zs))); |
|
1210 |
val induct' = Logic.list_implies (ind_prems', ind_concl'); |
|
1211 |
||
1212 |
fun mk_perm Ts (t, u) = |
|
1213 |
let |
|
1214 |
val T = fastype_of1 (Ts, t); |
|
1215 |
val U = fastype_of1 (Ts, u) |
|
19494 | 1216 |
in Const ("Nominal.perm", T --> U --> U) $ t $ u end; |
18658 | 1217 |
|
1218 |
val aux_ind_vars = |
|
1219 |
(DatatypeProp.indexify_names (replicate (length dt_atomTs) "pi") ~~ |
|
1220 |
map mk_permT dt_atomTs) @ [("z", fsT')]; |
|
1221 |
val aux_ind_Ts = rev (map snd aux_ind_vars); |
|
1222 |
val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") |
|
1223 |
(map (fn (((i, _), T), tname) => |
|
1224 |
HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $ |
|
1225 |
foldr (mk_perm aux_ind_Ts) (Free (tname, T)) |
|
1226 |
(map Bound (length dt_atomTs downto 1)))) |
|
1227 |
(descr'' ~~ recTs ~~ tnames))); |
|
1228 |
||
1229 |
fun mk_ind_perm i k p l vs j = |
|
1230 |
let |
|
1231 |
val n = length vs; |
|
1232 |
val Ts = map snd vs; |
|
1233 |
val T = List.nth (Ts, i - j); |
|
1234 |
val pT = NominalAtoms.mk_permT T |
|
1235 |
in |
|
1236 |
Const ("List.list.Cons", HOLogic.mk_prodT (T, T) --> pT --> pT) $ |
|
1237 |
(HOLogic.pair_const T T $ Bound (l - j) $ foldr (mk_perm Ts) |
|
1238 |
(Bound (i - j)) |
|
1239 |
(map (mk_ind_perm i k p l vs) (j - 1 downto 0) @ |
|
1240 |
map Bound (n - k - 1 downto n - k - p))) $ |
|
1241 |
Const ("List.list.Nil", pT) |
|
1242 |
end; |
|
1243 |
||
19710 | 1244 |
fun mk_fresh i i' j k p l is vs _ _ = |
18658 | 1245 |
let |
1246 |
val n = length vs; |
|
1247 |
val Ts = map snd vs; |
|
1248 |
val T = List.nth (Ts, n - i - 1 - j); |
|
1249 |
val f = the (AList.lookup op = fresh_fs T); |
|
1250 |
val U = List.nth (Ts, n - i' - 1); |
|
1251 |
val S = HOLogic.mk_setT T; |
|
19710 | 1252 |
val prms' = map Bound (n - k downto n - k - p + 1); |
18658 | 1253 |
val prms = map (mk_ind_perm (n - i) k p (n - l) (("a", T) :: vs)) |
19710 | 1254 |
(j - 1 downto 0) @ prms'; |
1255 |
val bs = rev (List.mapPartial |
|
1256 |
(fn ((_, T'), i) => if T = T' then SOME (Bound i) else NONE) |
|
1257 |
(List.take (vs, n - k - p - 1) ~~ (1 upto n - k - p - 1))); |
|
1258 |
val ts = map (fn i => |
|
1259 |
Const ("Nominal.supp", List.nth (Ts, n - i - 1) --> S) $ |
|
1260 |
foldr (mk_perm (T :: Ts)) (Bound (n - i)) prms') is |
|
18658 | 1261 |
in |
1262 |
HOLogic.mk_Trueprop (Const ("Ex", (T --> HOLogic.boolT) --> HOLogic.boolT) $ |
|
1263 |
Abs ("a", T, HOLogic.Not $ |
|
1264 |
(Const ("op :", T --> S --> HOLogic.boolT) $ Bound 0 $ |
|
19710 | 1265 |
(foldr (fn (t, u) => Const ("insert", T --> S --> S) $ t $ u) |
1266 |
(foldl (fn (t, u) => Const ("op Un", S --> S --> S) $ u $ t) |
|
1267 |
(f $ Bound (n - k - p)) |
|
1268 |
(Const ("Nominal.supp", U --> S) $ |
|
1269 |
foldr (mk_perm (T :: Ts)) (Bound (n - i')) prms :: ts)) |
|
1270 |
(foldr (mk_perm (T :: Ts)) (Bound (n - i - j)) prms :: bs))))) |
|
18658 | 1271 |
end; |
18104
dbe58b104cb9
added thms perm, distinct and fresh to the simplifier.
urbanc
parents:
18068
diff
changeset
|
1272 |
|
18658 | 1273 |
fun mk_fresh_constr is p vs _ concl = |
1274 |
let |
|
1275 |
val n = length vs; |
|
1276 |
val Ts = map snd vs; |
|
1277 |
val _ $ (_ $ _ $ t) = concl; |
|
1278 |
val c = head_of t; |
|
1279 |
val T = body_type (fastype_of c); |
|
1280 |
val k = foldr op + 0 (map (fn (_, i) => i + 1) is); |
|
1281 |
val ps = map Bound (n - k - 1 downto n - k - p); |
|
1282 |
val (_, _, ts, us) = foldl (fn ((_, i), (m, n, ts, us)) => |
|
1283 |
(m - i - 1, n - i, |
|
1284 |
ts @ map Bound (n downto n - i + 1) @ |
|
1285 |
[foldr (mk_perm Ts) (Bound (m - i)) |
|
1286 |
(map (mk_ind_perm m k p n vs) (i - 1 downto 0) @ ps)], |
|
1287 |
us @ map (fn j => foldr (mk_perm Ts) (Bound j) ps) (m downto m - i))) |
|
1288 |
(n - 1, n - k - p - 2, [], []) is |
|
1289 |
in |
|
1290 |
HOLogic.mk_Trueprop (HOLogic.eq_const T $ list_comb (c, ts) $ list_comb (c, us)) |
|
1291 |
end; |
|
1292 |
||
1293 |
val abs_fun_finite_supp = PureThy.get_thm thy9 (Name "abs_fun_finite_supp"); |
|
1294 |
||
1295 |
val at_finite_select = PureThy.get_thm thy9 (Name "at_finite_select"); |
|
1296 |
||
1297 |
val induct_aux_lemmas = List.concat (map (fn Type (s, _) => |
|
1298 |
[PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "_inst")), |
|
1299 |
PureThy.get_thm thy9 (Name ("fs_" ^ Sign.base_name s ^ "1")), |
|
1300 |
PureThy.get_thm thy9 (Name ("at_" ^ Sign.base_name s ^ "_inst"))]) dt_atomTs); |
|
1301 |
||
1302 |
val induct_aux_lemmas' = map (fn Type (s, _) => |
|
1303 |
PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "2")) RS sym) dt_atomTs; |
|
1304 |
||
19710 | 1305 |
val fresh_aux = PureThy.get_thms thy9 (Name "fresh_aux"); |
1306 |
||
1307 |
(********************************************************************** |
|
1308 |
The subgoals occurring in the proof of induct_aux have the |
|
1309 |
following parameters: |
|
1310 |
||
1311 |
x_1 ... x_k p_1 ... p_m z b_1 ... b_n |
|
1312 |
||
1313 |
where |
|
1314 |
||
1315 |
x_i : constructor arguments (introduced by weak induction rule) |
|
1316 |
p_i : permutations (one for each atom type in the data type) |
|
1317 |
z : freshness context |
|
1318 |
b_i : newly introduced names for binders (sufficiently fresh) |
|
1319 |
***********************************************************************) |
|
1320 |
||
1321 |
val _ = warning "proving strong induction theorem ..."; |
|
1322 |
||
20046 | 1323 |
val induct_aux = Goal.prove_global thy9 [] ind_prems' ind_concl' |
18658 | 1324 |
(fn prems => EVERY |
1325 |
([mk_subgoal 1 (K (K (K aux_ind_concl))), |
|
1326 |
indtac dt_induct tnames 1] @ |
|
1327 |
List.concat (map (fn ((_, (_, _, constrs)), (_, constrs')) => |
|
1328 |
List.concat (map (fn ((cname, cargs), is) => |
|
1329 |
[simp_tac (HOL_basic_ss addsimps List.concat perm_simps') 1, |
|
1330 |
REPEAT (rtac allI 1)] @ |
|
1331 |
List.concat (map |
|
1332 |
(fn ((_, 0), _) => [] |
|
1333 |
| ((i, j), k) => List.concat (map (fn j' => |
|
1334 |
let |
|
1335 |
val DtType (tname, _) = List.nth (cargs, i + j'); |
|
1336 |
val atom = Sign.base_name tname |
|
1337 |
in |
|
1338 |
[mk_subgoal 1 (mk_fresh i (i + j) j' |
|
1339 |
(length cargs) (length dt_atomTs) |
|
19710 | 1340 |
(length cargs + length dt_atomTs + 1 + i - k) |
1341 |
(List.mapPartial (fn (i', j) => |
|
1342 |
if i = i' then NONE else SOME (i' + j)) is)), |
|
18658 | 1343 |
rtac at_finite_select 1, |
1344 |
rtac (PureThy.get_thm thy9 (Name ("at_" ^ atom ^ "_inst"))) 1, |
|
1345 |
asm_full_simp_tac (simpset_of thy9 addsimps |
|
1346 |
[PureThy.get_thm thy9 (Name ("fs_" ^ atom ^ "1"))]) 1, |
|
1347 |
resolve_tac prems 1, |
|
1348 |
etac exE 1, |
|
1349 |
asm_full_simp_tac (simpset_of thy9 addsimps |
|
1350 |
[symmetric fresh_def]) 1] |
|
1351 |
end) (0 upto j - 1))) (is ~~ (0 upto length is - 1))) @ |
|
1352 |
(if exists (not o equal 0 o snd) is then |
|
1353 |
[mk_subgoal 1 (mk_fresh_constr is (length dt_atomTs)), |
|
1354 |
asm_full_simp_tac (simpset_of thy9 addsimps |
|
1355 |
(List.concat inject_thms @ |
|
1356 |
alpha @ abs_perm @ abs_fresh @ [abs_fun_finite_supp] @ |
|
1357 |
induct_aux_lemmas)) 1, |
|
1358 |
dtac sym 1, |
|
19710 | 1359 |
asm_full_simp_tac (simpset_of thy9) 1, |
18658 | 1360 |
REPEAT (etac conjE 1)] |
1361 |
else |
|
1362 |
[]) @ |
|
1363 |
[(resolve_tac prems THEN_ALL_NEW |
|
19710 | 1364 |
(atac ORELSE' |
1365 |
SUBGOAL (fn (t, i) => case Logic.strip_assums_concl t of |
|
1366 |
_ $ (Const ("Nominal.fresh", _) $ _ $ _) => |
|
1367 |
asm_simp_tac (simpset_of thy9 addsimps fresh_aux) i |
|
1368 |
| _ => |
|
1369 |
asm_simp_tac (simpset_of thy9 |
|
1370 |
addsimps induct_aux_lemmas' |
|
1371 |
addsimprocs [perm_simproc]) i))) 1]) |
|
18658 | 1372 |
(constrs ~~ constrs'))) (descr'' ~~ ndescr)) @ |
1373 |
[REPEAT (eresolve_tac [conjE, allE_Nil] 1), |
|
1374 |
REPEAT (etac allE 1), |
|
20046 | 1375 |
REPEAT (TRY (rtac conjI 1) THEN asm_full_simp_tac (simpset_of thy9) 1)])); |
18658 | 1376 |
|
1377 |
val induct_aux' = Thm.instantiate ([], |
|
1378 |
map (fn (s, T) => |
|
1379 |
let val pT = TVar (("'n", 0), HOLogic.typeS) --> T --> HOLogic.boolT |
|
1380 |
in (cterm_of thy9 (Var ((s, 0), pT)), cterm_of thy9 (Free (s, pT))) end) |
|
1381 |
(pnames ~~ recTs) @ |
|
1382 |
map (fn (_, f) => |
|
1383 |
let val f' = Logic.varify f |
|
1384 |
in (cterm_of thy9 f', |
|
19494 | 1385 |
cterm_of thy9 (Const ("Nominal.supp", fastype_of f'))) |
18658 | 1386 |
end) fresh_fs) induct_aux; |
1387 |
||
20046 | 1388 |
val induct = Goal.prove_global thy9 [] ind_prems ind_concl |
18658 | 1389 |
(fn prems => EVERY |
1390 |
[rtac induct_aux' 1, |
|
1391 |
REPEAT (resolve_tac induct_aux_lemmas 1), |
|
1392 |
REPEAT ((resolve_tac prems THEN_ALL_NEW |
|
20046 | 1393 |
(etac meta_spec ORELSE' full_simp_tac (HOL_basic_ss addsimps [fresh_def]))) 1)]) |
18658 | 1394 |
|
1395 |
val (_, thy10) = thy9 |> |
|
18016 | 1396 |
Theory.add_path big_name |> |
18658 | 1397 |
PureThy.add_thms [(("induct'", induct_aux), [])] ||>> |
1398 |
PureThy.add_thms [(("induct", induct), [case_names_induct])] ||>> |
|
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1399 |
PureThy.add_thmss [(("inducts", projections induct), [case_names_induct])]; |
18658 | 1400 |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1401 |
(**** recursion combinator ****) |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1402 |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1403 |
val _ = warning "defining recursion combinator ..."; |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1404 |
|
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1405 |
val used = foldr add_typ_tfree_names [] recTs; |
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1406 |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1407 |
val (rec_result_Ts', rec_fn_Ts') = DatatypeProp.make_primrec_Ts descr' sorts' used; |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1408 |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
1409 |
val rec_sort = if null dt_atomTs then HOLogic.typeS else |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1410 |
let val names = map (Sign.base_name o fst o dest_Type) dt_atomTs |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1411 |
in Sign.certify_sort thy10 (map (Sign.intern_class thy10) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1412 |
(map (fn s => "pt_" ^ s) names @ |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1413 |
List.concat (map (fn s => List.mapPartial (fn s' => |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1414 |
if s = s' then NONE |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1415 |
else SOME ("cp_" ^ s ^ "_" ^ s')) names) names))) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1416 |
end; |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1417 |
|
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1418 |
val rec_result_Ts = map (fn TFree (s, _) => TFree (s, rec_sort)) rec_result_Ts'; |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1419 |
val rec_fn_Ts = map (typ_subst_atomic (rec_result_Ts' ~~ rec_result_Ts)) rec_fn_Ts'; |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1420 |
|
21021 | 1421 |
val rec_set_Ts = map (fn (T1, T2) => |
1422 |
rec_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts); |
|
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1423 |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1424 |
val big_rec_name = big_name ^ "_rec_set"; |
21021 | 1425 |
val rec_set_names' = |
1426 |
if length descr'' = 1 then [big_rec_name] else |
|
1427 |
map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int) |
|
1428 |
(1 upto (length descr'')); |
|
1429 |
val rec_set_names = map (Sign.full_name (Theory.sign_of thy10)) rec_set_names'; |
|
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1430 |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1431 |
val rec_fns = map (uncurry (mk_Free "f")) |
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1432 |
(rec_fn_Ts ~~ (1 upto (length rec_fn_Ts))); |
21021 | 1433 |
val rec_sets' = map (fn c => list_comb (Free c, rec_fns)) |
1434 |
(rec_set_names' ~~ rec_set_Ts); |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1435 |
val rec_sets = map (fn c => list_comb (Const c, rec_fns)) |
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1436 |
(rec_set_names ~~ rec_set_Ts); |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1437 |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1438 |
(* introduction rules for graph of recursion function *) |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1439 |
|
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1440 |
val rec_preds = map (fn (a, T) => |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1441 |
Free (a, T --> HOLogic.boolT)) (pnames ~~ rec_result_Ts); |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1442 |
|
20267 | 1443 |
fun mk_fresh3 rs [] = [] |
1444 |
| mk_fresh3 rs ((p as (ys, z)) :: yss) = List.concat (map (fn y as (_, T) => |
|
1445 |
List.mapPartial (fn ((_, (_, x)), r as (_, U)) => if z = x then NONE |
|
1446 |
else SOME (HOLogic.mk_Trueprop |
|
1447 |
(Const ("Nominal.fresh", T --> U --> HOLogic.boolT) $ Free y $ Free r))) |
|
1448 |
rs) ys) @ |
|
1449 |
mk_fresh3 rs yss; |
|
1450 |
||
21088 | 1451 |
(* FIXME: avoid collisions with other variable names? *) |
1452 |
val rec_ctxt = Free ("z", fsT'); |
|
1453 |
||
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1454 |
fun make_rec_intr T p rec_set ((rec_intr_ts, rec_prems, rec_prems', |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1455 |
rec_eq_prems, l), ((cname, cargs), idxs)) = |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1456 |
let |
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1457 |
val Ts = map (typ_of_dtyp descr'' sorts') cargs; |
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1458 |
val frees = map (fn i => "x" ^ string_of_int i) (1 upto length Ts) ~~ Ts; |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1459 |
val frees' = partition_cargs idxs frees; |
21088 | 1460 |
val binders = List.concat (map fst frees'); |
20411
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1461 |
val atomTs = distinct op = (maps (map snd o fst) frees'); |
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1462 |
val recs = List.mapPartial |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1463 |
(fn ((_, DtRec i), p) => SOME (i, p) | _ => NONE) |
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1464 |
(partition_cargs idxs cargs ~~ frees'); |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1465 |
val frees'' = map (fn i => "y" ^ string_of_int i) (1 upto length recs) ~~ |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1466 |
map (fn (i, _) => List.nth (rec_result_Ts, i)) recs; |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1467 |
val prems1 = map (fn ((i, (_, x)), y) => HOLogic.mk_Trueprop |
21021 | 1468 |
(List.nth (rec_sets', i) $ Free x $ Free y)) (recs ~~ frees''); |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1469 |
val prems2 = |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1470 |
map (fn f => map (fn p as (_, T) => HOLogic.mk_Trueprop |
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1471 |
(Const ("Nominal.fresh", T --> fastype_of f --> HOLogic.boolT) $ |
21088 | 1472 |
Free p $ f)) binders) rec_fns; |
1473 |
val prems3 = mk_fresh1 [] binders @ mk_fresh2 [] frees'; |
|
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1474 |
val prems4 = map (fn ((i, _), y) => |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1475 |
HOLogic.mk_Trueprop (List.nth (rec_preds, i) $ Free y)) (recs ~~ frees''); |
20267 | 1476 |
val prems5 = mk_fresh3 (recs ~~ frees'') frees'; |
20411
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1477 |
val prems6 = maps (fn aT => map (fn y as (_, T) => HOLogic.mk_Trueprop |
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1478 |
(HOLogic.mk_mem (Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ Free y, |
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1479 |
Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT aT))))) |
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1480 |
frees'') atomTs; |
21088 | 1481 |
val prems7 = map (fn x as (_, T) => HOLogic.mk_Trueprop |
1482 |
(Const ("Nominal.fresh", T --> fsT' --> HOLogic.boolT) $ |
|
1483 |
Free x $ rec_ctxt)) binders; |
|
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1484 |
val result = list_comb (List.nth (rec_fns, l), map Free (frees @ frees'')); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1485 |
val result_freshs = map (fn p as (_, T) => |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1486 |
Const ("Nominal.fresh", T --> fastype_of result --> HOLogic.boolT) $ |
21088 | 1487 |
Free p $ result) binders; |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1488 |
val P = HOLogic.mk_Trueprop (p $ result) |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1489 |
in |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1490 |
(rec_intr_ts @ [Logic.list_implies (List.concat prems2 @ prems3 @ prems1, |
21021 | 1491 |
HOLogic.mk_Trueprop (rec_set $ |
1492 |
list_comb (Const (cname, Ts ---> T), map Free frees) $ result))], |
|
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1493 |
rec_prems @ [list_all_free (frees @ frees'', Logic.list_implies (prems4, P))], |
21054
6048c085c3ae
Split up FCBs into separate formulae for each binder.
berghofe
parents:
21021
diff
changeset
|
1494 |
rec_prems' @ map (fn fr => list_all_free (frees @ frees'', |
21088 | 1495 |
Logic.list_implies (List.nth (prems2, l) @ prems3 @ prems5 @ prems7 @ prems6 @ [P], |
21054
6048c085c3ae
Split up FCBs into separate formulae for each binder.
berghofe
parents:
21021
diff
changeset
|
1496 |
HOLogic.mk_Trueprop fr))) result_freshs, |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1497 |
rec_eq_prems @ [List.concat prems2 @ prems3], |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1498 |
l + 1) |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1499 |
end; |
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1500 |
|
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1501 |
val (rec_intr_ts, rec_prems, rec_prems', rec_eq_prems, _) = |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1502 |
Library.foldl (fn (x, ((((d, d'), T), p), rec_set)) => |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1503 |
Library.foldl (make_rec_intr T p rec_set) (x, #3 (snd d) ~~ snd d')) |
21021 | 1504 |
(([], [], [], [], 0), descr'' ~~ ndescr ~~ recTs ~~ rec_preds ~~ rec_sets'); |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1505 |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
1506 |
val ({intrs = rec_intrs, elims = rec_elims, raw_induct = rec_induct, ...}, thy11) = |
21055
e053811d680e
Induction rule for graph of recursion combinator
berghofe
parents:
21054
diff
changeset
|
1507 |
thy10 |> |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1508 |
setmp InductivePackage.quiet_mode (!quiet_mode) |
21021 | 1509 |
(TheoryTarget.init NONE #> |
1510 |
InductivePackage.add_inductive_i false big_rec_name false false false |
|
1511 |
(map (fn (s, T) => (s, SOME T, NoSyn)) (rec_set_names' ~~ rec_set_Ts)) |
|
1512 |
(map (apsnd SOME o dest_Free) rec_fns) |
|
1513 |
(map (fn x => (("", []), x)) rec_intr_ts) [] #> |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
1514 |
apsnd (ProofContext.theory_of o LocalTheory.exit)) ||> |
21055
e053811d680e
Induction rule for graph of recursion combinator
berghofe
parents:
21054
diff
changeset
|
1515 |
PureThy.hide_thms true [NameSpace.append |
e053811d680e
Induction rule for graph of recursion combinator
berghofe
parents:
21054
diff
changeset
|
1516 |
(Sign.full_name thy10 big_rec_name) "induct"]; |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1517 |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1518 |
(** equivariance **) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1519 |
|
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1520 |
val fresh_bij = PureThy.get_thms thy11 (Name "fresh_bij"); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1521 |
val perm_bij = PureThy.get_thms thy11 (Name "perm_bij"); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1522 |
|
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1523 |
val (rec_equiv_thms, rec_equiv_thms') = ListPair.unzip (map (fn aT => |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1524 |
let |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1525 |
val permT = mk_permT aT; |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1526 |
val pi = Free ("pi", permT); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1527 |
val rec_fns_pi = map (curry (mk_perm []) pi o uncurry (mk_Free "f")) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1528 |
(rec_fn_Ts ~~ (1 upto (length rec_fn_Ts))); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1529 |
val rec_sets_pi = map (fn c => list_comb (Const c, rec_fns_pi)) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1530 |
(rec_set_names ~~ rec_set_Ts); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1531 |
val ps = map (fn ((((T, U), R), R'), i) => |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1532 |
let |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1533 |
val x = Free ("x" ^ string_of_int i, T); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1534 |
val y = Free ("y" ^ string_of_int i, U) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1535 |
in |
21021 | 1536 |
(R $ x $ y, R' $ mk_perm [] (pi, x) $ mk_perm [] (pi, y)) |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1537 |
end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ rec_sets_pi ~~ (1 upto length recTs)); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1538 |
val ths = map (fn th => standard (th RS mp)) (split_conj_thm |
20046 | 1539 |
(Goal.prove_global thy11 [] [] |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1540 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map HOLogic.mk_imp ps))) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1541 |
(fn _ => rtac rec_induct 1 THEN REPEAT |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1542 |
(NominalPermeq.perm_simp_tac (simpset_of thy11) 1 THEN |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1543 |
(resolve_tac rec_intrs THEN_ALL_NEW |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1544 |
asm_simp_tac (HOL_ss addsimps (fresh_bij @ perm_bij))) 1)))) |
20046 | 1545 |
val ths' = map (fn ((P, Q), th) => |
1546 |
Goal.prove_global thy11 [] [] |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1547 |
(Logic.mk_implies (HOLogic.mk_Trueprop Q, HOLogic.mk_Trueprop P)) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1548 |
(fn _ => dtac (Thm.instantiate ([], |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1549 |
[(cterm_of thy11 (Var (("pi", 0), permT)), |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1550 |
cterm_of thy11 (Const ("List.rev", permT --> permT) $ pi))]) th) 1 THEN |
20046 | 1551 |
NominalPermeq.perm_simp_tac HOL_ss 1)) (ps ~~ ths) |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1552 |
in (ths, ths') end) dt_atomTs); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1553 |
|
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1554 |
(** finite support **) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1555 |
|
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1556 |
val rec_fin_supp_thms = map (fn aT => |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1557 |
let |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1558 |
val name = Sign.base_name (fst (dest_Type aT)); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1559 |
val fs_name = PureThy.get_thm thy11 (Name ("fs_" ^ name ^ "1")); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1560 |
val aset = HOLogic.mk_setT aT; |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1561 |
val finites = Const ("Finite_Set.Finites", HOLogic.mk_setT aset); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1562 |
val fins = map (fn (f, T) => HOLogic.mk_Trueprop (HOLogic.mk_mem |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1563 |
(Const ("Nominal.supp", T --> aset) $ f, finites))) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1564 |
(rec_fns ~~ rec_fn_Ts) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1565 |
in |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1566 |
map (fn th => standard (th RS mp)) (split_conj_thm |
20046 | 1567 |
(Goal.prove_global thy11 [] fins |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1568 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1569 |
(map (fn (((T, U), R), i) => |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1570 |
let |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1571 |
val x = Free ("x" ^ string_of_int i, T); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1572 |
val y = Free ("y" ^ string_of_int i, U) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1573 |
in |
21021 | 1574 |
HOLogic.mk_imp (R $ x $ y, |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1575 |
HOLogic.mk_mem (Const ("Nominal.supp", U --> aset) $ y, finites)) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1576 |
end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ (1 upto length recTs))))) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1577 |
(fn fins => (rtac rec_induct THEN_ALL_NEW cut_facts_tac fins) 1 THEN REPEAT |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1578 |
(NominalPermeq.finite_guess_tac (HOL_ss addsimps [fs_name]) 1)))) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1579 |
end) dt_atomTs; |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1580 |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1581 |
(** freshness **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1582 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1583 |
val perm_fresh_fresh = PureThy.get_thms thy11 (Name "perm_fresh_fresh"); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1584 |
val perm_swap = PureThy.get_thms thy11 (Name "perm_swap"); |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1585 |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1586 |
fun perm_of_pair (x, y) = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1587 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1588 |
val T = fastype_of x; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1589 |
val pT = mk_permT T |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1590 |
in Const ("List.list.Cons", HOLogic.mk_prodT (T, T) --> pT --> pT) $ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1591 |
HOLogic.mk_prod (x, y) $ Const ("List.list.Nil", pT) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1592 |
end; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1593 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1594 |
val finite_premss = map (fn aT => |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1595 |
map (fn (f, T) => HOLogic.mk_Trueprop (HOLogic.mk_mem |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1596 |
(Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ f, |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1597 |
Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT aT))))) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1598 |
(rec_fns ~~ rec_fn_Ts)) dt_atomTs; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1599 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1600 |
val rec_fresh_thms = map (fn ((aT, eqvt_ths), finite_prems) => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1601 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1602 |
val name = Sign.base_name (fst (dest_Type aT)); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1603 |
val fs_name = PureThy.get_thm thy11 (Name ("fs_" ^ name ^ "1")); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1604 |
val a = Free ("a", aT); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1605 |
val freshs = map (fn (f, fT) => HOLogic.mk_Trueprop |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1606 |
(Const ("Nominal.fresh", aT --> fT --> HOLogic.boolT) $ a $ f)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1607 |
(rec_fns ~~ rec_fn_Ts) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1608 |
in |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1609 |
map (fn (((T, U), R), eqvt_th) => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1610 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1611 |
val x = Free ("x", T); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1612 |
val y = Free ("y", U); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1613 |
val y' = Free ("y'", U) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1614 |
in |
21516 | 1615 |
standard (Goal.prove (ProofContext.init thy11) [] (finite_prems @ |
21021 | 1616 |
[HOLogic.mk_Trueprop (R $ x $ y), |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1617 |
HOLogic.mk_Trueprop (HOLogic.mk_all ("y'", U, |
21021 | 1618 |
HOLogic.mk_imp (R $ x $ y', HOLogic.mk_eq (y', y)))), |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1619 |
HOLogic.mk_Trueprop (Const ("Nominal.fresh", |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1620 |
aT --> T --> HOLogic.boolT) $ a $ x)] @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1621 |
freshs) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1622 |
(HOLogic.mk_Trueprop (Const ("Nominal.fresh", |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1623 |
aT --> U --> HOLogic.boolT) $ a $ y)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1624 |
(fn {prems, context} => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1625 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1626 |
val (finite_prems, rec_prem :: unique_prem :: |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1627 |
fresh_prems) = chop (length finite_prems) prems; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1628 |
val unique_prem' = unique_prem RS spec RS mp; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1629 |
val unique = [unique_prem', unique_prem' RS sym] MRS trans; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1630 |
val _ $ (_ $ (_ $ S $ _)) $ _ = prop_of supports_fresh; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1631 |
val tuple = foldr1 HOLogic.mk_prod (x :: rec_fns) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1632 |
in EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1633 |
[rtac (Drule.cterm_instantiate |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1634 |
[(cterm_of thy11 S, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1635 |
cterm_of thy11 (Const ("Nominal.supp", |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1636 |
fastype_of tuple --> HOLogic.mk_setT aT) $ tuple))] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1637 |
supports_fresh) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1638 |
simp_tac (HOL_basic_ss addsimps |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1639 |
[supports_def, symmetric fresh_def, fresh_prod]) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1640 |
REPEAT_DETERM (resolve_tac [allI, impI] 1), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1641 |
REPEAT_DETERM (etac conjE 1), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1642 |
rtac unique 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1643 |
SUBPROOF (fn {prems = prems', params = [a, b], ...} => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1644 |
[cut_facts_tac [rec_prem] 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1645 |
rtac (Thm.instantiate ([], |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1646 |
[(cterm_of thy11 (Var (("pi", 0), mk_permT aT)), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1647 |
cterm_of thy11 (perm_of_pair (term_of a, term_of b)))]) eqvt_th) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1648 |
asm_simp_tac (HOL_ss addsimps |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1649 |
(prems' @ perm_swap @ perm_fresh_fresh)) 1]) context 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1650 |
rtac rec_prem 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1651 |
simp_tac (HOL_ss addsimps (fs_name :: |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1652 |
supp_prod :: finite_Un :: finite_prems)) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1653 |
simp_tac (HOL_ss addsimps (symmetric fresh_def :: |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1654 |
fresh_prod :: fresh_prems)) 1] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1655 |
end)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1656 |
end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ eqvt_ths) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1657 |
end) (dt_atomTs ~~ rec_equiv_thms' ~~ finite_premss); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1658 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1659 |
(** uniqueness **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1660 |
|
21377
c29146dc14f1
replaced exists_fresh lemma with a version formulated with obtains;
urbanc
parents:
21365
diff
changeset
|
1661 |
val exists_fresh' = PureThy.get_thms thy11 (Name "exists_fresh'"); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1662 |
val fs_atoms = map (fn Type (s, _) => PureThy.get_thm thy11 |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1663 |
(Name ("fs_" ^ Sign.base_name s ^ "1"))) dt_atomTs; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1664 |
val fresh_atm = PureThy.get_thms thy11 (Name "fresh_atm"); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1665 |
val calc_atm = PureThy.get_thms thy11 (Name "calc_atm"); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1666 |
val fresh_left = PureThy.get_thms thy11 (Name "fresh_left"); |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1667 |
|
21088 | 1668 |
val fun_tuple = foldr1 HOLogic.mk_prod (rec_ctxt :: rec_fns); |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1669 |
val fun_tupleT = fastype_of fun_tuple; |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1670 |
val rec_unique_frees = |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1671 |
DatatypeProp.indexify_names (replicate (length recTs) "x") ~~ recTs; |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1672 |
val rec_unique_frees'' = map (fn (s, T) => (s ^ "'", T)) rec_unique_frees; |
20267 | 1673 |
val rec_unique_frees' = |
1674 |
DatatypeProp.indexify_names (replicate (length recTs) "y") ~~ rec_result_Ts; |
|
21021 | 1675 |
val rec_unique_concls = map (fn ((x, U), R) => |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1676 |
Const ("Ex1", (U --> HOLogic.boolT) --> HOLogic.boolT) $ |
21021 | 1677 |
Abs ("y", U, R $ Free x $ Bound 0)) |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1678 |
(rec_unique_frees ~~ rec_result_Ts ~~ rec_sets); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1679 |
|
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1680 |
val induct_aux_rec = Drule.cterm_instantiate |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1681 |
(map (pairself (cterm_of thy11)) |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1682 |
(map (fn (aT, f) => (Logic.varify f, Abs ("z", HOLogic.unitT, |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1683 |
Const ("Nominal.supp", fun_tupleT --> HOLogic.mk_setT aT) $ fun_tuple))) |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1684 |
fresh_fs @ |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1685 |
map (fn (((P, T), (x, U)), Q) => |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1686 |
(Var ((P, 0), HOLogic.unitT --> Logic.varifyT T --> HOLogic.boolT), |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1687 |
Abs ("z", HOLogic.unitT, absfree (x, U, Q)))) |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1688 |
(pnames ~~ recTs ~~ rec_unique_frees ~~ rec_unique_concls) @ |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1689 |
map (fn (s, T) => (Var ((s, 0), Logic.varifyT T), Free (s, T))) |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1690 |
rec_unique_frees)) induct_aux; |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1691 |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1692 |
fun obtain_fresh_name vs ths rec_fin_supp T (freshs1, freshs2, ctxt) = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1693 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1694 |
val p = foldr1 HOLogic.mk_prod (vs @ freshs1); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1695 |
val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1696 |
(HOLogic.exists_const T $ Abs ("x", T, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1697 |
Const ("Nominal.fresh", T --> fastype_of p --> HOLogic.boolT) $ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1698 |
Bound 0 $ p))) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1699 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1700 |
[cut_facts_tac ths 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1701 |
REPEAT_DETERM (dresolve_tac (the (AList.lookup op = rec_fin_supp T)) 1), |
21377
c29146dc14f1
replaced exists_fresh lemma with a version formulated with obtains;
urbanc
parents:
21365
diff
changeset
|
1702 |
resolve_tac exists_fresh' 1, |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1703 |
asm_simp_tac (HOL_ss addsimps (supp_prod :: finite_Un :: fs_atoms)) 1]); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1704 |
val (([cx], ths), ctxt') = Obtain.result |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1705 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1706 |
[etac exE 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1707 |
full_simp_tac (HOL_ss addsimps (fresh_prod :: fresh_atm)) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1708 |
REPEAT (etac conjE 1)]) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1709 |
[ex] ctxt |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1710 |
in (freshs1 @ [term_of cx], freshs2 @ ths, ctxt') end; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1711 |
|
21088 | 1712 |
val finite_ctxt_prems = map (fn aT => |
1713 |
HOLogic.mk_Trueprop (HOLogic.mk_mem |
|
1714 |
(Const ("Nominal.supp", fsT' --> HOLogic.mk_setT aT) $ rec_ctxt, |
|
1715 |
Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT aT))))) dt_atomTs; |
|
1716 |
||
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1717 |
val rec_unique_thms = split_conj_thm (Goal.prove |
21516 | 1718 |
(ProofContext.init thy11) (map fst rec_unique_frees) |
21088 | 1719 |
(List.concat finite_premss @ finite_ctxt_prems @ rec_prems @ rec_prems') |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1720 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj rec_unique_concls)) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1721 |
(fn {prems, context} => |
20267 | 1722 |
let |
1723 |
val k = length rec_fns; |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1724 |
val (finite_thss, ths1) = fold_map (fn T => fn xs => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1725 |
apfst (pair T) (chop k xs)) dt_atomTs prems; |
21088 | 1726 |
val (finite_ctxt_ths, ths2) = chop (length dt_atomTs) ths1; |
1727 |
val (P_ind_ths, fcbs) = chop k ths2; |
|
20267 | 1728 |
val P_ths = map (fn th => th RS mp) (split_conj_thm |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1729 |
(Goal.prove context |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1730 |
(map fst (rec_unique_frees'' @ rec_unique_frees')) [] |
20267 | 1731 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
21021 | 1732 |
(map (fn (((x, y), S), P) => HOLogic.mk_imp |
1733 |
(S $ Free x $ Free y, P $ (Free y))) |
|
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1734 |
(rec_unique_frees'' ~~ rec_unique_frees' ~~ rec_sets ~~ rec_preds)))) |
20267 | 1735 |
(fn _ => |
1736 |
rtac rec_induct 1 THEN |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1737 |
REPEAT ((resolve_tac P_ind_ths THEN_ALL_NEW assume_tac) 1)))); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1738 |
val rec_fin_supp_thms' = map |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1739 |
(fn (ths, (T, fin_ths)) => (T, map (curry op MRS fin_ths) ths)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1740 |
(rec_fin_supp_thms ~~ finite_thss); |
20267 | 1741 |
in EVERY |
1742 |
([rtac induct_aux_rec 1] @ |
|
21088 | 1743 |
maps (fn ((_, finite_ths), finite_th) => |
1744 |
[cut_facts_tac (finite_th :: finite_ths) 1, |
|
1745 |
asm_simp_tac (HOL_ss addsimps [supp_prod, finite_Un]) 1]) |
|
1746 |
(finite_thss ~~ finite_ctxt_ths) @ |
|
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1747 |
maps (fn ((_, idxss), elim) => maps (fn idxs => |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1748 |
[full_simp_tac (HOL_ss addsimps [symmetric fresh_def, supp_prod, Un_iff]) 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1749 |
REPEAT_DETERM (eresolve_tac [conjE, ex1E] 1), |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1750 |
rtac ex1I 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1751 |
(resolve_tac rec_intrs THEN_ALL_NEW atac) 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1752 |
rotate_tac ~1 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1753 |
((DETERM o etac elim) THEN_ALL_NEW full_simp_tac |
21021 | 1754 |
(HOL_ss addsimps List.concat distinct_thms)) 1] @ |
1755 |
(if null idxs then [] else [hyp_subst_tac 1, |
|
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1756 |
SUBPROOF (fn {asms, concl, prems = prems', params, context = context', ...} => |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1757 |
let |
21021 | 1758 |
val SOME prem = find_first (can (HOLogic.dest_eq o |
1759 |
HOLogic.dest_Trueprop o prop_of)) prems'; |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1760 |
val _ $ (_ $ lhs $ rhs) = prop_of prem; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1761 |
val _ $ (_ $ lhs' $ rhs') = term_of concl; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1762 |
val rT = fastype_of lhs'; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1763 |
val (c, cargsl) = strip_comb lhs; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1764 |
val cargsl' = partition_cargs idxs cargsl; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1765 |
val boundsl = List.concat (map fst cargsl'); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1766 |
val (_, cargsr) = strip_comb rhs; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1767 |
val cargsr' = partition_cargs idxs cargsr; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1768 |
val boundsr = List.concat (map fst cargsr'); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1769 |
val (params1, _ :: params2) = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1770 |
chop (length params div 2) (map term_of params); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1771 |
val params' = params1 @ params2; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1772 |
val rec_prems = filter (fn th => case prop_of th of |
21021 | 1773 |
_ $ (S $ _ $ _) => S mem rec_sets | _ => false) prems'; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1774 |
val fresh_prems = filter (fn th => case prop_of th of |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1775 |
_ $ (Const ("Nominal.fresh", _) $ _ $ _) => true |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1776 |
| _ $ (Const ("Not", _) $ _) => true |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1777 |
| _ => false) prems'; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1778 |
val Ts = map fastype_of boundsl; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1779 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1780 |
val _ = warning "step 1: obtaining fresh names"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1781 |
val (freshs1, freshs2, context'') = fold |
21088 | 1782 |
(obtain_fresh_name (rec_ctxt :: rec_fns @ params') |
1783 |
(List.concat (map snd finite_thss) @ |
|
1784 |
finite_ctxt_ths @ rec_prems) |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1785 |
rec_fin_supp_thms') |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1786 |
Ts ([], [], context'); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1787 |
val pi1 = map perm_of_pair (boundsl ~~ freshs1); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1788 |
val rpi1 = rev pi1; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1789 |
val pi2 = map perm_of_pair (boundsr ~~ freshs1); |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1790 |
val rpi2 = rev pi2; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1791 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1792 |
fun mk_not_sym ths = List.concat (map (fn th => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1793 |
case prop_of th of |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1794 |
_ $ (Const ("Not", _) $ _) => [th, th RS not_sym] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1795 |
| _ => [th]) ths); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1796 |
val fresh_prems' = mk_not_sym fresh_prems; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1797 |
val freshs2' = mk_not_sym freshs2; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1798 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1799 |
(** as, bs, cs # K as ts, K bs us **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1800 |
val _ = warning "step 2: as, bs, cs # K as ts, K bs us"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1801 |
val prove_fresh_ss = HOL_ss addsimps |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1802 |
(finite_Diff :: List.concat fresh_thms @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1803 |
fs_atoms @ abs_fresh @ abs_supp @ fresh_atm); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1804 |
(* FIXME: avoid asm_full_simp_tac ? *) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1805 |
fun prove_fresh ths y x = Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1806 |
(HOLogic.mk_Trueprop (Const ("Nominal.fresh", |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1807 |
fastype_of x --> fastype_of y --> HOLogic.boolT) $ x $ y)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1808 |
(fn _ => cut_facts_tac ths 1 THEN asm_full_simp_tac prove_fresh_ss 1); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1809 |
val constr_fresh_thms = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1810 |
map (prove_fresh fresh_prems lhs) boundsl @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1811 |
map (prove_fresh fresh_prems rhs) boundsr @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1812 |
map (prove_fresh freshs2 lhs) freshs1 @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1813 |
map (prove_fresh freshs2 rhs) freshs1; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1814 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1815 |
(** pi1 o (K as ts) = pi2 o (K bs us) **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1816 |
val _ = warning "step 3: pi1 o (K as ts) = pi2 o (K bs us)"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1817 |
val pi1_pi2_eq = Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1818 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1819 |
(foldr (mk_perm []) lhs pi1, foldr (mk_perm []) rhs pi2))) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1820 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1821 |
[cut_facts_tac constr_fresh_thms 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1822 |
asm_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1823 |
rtac prem 1]); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1824 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1825 |
(** pi1 o ts = pi2 o us **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1826 |
val _ = warning "step 4: pi1 o ts = pi2 o us"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1827 |
val pi1_pi2_eqs = map (fn (t, u) => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1828 |
Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1829 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1830 |
(foldr (mk_perm []) t pi1, foldr (mk_perm []) u pi2))) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1831 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1832 |
[cut_facts_tac [pi1_pi2_eq] 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1833 |
asm_full_simp_tac (HOL_ss addsimps |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1834 |
(calc_atm @ List.concat perm_simps' @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1835 |
fresh_prems' @ freshs2' @ abs_perm @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1836 |
alpha @ List.concat inject_thms)) 1])) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1837 |
(map snd cargsl' ~~ map snd cargsr'); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1838 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1839 |
(** pi1^-1 o pi2 o us = ts **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1840 |
val _ = warning "step 5: pi1^-1 o pi2 o us = ts"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1841 |
val rpi1_pi2_eqs = map (fn ((t, u), eq) => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1842 |
Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1843 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1844 |
(foldr (mk_perm []) u (rpi1 @ pi2), t))) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1845 |
(fn _ => simp_tac (HOL_ss addsimps |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1846 |
((eq RS sym) :: perm_swap)) 1)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1847 |
(map snd cargsl' ~~ map snd cargsr' ~~ pi1_pi2_eqs); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1848 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1849 |
val (rec_prems1, rec_prems2) = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1850 |
chop (length rec_prems div 2) rec_prems; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1851 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1852 |
(** (ts, pi1^-1 o pi2 o vs) in rec_set **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1853 |
val _ = warning "step 6: (ts, pi1^-1 o pi2 o vs) in rec_set"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1854 |
val rec_prems' = map (fn th => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1855 |
let |
21021 | 1856 |
val _ $ (S $ x $ y) = prop_of th; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1857 |
val k = find_index (equal S) rec_sets; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1858 |
val pi = rpi1 @ pi2; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1859 |
fun mk_pi z = foldr (mk_perm []) z pi; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1860 |
fun eqvt_tac p = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1861 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1862 |
val U as Type (_, [Type (_, [T, _])]) = fastype_of p; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1863 |
val l = find_index (equal T) dt_atomTs; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1864 |
val th = List.nth (List.nth (rec_equiv_thms', l), k); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1865 |
val th' = Thm.instantiate ([], |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1866 |
[(cterm_of thy11 (Var (("pi", 0), U)), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1867 |
cterm_of thy11 p)]) th; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1868 |
in rtac th' 1 end; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1869 |
val th' = Goal.prove context'' [] [] |
21021 | 1870 |
(HOLogic.mk_Trueprop (S $ mk_pi x $ mk_pi y)) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1871 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1872 |
(map eqvt_tac pi @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1873 |
[simp_tac (HOL_ss addsimps (fresh_prems' @ freshs2' @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1874 |
perm_swap @ perm_fresh_fresh)) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1875 |
rtac th 1])) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1876 |
in |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1877 |
Simplifier.simplify |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1878 |
(HOL_basic_ss addsimps rpi1_pi2_eqs) th' |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1879 |
end) rec_prems2; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1880 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1881 |
val ihs = filter (fn th => case prop_of th of |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1882 |
_ $ (Const ("All", _) $ _) => true | _ => false) prems'; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1883 |
|
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1884 |
(** pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs **) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1885 |
val _ = warning "step 7: pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs"; |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1886 |
val rec_eqns = map (fn (th, ih) => |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1887 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1888 |
val th' = th RS (ih RS spec RS mp) RS sym; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1889 |
val _ $ (_ $ lhs $ rhs) = prop_of th'; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1890 |
fun strip_perm (_ $ _ $ t) = strip_perm t |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1891 |
| strip_perm t = t; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1892 |
in |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1893 |
Goal.prove context'' [] [] |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1894 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1895 |
(foldr (mk_perm []) lhs pi1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1896 |
foldr (mk_perm []) (strip_perm rhs) pi2))) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1897 |
(fn _ => simp_tac (HOL_basic_ss addsimps |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1898 |
(th' :: perm_swap)) 1) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1899 |
end) (rec_prems' ~~ ihs); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1900 |
|
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1901 |
(** as # rs **) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1902 |
val _ = warning "step 8: as # rs"; |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1903 |
val rec_freshs = List.concat |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1904 |
(map (fn (rec_prem, ih) => |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1905 |
let |
21021 | 1906 |
val _ $ (S $ x $ (y as Free (_, T))) = |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1907 |
prop_of rec_prem; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1908 |
val k = find_index (equal S) rec_sets; |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1909 |
val atoms = List.concat (List.mapPartial (fn (bs, z) => |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1910 |
if z = x then NONE else SOME bs) cargsl') |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1911 |
in |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1912 |
map (fn a as Free (_, aT) => |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1913 |
let val l = find_index (equal aT) dt_atomTs; |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1914 |
in |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1915 |
Goal.prove context'' [] [] |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1916 |
(HOLogic.mk_Trueprop (Const ("Nominal.fresh", |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1917 |
aT --> T --> HOLogic.boolT) $ a $ y)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1918 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1919 |
(rtac (List.nth (List.nth (rec_fresh_thms, l), k)) 1 :: |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1920 |
map (fn th => rtac th 1) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1921 |
(snd (List.nth (finite_thss, l))) @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1922 |
[rtac rec_prem 1, rtac ih 1, |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1923 |
REPEAT_DETERM (resolve_tac fresh_prems 1)])) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1924 |
end) atoms |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1925 |
end) (rec_prems1 ~~ ihs)); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1926 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1927 |
(** as # fK as ts rs , bs # fK bs us vs **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1928 |
val _ = warning "step 9: as # fK as ts rs , bs # fK bs us vs"; |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1929 |
fun prove_fresh_result (a as Free (_, aT)) = |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1930 |
Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1931 |
(HOLogic.mk_Trueprop (Const ("Nominal.fresh", |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1932 |
aT --> rT --> HOLogic.boolT) $ a $ rhs')) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1933 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1934 |
[resolve_tac fcbs 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1935 |
REPEAT_DETERM (resolve_tac |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1936 |
(fresh_prems @ rec_freshs) 1), |
20411
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1937 |
REPEAT_DETERM (resolve_tac (maps snd rec_fin_supp_thms') 1 |
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1938 |
THEN resolve_tac rec_prems 1), |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1939 |
resolve_tac P_ind_ths 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1940 |
REPEAT_DETERM (resolve_tac (P_ths @ rec_prems) 1)]); |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
1941 |
|
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1942 |
val fresh_results'' = map prove_fresh_result boundsl; |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1943 |
|
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1944 |
fun prove_fresh_result'' ((a as Free (_, aT), b), th) = |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1945 |
let val th' = Goal.prove context'' [] [] |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1946 |
(HOLogic.mk_Trueprop (Const ("Nominal.fresh", |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1947 |
aT --> rT --> HOLogic.boolT) $ |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1948 |
foldr (mk_perm []) a (rpi2 @ pi1) $ |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1949 |
foldr (mk_perm []) rhs' (rpi2 @ pi1))) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1950 |
(fn _ => simp_tac (HOL_ss addsimps fresh_bij) 1 THEN |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1951 |
rtac th 1) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1952 |
in |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1953 |
Goal.prove context'' [] [] |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1954 |
(HOLogic.mk_Trueprop (Const ("Nominal.fresh", |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1955 |
aT --> rT --> HOLogic.boolT) $ b $ lhs')) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1956 |
(fn _ => EVERY |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1957 |
[cut_facts_tac [th'] 1, |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1958 |
NominalPermeq.perm_simp_tac (HOL_ss addsimps |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1959 |
(rec_eqns @ pi1_pi2_eqs @ perm_swap)) 1, |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1960 |
full_simp_tac (HOL_ss addsimps (calc_atm @ |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1961 |
fresh_prems' @ freshs2' @ perm_fresh_fresh)) 1]) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1962 |
end; |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1963 |
|
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1964 |
val fresh_results = fresh_results'' @ map prove_fresh_result'' |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1965 |
(boundsl ~~ boundsr ~~ fresh_results''); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1966 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1967 |
(** cs # fK as ts rs , cs # fK bs us vs **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1968 |
val _ = warning "step 10: cs # fK as ts rs , cs # fK bs us vs"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1969 |
fun prove_fresh_result' recs t (a as Free (_, aT)) = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1970 |
Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1971 |
(HOLogic.mk_Trueprop (Const ("Nominal.fresh", |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1972 |
aT --> rT --> HOLogic.boolT) $ a $ t)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1973 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1974 |
[cut_facts_tac recs 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1975 |
REPEAT_DETERM (dresolve_tac |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1976 |
(the (AList.lookup op = rec_fin_supp_thms' aT)) 1), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1977 |
NominalPermeq.fresh_guess_tac |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1978 |
(HOL_ss addsimps (freshs2 @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1979 |
fs_atoms @ fresh_atm @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1980 |
List.concat (map snd finite_thss))) 1]); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1981 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1982 |
val fresh_results' = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1983 |
map (prove_fresh_result' rec_prems1 rhs') freshs1 @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1984 |
map (prove_fresh_result' rec_prems2 lhs') freshs1; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1985 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1986 |
(** pi1 o (fK as ts rs) = pi2 o (fK bs us vs) **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1987 |
val _ = warning "step 11: pi1 o (fK as ts rs) = pi2 o (fK bs us vs)"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1988 |
val pi1_pi2_result = Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1989 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1990 |
(foldr (mk_perm []) rhs' pi1, foldr (mk_perm []) lhs' pi2))) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1991 |
(fn _ => NominalPermeq.perm_simp_tac (HOL_ss addsimps |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1992 |
pi1_pi2_eqs @ rec_eqns) 1 THEN |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1993 |
TRY (simp_tac (HOL_ss addsimps |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1994 |
(fresh_prems' @ freshs2' @ calc_atm @ perm_fresh_fresh)) 1)); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1995 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1996 |
val _ = warning "final result"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1997 |
val final = Goal.prove context'' [] [] (term_of concl) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1998 |
(fn _ => cut_facts_tac [pi1_pi2_result RS sym] 1 THEN |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1999 |
full_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
2000 |
fresh_results @ fresh_results') 1); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
2001 |
val final' = ProofContext.export context'' context' [final]; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
2002 |
val _ = warning "finished!" |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
2003 |
in |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
2004 |
resolve_tac final' 1 |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2005 |
end) context 1])) idxss) (ndescr ~~ rec_elims)) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2006 |
end)); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2007 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2008 |
val rec_total_thms = map (fn r => r RS theI') rec_unique_thms; |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2009 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2010 |
(* define primrec combinators *) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2011 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2012 |
val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2013 |
val reccomb_names = map (Sign.full_name thy11) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2014 |
(if length descr'' = 1 then [big_reccomb_name] else |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2015 |
(map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2016 |
(1 upto (length descr'')))); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2017 |
val reccombs = map (fn ((name, T), T') => list_comb |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2018 |
(Const (name, rec_fn_Ts @ [T] ---> T'), rec_fns)) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2019 |
(reccomb_names ~~ recTs ~~ rec_result_Ts); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2020 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2021 |
val (reccomb_defs, thy12) = |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2022 |
thy11 |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2023 |
|> Theory.add_consts_i (map (fn ((name, T), T') => |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2024 |
(Sign.base_name name, rec_fn_Ts @ [T] ---> T', NoSyn)) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2025 |
(reccomb_names ~~ recTs ~~ rec_result_Ts)) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2026 |
|> (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') => |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2027 |
((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2028 |
Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T', |
21021 | 2029 |
set $ Free ("x", T) $ Free ("y", T')))))) |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2030 |
(reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2031 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2032 |
(* prove characteristic equations for primrec combinators *) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2033 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2034 |
val rec_thms = map (fn (prems, concl) => |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2035 |
let |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2036 |
val _ $ (_ $ (_ $ x) $ _) = concl; |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2037 |
val (_, cargs) = strip_comb x; |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2038 |
val ps = map (fn (x as Free (_, T), i) => |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2039 |
(Free ("x" ^ string_of_int i, T), x)) (cargs ~~ (1 upto length cargs)); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2040 |
val concl' = subst_atomic_types (rec_result_Ts' ~~ rec_result_Ts) concl; |
21088 | 2041 |
val prems' = List.concat finite_premss @ finite_ctxt_prems @ |
2042 |
rec_prems @ rec_prems' @ map (subst_atomic ps) prems; |
|
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2043 |
fun solve rules prems = resolve_tac rules THEN_ALL_NEW |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2044 |
(resolve_tac prems THEN_ALL_NEW atac) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2045 |
in |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2046 |
Goal.prove_global thy12 [] prems' concl' |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2047 |
(fn prems => EVERY |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2048 |
[rewrite_goals_tac reccomb_defs, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2049 |
rtac the1_equality 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2050 |
solve rec_unique_thms prems 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2051 |
resolve_tac rec_intrs 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2052 |
REPEAT (solve (prems @ rec_total_thms) prems 1)]) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2053 |
end) (rec_eq_prems ~~ |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2054 |
DatatypeProp.make_primrecs new_type_names descr' sorts' thy12); |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
2055 |
|
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset
|
2056 |
val dt_infos = map (make_dt_info descr'' sorts induct reccomb_names rec_thms) |
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset
|
2057 |
((0 upto length descr1 - 1) ~~ descr1 ~~ distinct_thms ~~ inject_thms); |
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset
|
2058 |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
2059 |
(* FIXME: theorems are stored in database for testing only *) |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2060 |
val (_, thy13) = thy12 |> |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
2061 |
PureThy.add_thmss |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
2062 |
[(("rec_equiv", List.concat rec_equiv_thms), []), |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
2063 |
(("rec_equiv'", List.concat rec_equiv_thms'), []), |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
2064 |
(("rec_fin_supp", List.concat rec_fin_supp_thms), []), |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
2065 |
(("rec_fresh", List.concat rec_fresh_thms), []), |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2066 |
(("rec_unique", map standard rec_unique_thms), []), |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2067 |
(("recs", rec_thms), [])] ||> |
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset
|
2068 |
Theory.parent_path ||> |
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset
|
2069 |
map_nominal_datatypes (fold Symtab.update dt_infos); |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
2070 |
|
17870 | 2071 |
in |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2072 |
thy13 |
17870 | 2073 |
end; |
2074 |
||
2075 |
val add_nominal_datatype = gen_add_nominal_datatype read_typ true; |
|
2076 |
||
2077 |
||
2078 |
(* FIXME: The following stuff should be exported by DatatypePackage *) |
|
2079 |
||
2080 |
local structure P = OuterParse and K = OuterKeyword in |
|
2081 |
||
2082 |
val datatype_decl = |
|
2083 |
Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix -- |
|
2084 |
(P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix)); |
|
2085 |
||
2086 |
fun mk_datatype args = |
|
2087 |
let |
|
2088 |
val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args; |
|
2089 |
val specs = map (fn ((((_, vs), t), mx), cons) => |
|
2090 |
(vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args; |
|
18068 | 2091 |
in add_nominal_datatype false names specs end; |
17870 | 2092 |
|
2093 |
val nominal_datatypeP = |
|
2094 |
OuterSyntax.command "nominal_datatype" "define inductive datatypes" K.thy_decl |
|
2095 |
(P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype)); |
|
2096 |
||
2097 |
val _ = OuterSyntax.add_parsers [nominal_datatypeP]; |
|
2098 |
||
2099 |
end; |
|
2100 |
||
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
2101 |
end |